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The VIGRE Program at the University of Utah
Report on the Year 2001  2002
Prologue
Award Notification
VIGRE Highlights
People Involved in the VIGRE Program
Programs for High School Students
 Summer Mathematics Program for High School Students
 Math Circle 2001  2002
Programs for Undergraduate Students
 Summer 2001 REU Program
 Academic Year 2001  2002 REU
 Summer 2002 REU Program
 Undergraduate Colloquium
 Summer ACCESS Program
 Internship Program
 Problem Solving Competition
 Modules
Programs for Graduate Students
 Graduate Colloquium
 Qualifying Exam Problem Sessions
 Grant Proposal Seminar
 TA/TF Training
 Graduate Student Recruiting
 MiniCourse on Complex Hyperbolic Geometry
 MiniCourse on Variational Methods and Nonlinear PDE
 2001  2002 VIGRE Graduate Fellows
 2002  2003 VIGRE Graduate Fellows
The PostDoctoral Program
 VIGRE Assistant Professors
 2001 Recruitment Statistics
 2002 Recruitment Statistics
 2002  2003 VIGRE Duties
Master Calendar
The Department of Mathematics at the University of Utah successfully
competed for a National Science Foundation fiveyear VIGRE grant
and received the funding during late summer of 2001. This NSF program
started about five years ago and approximately thirty departments
across the United States have been awarded such a grant. VIGRE is
the acronym for Vertical InteGration of
Research and Education and the program's aims are to
strengthen research in mathematics by having departments produce more, better,
and more broadly trained mathematicians. To follow these aims the Department
has started several new programs and amplified existing programs to foster
research and research interaction from the high school to the postdoctoral
level.
A group of faculty members started preparing a proposal for
submission to the NSF during the autumn of 1998. The proposal, which reflects
input from a broad base of the faculty, was finally submitted to the NSF during
July 2000 and we were notified of our success in late December 2000. We
immediately proceeded with full force recruiting of graduate students and postdoctoral assistant professors
during the spring of 2001 and ran successful summer programs for high school
students and an REU program for college students during the summer of 2001. (The
grant's website gives information on all facets of
our VIGREprogram.) The funds obtained are for a three year
period and support eight graduate students full time, fund our recruitment
efforts to attract graduate students, support four postdoctoral instructors
nearly half time (during the second year five and in subsequent years six), run
yearlong research programs for sixteen undergraduates (REU), run a summer
program for fifteen talented high school students and partially support our
Math Circle.
During the third year of the grant there will be an
evaluation by the NSF and, pending a positive outcome of this evaluation, funds
for two additional years will become available.
As already mentioned, some parts of the program started
early last year. During the spring of 2001, we were able to hire four
VIGRE assistant professors and six graduate students. Two more
advanced graduate students, already in residence,
were also appointed to the program. Jim Carlson and Hugo Rossi ran an
intensive threeweek summer mathematics
program for high school students, and Jim Carlson and Domingo Toledo conducted
our summer REU, with Jim supervising several projects. Fred Adler, Stew Ethier, and Hugo Rossi
supervised other projects. Nine additional REU projects were
supervised during the academic year and Davar
Khoshnevisan will run a summer REU in 2002 on random processes and simulation
analysis during July and August of 2002. Now that our new Honors
Program is in place, honors projects may be supported in the future by
the REU program. During the spring of 2002, we conducted a successful
recruiting campaign and were able to appoint four new graduate
students and four graduate students already in
residence to the VIGRE program. One of our present
VIGRE assistant professors (Thom Pietraho) unfortunately decided to leave our
department at the end of the present academic year to assume a tenure track
position elsewhere. He has been replaced by a new VIGRE assistant
professor. Unfortunately, we were unable to fulfill our goal, to have
five VIGRE assistant professors on board for next year. We
made several offers to excellent candidates with having only one of
our offers accepted.
The undergraduate and graduate colloquium series were moderately
successful, as were the prelim bootcamps held during the summer
2001. Other VIGRE events that took place during the 2001  2002 academic
year were two minicourses (each a two week duration) for our graduate
students plus several invited (and supported by the grant) graduate students from
other universities. These courses took place during May and June,
2002 and were organized by Jim Carlson and Domingo
Toledo (Complex Hyperbolic Geometry), and David Hartenstine and Klaus Schmitt
(Variational Methods and Nonlinear PDE).
External and Internal Advisory and Assessment Committees
support our efforts of continuous progress assessment. Several members of these committees
visited our department at the end of November, 2001 and provided valuable input
on the program's structure and progress.
Recruiting excellent students to study our subject is a
difficult task. With the help of the grant, our department now can
play a much more aggressive role (and has
done so during spring of 2002) in the recruitment process and attract more and
better students to our programs. This will help us increase the size,
scope, vitality, and attractiveness of the undergraduate major and
increase the efficiency and intensity of our graduate program.
The steering committee of the grant feels that the VIGRE grant
already has had a very positive impact on many of our activities and
will continue to have such in the months and years to come.
The following pages constitute a collection of descriptions
of the various activities undertaken by the Department during the past year.
These pages are preceded by a list of highlights and a list of all the people
involved in the program, people from both the University of Utah, as well as
those from outside who have played a role in advising us or who participated in
one part or another of the program. Also included are various
statistics about recruiting.
Back to Table of Contents
NSF Award Abstract 
#0091675 
AWSFL008 
Integrated Program for Training in Mathematics
NSF Org

DMS

Latest Amendment Date

September 6, 2001

Award Number

0091675

Award Instrument

Continuing grant

Program Manager

Thomas W. Fogwell DMS DIVISION OF MATHEMATICAL SCIENCES MPS DIRECT FOR
MATHEMATICAL & PHYSICAL SCIEN

Start Date

September 1, 2001

Expires

September 30, 2006 (Estimated)

Expected Total Amount

$3888402 (Estimated)

Investigator

Klaus Schmitt schmitt@math.utah.edu (Principal Investigator current) David
Eyre (CoPrincipal Investigator current) Hugo Rossi (CoPrincipal
Investigator current) Gordan Savin (CoPrincipal Investigator
current) James A. Carlson (CoPrincipal Investigator current)

Sponsor

University of Utah 1471 Federal Way Salt Lake City, UT 84102 801/581
7200

NSF Program

1260 INFRASTRUCTURE PROGRAM

Field Application

0000099 Other Applications NEC

Abstract
The aim of the University of Utah VIGRE program is to quickly immerse
undergraduate and graduate students in research, to provide effective
mentorship for them and for postdoctoral instructors, and to foster interchange
of ideas and expertise among all three groups and the faculty. Its aim is
for all to be prepared 1. in effective communication of the ideas and
applications of mathematics in a range of contexts; 2. in depth to carry out
work or research creatively and independently; 3. in breadth to interact with
students or subordinates, with peers and with the public; 4. for leadership in
a broad range of careers, inside or outside of academia. The program will
draw larger numbers of talented high school students into mathematics through a
summer program which gives them early experience in learning by discovery;
followed by a challenging honors curriculum culminating in a senior research
thesis supported by summer research programs. Graduate students will pursue a
yearround program which ensures timely completion of the degree through early
immersion in research and seminars, summer workshops and tutorials, and close
interaction with faculty and postdoctoral fellows. Postdoctoral fellows play an
active role in all phases of the program and work closely with faculty
mentors
Back to Table of Contents
July, 2000
November, 2000
December, 2000
 Preliminary Notification of Proposal Approval
February, 2001
 VIGRE Assistant Professors Appointed
 External Advisory Committee Appointed
March, 2001
 VIGRE Graduate Students Appointed
 Outreach Advisory Committee Appointed
 Internal Advisory Committee Appointed
June, 2001
 Summer High School Program
July, 2001
 Summer REU
 Qualifying Examination Problem Sessions
 Summer ACCESS Program
August, 2001
 Summer ACCESS Program
 New Graduate Student Orientation
September, 2001
 NSF Funds Arrive
 Graduate Colloquium Starts
 Undergraduate Colloquium Starts
 New REU Students Appointed
October, 2001
November, 2001
 External Advisory Committee Visits
December, 2001
 Outreach Advisory Committee Visits
February, 2002
 New VIGRE Assistant Professor Appointed
March, 2002
 Graduate Student Recruitment Weekend
April, 2002
 New VIGRE Graduate Students Appointed
May, 2002
 MiniCourse on Complex Hyperbolic Geometry
June, 2002
 MiniCourse on Variational Methods and Nonlinear PDE
 Summer High School Program
 Summer Access Program
July, 2002
 Qualifying Examination Problem Sessions
 Summer REU on Random Walks and Simulation
Back to Table of Contents
The following is a list of people involved in the VIGRE Program
including their various activities. This list includes all
VIGRE Graduate Students, Assistant Professors, people from outside the
Mathematics Department who have contributed to the Program, as well as Faculty
and Staff from the Department who have made contributions. We note
that a large majority of our faculty and several of our graduate
students are involved in some form of activity related to the
VIGRE program.
Fred Adler, Associate Professor of Mathematics and Biology
VIGRE Activities: REU Mentor, Undergraduate Colloquium Lecturer
Efraim Armendariz, Professor of Mathematics and Chair,
University of Texas
VIGRE Activities: External Advisory Committee Member
Mark Avery, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer
Aaron Bertram, Professor of Mathematics
VIGRE Activities: Steering Committee Member, CoPI of the VIGRE Grant, Graduate Colloquium
Lecturer
Mladen Bestvina, Professor of Mathematics
VIGRE Activities: REU Mentor, Graduate Fellow Mentor, Graduate Colloquium Lecturer,
Undergraduate Colloquium Lecturer, Math Circle Lecturer
Paul Bressloff, Professor of Mathematics
VIGRE Activities: REU Mentor, Graduate Fellow Mentor, Undergraduate
Colloquium Lecturer
Robert Brooks, Professor of Mathematics
VIGRE Activities: Chair of Internal Assessment Committee, Preparation
of Module
James Carlson, Professor of Mathematics
VIGRE Activities: Coordinator of the Summer High School Program, REU Mentor, Assistant Professor
Mentor, CoOrganizer of and Lecturer at MiniCourse on Complex Hyperbolic
Geometry, Undergraduate Colloquium Lecturer, Steering Committee Member, CoPI
of the VIGRE Grant, Math Circle Lecturer
Renzo Cavalieri, Graduate Student
VIGRE Activities: Math Circle Mentor and Lecturer
David Chapman, Professor of Geology and Geophysics, Dean
Graduate School
VIGRE Activities: Internal Advisory Committee Member
Andrej Cherkaev, Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, VIGRE
Assistant Professor Recruitment
Kenneth Chu, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer
Eric Cook, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Undergraduate Mentor, Math Circle Mentor, High School Summer
Program Mentor
Carl Cowen, Professor of Mathematics at Purdue University
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer
Alastair Craw, Assistant Professor of Mathematics
VIGRE Activities: Undergraduate Colloquium Lecturer
Eric Cytrynbaum, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer
Martin Deraux, Associate Instructor
VIGRE Activities: Lecturer at MiniCourse on Complex Hyperbolic Geometry
Florian Enescu, Assistant Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer
Boas Erez, Visiting Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer
Stewart Ethier, Professor of Mathematics
VIGRE Activities: Undergraduate Colloquium Lecturer
Elisha Falbel, Professor of Mathematics, University of
Paris
VIGRE Activities: Lecturer at MiniCourse on Complex Hyperbolic Geometry
Javier Fernandez, VIGRE Assistant Professor
VIGRE Activities: Lecturer at MiniCourse on Complex Hyperbolic Geometry, Graduate
Colloquium Lecturer
Paul Fife, Professor Emeritus of Mathematics
VIGRE Activities: REU Mentor
Aaron Fogelson, Professor of Mathematics
VIGRE Activities: Graduate Fellow Mentor, Graduate Colloquium Lecturer, VIGRE Assistant
Professor Recruitment
Angie Gardiner, Director of Student Services
VIGRE Activities: Undergraduate Colloquium Series Organizer, Summer High School Program
Coordinator, Publicity
Sarah Geneser, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Undergraduate Mentor, Math Circle Mentor, Assistant with
Summer REU Program on Random Walks and Simulation
Pam Giles, Mathematics Specialist, Jordan School District
VIGRE Activities: Outreach Advisory Committee
Kenneth Golden, Professor of Mathematics
VIGRE Activities: REU Mentor, Graduate Fellow Mentor, Math Circle Lecturer
Fletcher Gross, Professor of Mathematics
VIGRE Activities: Undergraduate Colloquium Lecturer, Math
Circle Lecturer, Honors Program Director
Robert Guy, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Undergraduate Mentor, High School Summer Program Mentor,
Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer
Robert Hanson, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer, Math Circle Lecturer, Undergraduate
Colloquium Lecturer
David Hartenstine, VIGRE Assistant Professor
VIGRE Activities: Lecturer at and CoOrganizer of MiniCourse on Variational Methods and
Nonlinear PDE, Preparation of Modules, Organizer of PDE Seminar
Henryk Hecht, Professor of Mathematics
VIGRE Activities: REU Mentor, Graduate Fellow Mentor
Scott Hendrickson, Mathematics Specialist, Alpine School
District
VIGRE Activities: Outreach Advisory Committee Member
Jon Jacobson, Assistant Professor, Pennsylvania State
University
VIGRE Activities: Lecturer at MiniCourse on Variational Methods and Nonlinear PDE
Phil Johnson, Mathematics Specialist, Sevier School District
VIGRE Activities: Outreach Advisory Committee Member
Misha Kapovich, Professor of Mathematics
VIGRE Activities: Graduate Fellow Mentor, VIGRE Assistant Professor
Recruitment
James Keener, Professor of Mathematics
VIGRE Activities: Graduate Fellow Mentor, Undergraduate Colloquium
Lecturer
Marilyn Keir, Associate Instructor of Mathematics
VIGRE Activities: Outreach Advisory Committee
Davar Khoshnevisan, Professor of Mathematics
VIGRE Activities: Coordinator of the Summer REU Program on Random Walks and Simulation,
Undergraduate Colloquium Lecturer
Nick Korevaar, Professor of Mathematics
VIGRE Activities: Steering Committee Member, CoPI of VIGRE Grant, Undergraduate
Colloquium Lecturer, Preparation of Modules, CoOrganizer of ACCESS Summer
Program, Participant in VIGRE Conference, Lecturer in MiniCourse on
Variational Methods and Nonlinear PDE
Brynja Kohler, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer
Vy Le, Associate Professor, University of Missouri
VIGRE Activities: Lecturer at MiniCourse on Variational Methods and
Nonlinear PDE
Mary Levine, Graduate Secretary
VIGRE Activities: Recruiting Weekend Coordinator
Larsen Louder, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Undergraduate Mentor, Math Circle Mentor, Assistant with
Summer REU Program on Random Walks and Simulation, Graduate Colloquium
Lecturer
Jean Mawhin, Professor of Mathematics, Universite Catholique de
Louvain
VIGRE Activities: Principal Lecturer at MiniCourse on Variational Methods and Nonlinear
PDE
Meagan McNulty, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Undergraduate Mentor, Math Circle Mentor, Prelim Boot Camp
CoOrganizer
Grigory Mikhalkin, Associate Professor of Mathematics
VIGRE Activities:un: Graduate Colloquium Lecturer
Graeme Milton, Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate
Colloquium Lecturer
Wieslawa Niziol, Associate Professor of Mathematics
VIGRE Activities: REU Mentor
Brad Peercy, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer
Cindi Phillips, Mathematics Department Accountant
VIGRE Activities: VIGRE Grant Accountant, Graduate Colloquium
Lecturer
Thomas Pietraho, VIGRE Assistant Professor
VIGRE Activities: Math Circle Assistant and Lecturer, Assistant in Summer High School
Program
Paul Rabinowitz, Professor of Mathematics, University of Wisconsin
VIGRE Activities: External Advisory Committee
Jesse Ratzkin, VIGRE Assistant Professor
VIGRE Activities: High School Summer Program Mentor, Lecturer at MiniCourse on
Variational Methods and Nonlinear PDE, Graduate Colloquium Lecturer,
Undergraduate Colloquium Lecturer
Paul Roberts, Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer
Hugo Rossi, Professor of Mathematics
VIGRE Activities: Steering Committee Member, CoPI of VIGRE Grant, Coordinator of REU
Program, Undergraduate Colloquium Lecturer, CoOrganizer of Summer High School
Program, Graduate Student Recruitment, Participant in VIGRE Conference
Matthew Rudd, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Prelim Boot Camp Organizer, Assistant in Organizing and
Lecturer at MiniCourse on Variational Methods and Nonlinear PDE, Graduate
Colloquium Lecturer
Fumitoshi Sato, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer
Gordan Savin, Professor of Mathematics
VIGRE Activities: Steering Committee Member, CoPI of VIGRE Grant, Undergraduate
Colloquium Lecturer, CoOrganizer of Undergraduate Colloquium Series
Klaus Schmitt, Professor of Mathematics
VIGRE Activities: P.I. VIGRE Grant, Director of Steering Committee, REU Mentor, Graduate
Fellow Mentor, Assistant Professor Mentor, Undergraduate Colloquium Lecturer,
Preparation of Module, Organizer of and Lecturer at MiniCourse on Variational
Methods and Nonlinear PDE
Richard Schwartz, Professor of Mathematics, University of Maryland
VIGRE Activities: Lecturer at the MiniCourse on Complex Hyperbolic Geometry
Jon Seger, Professor of Biology
VIGRE Activities: Internal Advisory Committee Member
Anurag Singh, Assistant Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer
Nathan Smale, Professor of Mathematics
VIGRE Activities: Steering Committee Member, Undergraduate Colloquium Lecturer,
CoOrganizer of Undergraduate Colloquium, Internship Organizer, Lecturer in
MiniCourse on Variational Methods and Nonlinear PDE
Ryan Stones, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Undergraduate Mentor, Math Circle Mentor, Prelim Boot Camp
CoOrganizer
Sarah Strong, VIGRE Program Coordinator (Since December,
2001)
Jennifer Taback, Visiting Professor
VIGRE Activities: Math Circle Lecturer, High School Summer Program
Lecturer
Al Taylor, Professor of Mathematics, University of Michigan
VIGRE Activities: External Advisory Committee Member
Joseph Taylor, Professor of Mathematics
VIGRE Activities: Recruitment of VIGRE Assistant Professors
Brenlyn Thiriot, VIGRE Program Coordinator (Until December,
2001)
Robert Thorn, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Undergraduate Mentor, Math Circle Mentor, Assistant with
Summer REU Program on Random Walks and Simulation
Domingo Toledo, Professor of Mathematics
VIGRE Activities: CoOrganizer of and Lecturer at the MiniCourse on Complex Hyperbolic
Geometry
Peter Trapa, Assistant Professor of Mathematics
VIGRE Activities: Coordinator of and Lecturer at Math Circle, Assistant Professor Mentor,
Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer
Andrejs Treibergs, Professor of Mathematics
VIGRE Activities: REU Mentor, Undergraduate Colloquium Lecturer, Lecturer at MiniCourse
on Variational Methods and Nonlinear PDE
Peter Trombi, Professor of Mathematics
VIGRE Activities: Steering Committee Member, CoPI of VIGRE Grant, Graduate Recruitment,
Participant in VIGRE Conferences
Sylvia Wiegand, Professor of Mathematics, University of Nebraska
VIGRE Activities: External Advisory Committee Member
Jim White, University of Utah Career Services
VIGRE Activities: Undergraduate Colloquium Lecturer
Jingyi Zhu, Associate Professor of Mathematics
VIGRE Activities: REU Mentor, Undergraduate Colloquium Lecturer
MANAGEMENT
The program is managed by the Steering Committee whose director is
Klaus Schmitt and the program coordinator is Sarah Strong.
The Steering Committee meets on a regular basis (see the Master
Calendar at the end of the report) to discuss important upcoming
issues. The Committee makes the assignments of mentors for assistant
professors, graduate students, and REU students, and selects the
directors of the various subprograms. It also solicits recommendations for
minicourses, summer high school, and REU programs and selects these for the
coming year.
 Steering Committee: Director: Klaus Schmitt
Program
Coordinator: Sarah Strong
 Math Circle: Nick Korevaar (formerly Peter Trapa)
 High School Program: Jim Carlson
 REU: Hugo Rossi
 Undergraduate Colloquium: Gordan Savin and Nat Smale
 Graduate Recruiting: Hugo Rossi and Peter Trombi
 Graduate Training: Peter Trombi
 Grant Accountant: Cindi Phillips
Back to Table of Contents
Very many mathematically talented high school students are eager to
participate in mathematical activities outside their high school.
Offering challenging mathematical activities to such students serves our
profession well and will ultimately attract more young talent to the
university. With this in mind our VIGRE program offers two
such programs to students and also supports a third. The two
programs are the Summer Mathematics Program for High School
Students started in the summer 2000 and the Math Circle program
started in the autumn of 2001. The latter program takes place during the autumn
and spring semesters. The following are short descriptions of the highly
successful 2001 and 2002 summer programs and of the 20012002 Math
Circle. As one can see from our earlier table listing the people
involved in VIGRE and the descriptions to follow, our
organization of these programs are very much vertically integrated.
Senior faculty, postdoctoral faculty, as well as graduate students
work together as teams which interact with the high school
students. It should be noted that both of these programs have been effective in
recruiting top undergraduate students to the University of Utah amongst which
are Aaron Cohen, Song Du, Todd Hummell, Ryan Rettburg, who are now
participating in our REU programs.
SUMMER MATHEMATICS PROGRAM FOR HIGH SCHOOL STUDENTS
By Jim Carlson
The summer mathematics program for high school students is a three
week enrichment program directed by Jim Carlson that is now in its
third year of operation. Its mission is (a) to expose high school students to new
mathematical ideas and challenging problems that engage their enthusiasm and
develop their talent, (b) to give the students an idea of the broad range of
mathematical thought, its innate beauty, and its powerful role in science and
technology, and (c) to identify and nurture students of special talent, and
attract them into the mathematical sciences as a profession.
The first two years of the program were funded by a grant from the
Dean of the College of Science, from Departmental gift funds, and
other Departmental resources, including volunteer faculty time. In 2003, the program
received substantial VIGRE funding. The number of participants
in the program were 7, 19, and 20 in 2000, 2001, and 2002,
respectively. Hugo Rossi played an important role in running the
program during its first two years.
We target students who are between their junior and senior years, but
on occasion accept younger students and graduating seniors who we feel
will benefit from the program.
Program:
The program has undergone refinements each year, and is now structured
as follows:
08:30  12:00Number theory class
conducted by Jim Carlson with Eric Cook as principal assistant. One
halfhour break.
12:00  13:00Lunch on the plaza with
program personnel and participants
13:30  16:00Afternoon workshops
Week one:Knot theory; Jennifer Taback and Tom
Pietraho
Week two:Combinatorics and discrete
probability; Bobby Hanson
Week three:Discrete Dynamical Systems; Bob Guy
The morning session has evolved to a format rather similar to that of
the Math Circle inaugurated this year: presentation of new material is
interspersed with inclass work and discussion of problems that is
facilitated by the graduate students and postdoctoral
fellows. There is a great deal of give and take between the session
leader and the students. During work on problems, the session
leader, postdoctoral fellows, and graduate students circulate among the
participants and work with them individually or in small groups.
The afternoon sessions are conducted in much the same way, except that
a postdoctoral fellow or graduate student leads the session for a full
week devoted to a single theme.
Personnel:
The VIGRE personnel assigned to the program were graduate students
Eric Cook and Bob Guy and postdoctoral fellow Thom Pietraho. VIGRE funds
also supported graduate student Bobby Hanson for the three weeks of the high
school program, as well as program alumnus Collin Perschon. Collin was one of the outstanding
participants of the 2001 program who is a freshman majoring in mathematics at
the University of Utah this fall. Departmental funds were used to pay
Dr. Jennifer Taback an honorarium for designing and conducting a
weeklong afternoon workshop in knot theory.
Angie Gardiner, Director of Undergraduate Services, a fulltime
position created four years ago, provides invaluable program support
during the three week session itself and during the academic year. Her duties in the
latter period include preparation of brochures, publicity, liaison with high schools
and University outreach programs, and assistance with the application
process. Gardiner is a fulltime staff person paid entirely from
Departmental funds.
Outreach to the high schools is much facilitated by Marilyn Keir, a
respected high school teacher whom the department hired in 1999 to
help with its teacher education program.
Evaluation:
1. Reaction from the students has been, on the whole, very positive
and seems to improve from year to year as we learn from our
experiences. The most able students seem to like the program best,
but the others generally have a positive experience.
Attention to the social aspects of the program  the lunches together, the expedition
to play pool on the first day, the final picnic  help the students to develop
friendships with each other and good working relationships with the faculty,
postdocs, graduate student assistants, and alumni assistants.
2. Students are almost always surprised that there is so much mathematics that they never
heard about in school. Their encounter with new mathematical ideas, problems
challenging beyond what they thought possible, as well as with theorems,
proofs, and open problems is intellectually invigorating to them.
3. We are beginning to succeed at one of the primary goals of the
program: to identify talented students, to raise their level of
interest, knowledge, and commitment to mathematics, and to encourage
them to pursue mathematics as a career. Some notable finds:
Ryan Rettburg, 2000 program:
Ryan came to the University of Utah as a freshman in the fall of
2000. All who have taught him recognize his exceptional talent. Ryan
placed first in the Department's Second Annual Calculus Challenge, and
he was one of the outstanding participants in the summer 2001 REU.
The summer 2001 REU was devoted to Knot Theory and Hyperbolic Geometry
and conducted by Carlson and Domingo Toledo. Rettburg became fascinated
by the colorabilty of knots question, and came up with not only
interesting theoretical ideas, but also a Java program that allowed
one to draw a knot, determine its "colorability matrix", and the
integers modulo which the knot was colorable.
Collin Perschon, 2001 program:
Collin, with Tim Simmons, was one of the outstanding students identified in the 2001
program. He acted as an assistant to the 2002 program in the same capacity as
the graduate students (helping participants with problems), except that he did not
lead a session. Having "alumni program assistants" seems to be a successful practice
that we will continue in the future. It benefits both the alumni assistant and
the participants.
Collin is a now a freshman at the University of Utah majoring in
mathematics.
Tim Simmons, 2001 program:
Tim, like Collin, stood out in the 2001 program. Both Tim and Collin took an online
version of the Department's number theory course. Competing in a field of fifteen
students, all of the rest of whom were regular university students, Tim and Collin
placed first and third, respectively. (The number two student was mathphysics
joint major, Maria Bell, a first year VIGRE graduate student
this fall.)
Tim is a now a tutor for the Math Department.
Students in the 2002 Program:
Six of the students displayed that mathematical spark we look for.
Three of the students, as well as alumni assistant Collin Perschon,
participated in the Department's yearlong Math Circle program led by
Peter Trapa. This statistic is preliminary evidence that our
attention to the entire pipeline, which leads from high school to
university, graduate school, and faculty positions is producing the
desired results.
I was particularly gratified by the participation and experience of a
student from Shiprock High School in Teecnospos, Arizona, on the Navajo
Reservation. When we reviewed her application, she seemed somewhat
under prepared. However, her teacher gave a strong recommendation and
spoke highly of her interest in mathematics. We decided to take
a chance and admit her with the thought that she may need a little
extra help. It was the right decision, and no extra help was needed.
In fact, she helped several students who were weaker and not as
tenacious in trying to solve problems as she was.
Two students from the 2002 program will be at the University of Utah
this fall.
Below, for the record, is the list of participants for the last three
years.
Participants 2000
Assistant 2000
 Darrell Poore (between undergrad and grad)
Participants 2001
Assistants 2001:
 Darrell Poore (grad)
 Bobby Hanson (grad)
Participants 2002
Assistants 2002
 Collin Perschon (between HS and undergrad, alumni of the program)
 Bobby Hanson (grad student)
 Eric Cook (VIGRE grad student)
 Bob Guy (VIGRE grad student)
Also
 Jennifer Taback (Guest lecturer)
 Thom Pietraho (VIGRE postdoc)
MATH CIRCLE 20012002
By Peter Trapa
The purpose of these notes is to document the activities of the Math
Circle this year, comment on what worked and what didn't, and
propose some suggestions for the coming year. Many of the suggestions
are based on the comprehensive evaluations provided by the
participants.
Summary
I knew that the Math Circle had achieved a modest level of success
during its inaugural year, but I was genuinely surprised by uniformly
positive comments from the yearend survey. More than one remarked
that the Math Circle was the best math experience they had ever had.
One person viewed the Math Circle as the highlight of their academic
year. Another said the Circle was a kind of Salt Lake Math Club where
one could learn new things in a distinctly social environment. Yet another
said the only drawback of the program was that it met "only" two
hours each week.
Clearly, we have tapped into something significant. These kids are hungry for math
enrichment, and the Math Circle provides exactly that which they are
seeking. The program has gathered substantial momentum and, after
learning from the missteps inherit in essentially starting the program
from scratch this first year, I think we can add to that momentum.
Format
The Circle began October 3, 2001, and met from 46pm each subsequent
Wednesday of the Fall and Spring terms. In order to maintain some level of continuity, two
consecutive weeks were devoted to the same topic and were typically led by the
same person. A typical session consisted of about an hour of the
leader lecturing at the board and an hour of problem solving. It worked best
when the lecturing and problem solving were intermingled.
Initially, we closely modeled the Math Circle on the Berkeley template
where the main thrust of each session was developing techniques to
solve problems of the kind found on various international
contests such as the International Math Olympiad. This proved
problematic for several reasons, but perhaps most importantly, neither
I nor anyone involved in the program really had any experience with
contests like the IMO. I didn't have a catalog of techniques to share with the kids, and
the problems were too difficult to expect any participant (even the strongest)
to make any progress on their own.
Based on this experience, beginning in the second term we essentially
abandoned the contest problem focus. This proved much more
successful, and opened up many new avenues (like topology, for
instance, which certainly would never appear on any contest). We still emphasized
problem solving, only this time the problems were of our own devising and not
contesttype problems. This worked very well.
Topics
Topics, in chronological order, were as follows:
 Summing polynomial sequences, tiling problems (Peter Trapa, 1
week)
 Induction (Renzo Cavalieri, 1 week)
 Magic squares, modular arithmetic (Jim Carlson, 2 weeks)
 InclusionExclusion principle (Fletcher Gross, 2 weeks)
 Catalan number, bijective proofs (Mladen Bestvina, 2 weeks)
 The game of 16, length and sign of a permutation, RobinsonSchestedKnuth algorithm
(Peter Trapa, 3 weeks)
 Inversion in the plane (Zvezda Stankova, 1 week guest lecture)
 Classification of surfaces (Renzo Cavalieri, 2 weeks)
 Euler characteristic of polyhedra (Thom Pietraho, 2 weeks)
 Hyperbolic geometry (Jennifer Taback, 1 week)
 Five weeks were devoted to contests.
 Ken Golden gave a presentation on the mathematics of sea ice as part of the
last meeting's awards ceremony.
Homework
Assigning any kind of homework was usually a disaster. The kids seemed to have too much
already. The most one could reasonably expect is for them the think
carefully about one problem from week to week. (Even then, only about a
third of them actually did.) To encourage some thinking in between
meetings, I would suggest giving a weekly contest problem to be turned
in at the beginning of the next week. The person with the most correct
solutions at the end of the term could be awarded a book prize. The problem should be reasonably
accessible, and perhaps could be tied to the current topic in the
Circle. Each session could begin with someone
explaining their solution at the board. For this to work, it would be
important to limit this to the first 57
minutes of the session. If it took much longer, it would be too
distracting.
What Makes a Good Session?
One very positive aspect of this year's program was the atmosphere we
managed to achieve and, independent of any particular topic
or session leader, it seems that this positive atmosphere is essential to the
success of the program. To use a single word, I would characterize
the atmosphere this year as friendly. Renzo Cavalieri and I got to know
virtually all of the kids personally, and the relationships we developed were
less of a studenttoteacher than simply friendtofriend. For me, incidentally, this was the most
personally rewarding part of the program. I enjoyed watching the kids
mature mathematically.
This kind of friendly atmosphere immediately led to a freer
exchange of ideas. Most kids weren't bashful about trying out their ideas or going to the board to
explain their solution even if they ultimately turned out to be
wrong. When an explanation was correct, we often applauded.
Even more than the atmosphere, the session leader has the
largest hand in controlling the effectiveness of a particular
session. I found that lecturing for more than 35
minutes was generally a bad idea. These kids have been in school all
day, and it's hard for them to sit through another traditional
lecture. The best formula had the leader introduce new ideas in the initial 2030
minute segment, and then suggesting problems for the group to try. After a 15 minute problem solving
session (facilitated by Renzo Cavalieri and others walking around the room
helping individuals), volunteers presented their solution. After a short discussion, the process
would begin again with new ideas from the leader.
If a session leader wasn't familiar with working with
high school kids, I found it important to have them give a brief overview to me
before the actual meeting in order to headoff any potential
problems. In some cases (for instance, if a
graduate student is giving his first ever mathematical presentation in the
Circle), I think it would be appropriate to have the leader give a full dry run
in front of an actual audience.
One final comment: I found it important to have a couple people in the audience (like Renzo
Cavalieri, Thom Pietraho, and myself) who can gauge the level of understanding
of the students and interrupt to clarify the session leader's exposition
as appropriate. This also helps keep the atmosphere informal.
Crowd Control
Although generally a nonissue, occasionally there were some
disruptive kids. I found this particularly infuriating (perhaps I
need to mellow), but I suppose it comes with the territory. The kids are,
with a few exceptions, pretty good, and, if they got out of line, all it took
to correct the problem was a brief oneonone conversation. But it's important to address
this kind of problem almost immediately.
Contests
Initially, we tried distributing a contest at the beginning
of the month, and then collecting solutions at the end of the month.
This was a disaster. Hardly anyone submitted solutions and
those who did devoted little time to them.
We changed courses and started monthly inclass contests
that lasted for an hour. Thom Pietraho and I would determine winners
while Renzo Cavalieri presented the solutions. Then, I would return
and award book prizes for the best solutions. This worked well.
Every single survey (even those from the weaker kids)
commented positively on the monthly contests, and they should definitely be a
permanent feature of the program.
Suggestions for Next Year
My main suggestion would be to continue leading sessions in
the template we polished toward the end of the year and described above in the
"What makes a good session?" section. Renzo Cavalieri will be a crucial person to implement some
level of continuity from this year to the next. He will be an important resource.
As far as topics are concerned, I would suggest an early
installment of mathematical induction. Since we did that this year,
many participants will know the rudiments of induction, but the
spectrum of difficulty in induction problems is broad
enough to engage all levels. The concept is important enough that it
should be repeated. I might also suggest a few more
sessions devoted to counting (one reinforcing inclusionexclusion, for
instance). Applications include computing dice and card
probabilities. Learning to count is, by my estimation, an extremely important skill and
perfect for the Circle.
One idea, which we didn't explore at all this year, is
preparing the kids for the State Math Contest. Several of the kids indicated in their surveys that,
although everything we did in the Circle was interesting, it may be worth
devoting several sessions to contest preparation.
Based on the yearend surveys, meeting once a week for 2
hours was preferable to twiceweekly meetings. Many of these kids are
overprogrammed already, and even squeezing 2 additional hours into
their schedule can be problematic. The current Wednesday meeting time
seems to be the best compromise.
The homework section above suggests a kind of weekly contest. Some surveys suggested
contests between teams or headtohead competitions in the format of Jeopardy
or other game shows. The team idea seems intriguing to me.
The surveys are valuable. I suggest one a term (as we did this year).
It is always difficult to round up enough faculty members to lead the Circle. The list of
qualified and willing people is rather short. In addition to those we
tapped this year, I would recommend trying Hugo Rossi, Grigory
Mikhalkin, David Hartenstine, Florian Enescu, Aaron Bertram, and Alastair Craw.
One potential resource is the group of VIGRE graduate students
assigned to the Circle. This year, we had one or two on hand at each
session to mingle with the kids while they were working problems. (In
this context, I would like to single out Larsen Louder and Eric Cook
for their substantial contributions above and beyond the call of their official
duty.) Next year, I would suggest having the VIGRE students actually
lead some of the sessions. This is a little delicate, since they
would almost certainly need a lot of help not only in finding an appropriate
topic, but also in polishing their presentation skills. Some kind of dry run of their sessions
would likely need to be conducted. But I think having them lead
sessions offers the VIGRE students an important opportunity to learn
how to present mathematics to a general audience. It certainly fits nicely
with the overall VIGRE mission.
Back to Table of Contents
The purpose of the undergraduate component is to introduce
talented undergraduate students to mathematical research. The
Undergraduate Colloquium series gives faculty, graduate students, as well as
undergraduate students the opportunity to present a research topic to
undergraduate students. Students are encouraged to register for the
series and may obtain academic credit by attending the series and
writing a paper. This gives students a chance to see what types of mathematical research
may be of interest to them and consider enrolling in the REU
research programs. The latter are of two types: Firstly there is the REU
Summer Program where a small number of students is selected to
work on a common project. This project is supervised by a faculty mentor who in turn
is assisted by VIGRE graduate students and/or VIGRE
assistant professors. Each mentor usually will have at least three people to
provide assistance. The second REU program is conducted
throughout the academic year and ideally involves a student, a
graduate student, and a faculty mentor. A student chooses a research topic with
the approval of a faculty mentor. The team of three, just mentioned,
then meets at frequent intervals to discuss and assess progress made.
Several very interesting and successful projects of this type have been
conducted during the past year. Should a student not be able to make
satisfactory progress because of various reasons, the project will be
terminated. Unfortunately, a couple of projects had to be terminated
during the past year. VIGRE also supports the Summer Access
Program by providing assistance to Nick Korevaar who is in charge
of the mathematics portion of the program. The program is an eight week summer
program for incoming freshmen women who are interested in science and mathematics
and is run by the College of Science.
SUMMER 2001 REU PROGRAM
By Jim Carlson
The students in the Summer 2001 REU were Rex Butler, Aaron Cohen, Matt
Dalton, Lars Louder, Robert Palmer, Ryan Rettburg, and Allen Whitt. Two
additional students participated in individual REUs (Stephen Jensen and Tara
Henriksen).
The REU was conducted by faculty members Jim Carlson and Domingo
Toledo, assisted by graduate students Martin Deraux and Bobby Hanson.
The topic of the REU was knot theory and hyperbolic geometry with Colin Adams'
"Knot Book" as the principal reference. We learned about three quarters of the material in Adams
book, and used it as the point of departure for rather freewheeling problem
sessions. I met with the participants for two hours in the morning
four days a week for eight weeks. The graduate assistants met with the
participants for two hours in the afternoon to discuss and work on problems
together, and in some cases to present new material. Beginning the
second day of the REU, students presented solutions or attempted
solutions to problems, and the group as a whole worked on refractory
problems in discussion. Students also presented their own lectures on
material in Adams book.
An early focus of the group's activities was the problem of whether
knots could be distinguished from the trivial knot by "colorability
invariants". The group as a whole, with several notable leaders
(Aaron Cohen, Matt Dalton, Lars Louder, and Ryan Rettburg)
developed a theory of how to find colorability invariants by writing down a
certain integer matrix and considering its nullity mod n. The point
was that its nullity is always positive and, if it is greater than one, the
knot is ncolorable and hence not isotopic to the unknot. The entire theory grew out of their
study of two examples in Adams: the trefoil knot, which is tricolorable, and
the figure eight knot, which is nontrivial but not tricolorable.
Adams suggested a way to distinguish the figure eight knot using a coloring by elements
of Z/5.
The group wrote a joint paper on ncolorability and related
matters. In addition, and in addition to solving
many problems in Adams as a warmup, each participant did an individual project which was
reported in class and/or written up.
I was especially pleased by the independence the students showed, the
way in which they learned to work and talk about mathematics together,
and the fact that they learned to ask questions and formulate
problems. Rettburg and Dalton did exceptionally nice problems.
Outcomes So Far:
Rex Butler: Rex is a student from rural Tooele county. He has done a second REU during
the academic year on representations of finite groups with Henryk
Hecht. He will apply to graduate school. I think he is deep and has
talent. He has an omnivorous curiosity.
Rex participated in the summer REU on probability theory conducted by
Davar Khoshnevisan. Davar mentioned him to me as one of the
two outstanding participants in the program.
Rex is developing very well, and wants to go to graduate school in
mathematics. I think he has a bright future ahead of him.
Aaron Cohen: Aaron pursued an academic year REU with Paul Bressloff.
The aim of the project was to carry out linear analysis of an integrodifferential equation
that describes the way a local population of cells in the visual cortex detect the orientation
of a local visual stimulus.
Matt Dalton: Matt did an outstanding paper on the noncolorability of
pretzel knots. He gave an ifandonly if criterion using elementary
arguments. Although his result can be derived from much more
sophisticated theory, his elementary proof stands out. Dalton did a second REU with Mladen
Bestvina during the year. However, he was a disappointment. He stopped
showing up regularly and we had to terminate him. Matt has applied to our
Master's program. He is very talented, but must learn better work
habits. I've talked to him about this.
Matt was accepted into the Department's Master's program, but without
support. Unfortunately, his lack of discipline and attention to
detail is hurting him.
Lars Louder: Lars is a student from semirural Idaho and was accepted
into our Ph.D. program as a VIGRE graduate student for the fall of
2001. As of this writing (August 2002), he is doing very, very well
according to Mladen Bestvina. He acted as an assistant to the summer
2002 REU in probability theory conducted by Davar Khoshnevisan. Lars' interest is
topology and geometry. I think the breadth that the VIGRE experience
has forced upon him is a good thing.
Robert Palmer: Robert is finishing his degree in Computer Science and
has done a research project in that department as well.
Ryan Rettburg: Ryan is doing extremely well as an undergraduate and
will apply to graduate school. He is a graduate of the Department's
2000 High School Summer Program, where his talent first became evident
to us.
Allen Whitt: Last I heard from Allen, a student at the University of
Arizona, he was applying to an NSA summer program.
ACADEMIC YEAR 20012002 REU
Brian Budge
Alta High School 1997
Hometown: Sandy, UT
Majors: Mathematics, Computer Science
Year: Senior
Faculty Mentor: Klaus Schmitt

Project Proposal:
People have been generating fractals and making use of properties of
fractals  in image compression for example  for many years. The most common way to generate these entities is through what is called an Iterated
Function System (IFS).
An IFS works on the basis of Banach's Contraction Mapping Principle.
Basically what happens is the image is taken though any number of affine
linear transformations (these include scaling, shearing, rotation,
translation, and mirroring) to produce a new image. This new image is then
taken through the transformations, and so on. More formally:
Let f(x): x element of S → y element of S_{new}  f is an affine
transformation.
Let F(S): union over all x elements of S of f(x) → S_{new}
Then we can say that if set S is the original set of points, then
F(S) = S_{0}
F(S_{0}) = S_{1}...
F(S_{N1}) = S_{N}...
Until F(B) = B
This limit (where F is a map from a set to itself) is called the fractal.
I would like to work with Dr. Klaus Schmitt to create fractal images, and
possibly image compression techniques based on this principle. We hope to
introduce some new ideas to this including creating images from higher
dimension fractals (4 or 5D), and also we would like to look into using
nonlinear transformations to generate fractals and fractal image
compression techniques.


Rex Butler
Viewmont High School, 1998
Hometown: Tooele, Utah
Major: Mathematics
Year: Junior
Faculty Mentor: Henryk Hecht

Project Proposal:
My research project, under Professor Henryk Hecht, will be the study of the
representation theory of finite groups. Finite groups arise in many areas
of mathematics. One may study them through purely algebraic methods of
group theory, or through the perspective of representation theory, which
studies groups through their representations as linear transformations of
various spaces.
As it is well known, every irreducible representation of a finite group is
fully determined by its character, or in other words, the trace of the
resulting linear transformation. Thus, in order to study representations,
we may, equivalently, study their characters, which are functions on the
group in question. I propose to compute characters of a variety of concrete
representations of specific groups and study their features beginning fall
semester 2001 through spring semester 2002.
This subject is of interest to me for multiple reasons. Representation
theory involves groups structures that lie at the heart of abstract
algebra and mathematics as a whole. This subject will also allow me to work
with tangible examples while also developing the ability to deal with
abstract structures.


Aaron Cohen
East High School, 2000
Hometown: Salt Lake City, Utah
Major:
Year:
Faculty Mentor: Paul Bressloff

Project Proposal:
My project will be concerned with the study of spontaneous pattern formation
in activationinhibition systems. I will begin by studying the classical
Turing instability in diffusiondriven systems, in order to gain insight
into some of the modeling and mathematical issues concerned. I will then
focus on the role of pattern formation in cortical dynamics, including a
theory of geometric visual hallucinations that has recently been developed
by Dr. Paul Bressloff (my faculty mentor) and Dr. Jack Cowan (University of
Chicago).
One of the major goals of the project will be to gain an understanding of
the role of symmetry and group theory in pattern formation, especially
within the context of geometric hallucinations and the emergent patterns of
certain cellular automata.


Matthew Dalton
Mountain View High School, 1998
Hometown: Orem, Utah
Major: Mathematics (Physics and Spanish minor)
Year: Senior
Faculty Mentor: Mladen Bestvina

Project Proposal:
There is a special type of automorphism for closed surfaces with hyperbolic
structure, known as PseudoAnosov automorphisms. Under iterations of such an
automorphism, it has been shown that the length L of a geodesic grows as
L(n) = C(lambda)^{f}_{n}, where C is a constant and lambda is determined by the automorphism
f. It has also been shown that lambda > 1 as the genus of the surface goes to infinity.
There are still, however, many things not known about lambda. For instance, for
a given surface, what is the smallest possible lamda?
My proposal for the REU program is to (1) bring up my level of understanding
of hyperbolic surfaces, PseudoAnosov automorphisms, and the origin of this l
factor, and (2) attempt to answer some of these unanswered questions about
l. If the problem is satisfactorily completed by the end of this semester,
I will seek a new project for next semester.


Song Du
Hometown: Wuhan, China
Majors: Mathematics, Electrical Engineering
Year: Freshman
Faculty Mentor: Paul Fife

Project Proposal:
This is a project in "experimental mathematical materials science." Its
purpose is to test the validity of the wellknown "motion by curvature law"
for the motion of grain boundaries of many varieties, when the motion is
modeled by a system discrete in space and time. The approach will be to
approximate a twophase (or twograin) material by a lattice structure with
the state of the material being specified in some discrete manner at each
lattice point. Then various supposed dynamical laws regarding how the
system changes from one discrete time to the next are tested by numerical
simulation. There will be an approximate boundary between two grains, and
its motion will be simulated. Its curvature will also be calculated, and
the validity of the aforementioned law tested within the confines of these
various approximate models. The simulations will be performed through use
of Matlab or C++.


Troy Finlayson
HS
Hometown:
Major: Physics
Year: Junior
Faculty Mentor: Kenneth Golden

Project Proposal:
I'd like to work with Professor Ken Golden on theoretically and numerically
estimating the thermal conductivity of sea ice, and its role in mediating
heat transfer between the ocean and the atmosphere in the polar regions.
Seawater freezes into a composite material, containing pockets of air and
inclusions of brine with high concentrations of salt throughout the ice. As
the microstructural composition of the sea ice changes, through variations
in temperature and growth processes, the thermal conductivity of the sea ice
changes. The amount of trapped air and brine in the sea ice is directly
correlated with the rate at which the seawater freezes. Large variations in
temperature, due to meteorological or perhaps longer term global warming
effects, can significantly affect the thermal conductivity properties of the
ice, which can in turn affect growth processes, leading to ice of a
different composition. Subsequently, the heat transfer that occurs between
the vast ocean and the air is also affected.
Sea ice is made up of three components; ice, inclusions of highly saline
seawater, or brine, and pockets of air. The thermal conductivity of brine
is close to that of pure ice, but the conductivity of the air phase is quite
different. Thus as a first approximation we may treat the sea ice as two
component medium, and we plan to apply the mathematical theory of bounds on
transport coefficients to estimate the thermal conductivity of the sea ice,
about which very little is currently known. In subsequent work we hope to
be able to incorporate the effects of brine moving through the ice when it
is warm enough that a percolating network of brine exists, and model how the
advection of the brine through the ice can enhance the ability of the sea
ice to transfer heat from the ocean to the air. Mathematically this will
involve the analysis of nonlinear heat equations, as well as percolation
theory.


Tara Henriksen
CimarronMemorial High School, 1999
Hometown: Las Vegas, Nevada
Major:
Year:
Faculty Mentor: Fred Adler

Project Proposal:
In a continued study (from the summer), I will attempt to explain why FEV1
is such an unpredictable variable. I will also separate the patients into
groups by their predicted survivorship, and determine whether or not FEV1 is
dropping yearly. An interesting variable to test its acute exacerbations
the only variable that is not directly a measurement of a patient¹s physical
health. It is almost a judgment call by the doctor admitting the patient to
decide whether or not the visit should be counted as an acute exacerbation.
For this reason we have decided that I will test the accuracy of the model
excluding this variable. After completing the aforementioned tasks, I hope
to answer the question about how accurate a oneyear assessment of a CF
patient actually is.


David Lindsay (Nov.  Dec. 2001)
Viewmont High School, 1997
Hometown: Centerville, Utah
Majors: Mathematics, Physics
Year: Junior
Faculty Mentor: Wieslawa Niziol

Project Proposal:
For my research project, I intend to study the theory of elliptic curves.
This area of mathematics is of interest for many reasons. First, is that
the study of elliptic curves brings together many different branches of
mathematics: geometry, number theory, and modern algebra. Second, the study
of elliptic curves is of interest because Fermat's Last Theorem, on of the
most famous conjectures ever, was recently proven using ideas based in this
theory. Third, the study of elliptic curves has many useful modern
applications; in particular, elliptic curves can be used to construct
cryptographic systems.
In my project, I plan on studying various computational aspects of elliptic
curves. In simpler terms that means I plan on studying certain invariants
of elliptic curves and how complex it is to compute such invariants. Along
with this, I plan to research many already existing techniques and
algorithms used to compute such invariants.


Josh Stewart
HS
Hometown:
Major:
Year:
Faculty Mentor: Jingyi Zhu

Project Proposal:
For my REU project I plan to explore the utility of mathematical models in
finance, particularly in the area of derivative securities. I am certainly
interested in studying the basic modern theory behind some models and their
real world applications; in addition I will equally attempt to discover
their strengths and weaknesses, efficacy and limitations in portraying
pertinent information for investors.
During my project I will receive help and direction from Professor Jingyi
Zhu who has suggested the following list of topics for my studies:
I. Motivations and derivatives of the BlackScholes model and the formula
II. Application of the BlackScholes model to interest rate derivatives
III. Consideration of the Vasicek model for the term structure of interest
rates
IV. Valuation of some sample portfolios using the Vasicek model
V. Dependence and sensitivity of the Vasicek model to various parameters
VI. Creation of spreadsheets that employ the Vasicek model
VII. Daytoday tracking of portfolios with the help of the model
One of my main goals for this project is to apply the knowledge I gain to
real life, thus to complement my theoretical studies, I have agreement from
Sam Stewart, Portfolio Manager at Wasatch Funds Inc., to apply valuation
models to the funds and portfolios at Wasatch. I will also complete other
projects for the company, for example I have agreed to study certain
statistics used to rate or measure the success of a portfolio such as the
tracking error, the sharpe ratio and the alpha, in order to discover the
assumptions being made in their calculation and to gauge their effectiveness
in measuring a funds performance.

SUMMER 2002 REU PROGRAM
This program, devoted to random walks and simulation analysis, will be
conducted by Davar Khoshnevisan with the help of three VIGRE
graduate students (Sarah Geneser, Larsen Louder, and Robert Thorn) during parts
of July and August 2002. It has been advertised widely and is open to
sixteen undergraduate students; for more information, please click here.
Out of an application pool of 25 people, 7 students were
chosen to do individual REU projects and the following 7 were chosen to do the
REU with Davar Khoshnevisan:
Micah Allred
 Bonita Vista High School, 1997
 Hometown: San Diego, CA
 Major: Mathematics
 Year: Junior, Brigham Young University
Rex Butler
 Viewmont High School, 1998
 Hometown: Farmington, UT
 Major: Mathematics
 Year: Junior
Song Du
 Highland High School, 2001
 Hometown: Wuhan, China
 Major: Mathematics and Electrical Engineering
 Year: Freshman
Amanda Ellis
 Brighton High School, 2001
 Hometown: Riverton, UT
 Major: Mathematics with emphasis in Statistics
 Year: Junior
Ronald McKay
 Penncrest High School, 1988
 Hometown: Media, PA
 Major: Mathematics
 Year: Senior
John Schweitzer
 Homeschooled
 Hometown: Bountiful, UT
 Major: Mathematics and Physics
 Year: Junior, Hillsdale College
Matthew Taylor
 Provo High School, 1995
 Hometown: Provo, UT
 Major: Mathematics
 Year: Senior
UNDERGRADUATE COLLOQUIUM
This colloquium series is organized by Angie Gardiner, Gordan Savin,
and Nathan Smale.
The following report is by Nat:
The Undergraduate Colloquium of 2001  2002 was
organized by myself (Nat Smale), Gordan Savin, and Angie Gardiner.
The colloquium consisted of a weekly talk on a wide variety of topics,
ranging from probability and mathematical biology to topology,
geometry, and number theory. The speakers were regular faculty members, instructors
(including VIGRE Assistant Professors), and graduate students. After
the talk, typically pizza was served, and informal discussions were
held. The purpose of the colloquium is to expose undergraduates to
a wide variety of topics in math, both pure and applied. Students may
enroll in it as a course, or simply show up when a topic interests
them. We had about five students per semester enroll in the
course. The requirements for them were to attend regularly, and write
a short paper on one of the topics presented. Many others attended,
with typically around 15 to 20 students showing up (sometimes as many as
30). Attendance should increase next year, as the colloquium will be
required for those in the new Honors Program.
The following report is by Angie:
Overall, I think that the Undergraduate Colloquium Series is
going well. The students who attend are exposed to a wide variety of
mathematical topics, and most seem to enjoy the talks. I have received
some positive feedback about the series, and there are a few students each
semester who register for credit and attend on a consistent basis.
However, I do see a couple of problems that we need to address.
First, attendance has declined, at least for Spring 2002, after
increasing for the last couple of years. We may want to look at
scheduling the colloquia on a different day or time, or possibly
rescheduling the key classes that conflict with the colloquia. (I don't
know how feasible this would be). We may also need to take a look at
our publicity, and how we could more effectively publicize the talks.
Another problem that I see (and that was pointed out to me
by a student last week) is that the level of the talks seems to be getting
higher and higher. In the beginning, we tried to be very careful to
schedule talks that would be accessible to many students, many
requiring only a background of Calculus, or sometimes Ordinary
Differential Equations or other 2000 level mathematics. The thinking
was that, if the majority of the students could understand most of the
talk and only get lost in the last 5 or 10 minutes, that was okay.
But I think that many of the talks given lately have been likely to lose
students within the first 10 or 15 minutes, unless the students are already
quite far along in their studies. We need to seriously think about
who we want the audience for these talks to be, and then be careful to
schedule talks at a level geared for that particular audience.
The list of lectures presented during the 2001  2002 academic year
may be seen here.
SUMMER ACCESS PROGRAM
By Nick Korevaar
ACCESS is an eightweek, half day program for incoming freshman women
interested in science and engineering. This College of Science program was
created a decade ago by then Dean Hugo Rossi, and is currently directed by
Professor Sid Rudolph in the Physics Department. Each summer, 21
bright and energetic students arrive on campus and spend different
weeks in the various science disciplines. Nick Korevaar led the two Math weeks in
2001 and 2002, assisted most recently by Emina Alibegovic. The goals of the summer session are to
familiarize the students with the University, with the opportunities in each discipline, with
collegelevel work, and, most importantly, to let them develop supportive peer
relationships.
The first math week was built around Simon Singh's The Code Book ,
moving historically from substitution ciphers to
the number theory behind RSA internet security. Jim Carlson delivered
guest lectures on number theory and RSA security; Biology Professor
Jon Seger spoke on the genetic code and its history, including the
recent discovery that, in some strange organisms, one of
the universal "stop" codons has evolved to encode a novel amino
acid. At the beginning of the week students were solving substitution
ciphers; by the end of the week they were ready to tackle their group
projects: create a moderately scaled RSA cryptosystem, and test it by
sending messages to each other.
The second math week was devoted to classical and fractional scaling
laws in mathematics and science. Fred Adler presented an interesting
theory in mathematical biology which attempts to explain the empirical
3/4power law between animal mass and animal metabolism. This law holds for the smallest to the
largest of animals. Assuming energy production is proportional to
surface area and mass is proportional to volume, then if animals were
balls one would expect a 2/3 power law; some mathematical biologists
have tried to explain the higher power in terms of branching
structures in the circulatory and respiratory systems of animals
which lead to more surface area. Ken Golden gave a guest lecture about
material structures and his own work on sea ice. For their projects,
students used contraction mappings to create original fractals. They
also used their own and national data to deduce that there is an empirical
power law relating human heights to weights, but that this power is not the one
used in the wellknown body mass index.
During the second week, Angie Gardiner led an advising session about
math classes and the math major and minor. Ken Golden also spoke
enthusiastically about the mathematics concentration, in his new role as the
departmental director of undergraduate studies. A significant
fraction of ACCESS students this year indicated an interest in at
least minoring in math.
For more information on the ACCESS program, click here. For more
details about this year's mathematics component, click here.
INTERNSHIP PROGRAM
By Nat Smale
I have been in charge of the VIGRE Internship Program for 2001 
2002. So far, this program has acted mainly as a "clearing house",
that is, when a firm needs to fill an internship position and contacts the
department, I try to find appropriate candidates for this through faculty who
teach courses most closely related to the desired area. This has been done twice, when David
Wavrick, the head of a small energy firm in Salt Lake, was looking for an
intern with some expertise in a certain area of statistics. The first time, I tried to find
students through Lajos Horvath and Stew Ethier. Unfortunately, all of
their students already had summer employment. The second time, I put
Dave Wavrick in touch with Marlene Egger who was the head of the Biostatistics
Program (Stew Ethier recommended her as having the most contact with potential
candidates for the internship). In the future, I will try to develop
some ties to particular firms that could possibly use math
undergraduates as interns.
PROBLEM SOLVING COMPETITION
By Angie Gardiner
This year, our department participated in The Problem
Solving Competition, run by Dr. Richard S. Neal, President ASCM. The
Problem Solving Competition is open to all undergraduates. Problems
are posted roughly monthly, and monthly winners receive a book, such as Journey
Through Genius, What is Mathematics?, or The Code
Book. We began with Hugo Rossi as our faculty
advisor for the competition, but about halfway through the year, the
competition was turned over to David Hartenstine. The undergraduate
who selected and graded the problems (each month there was a choice of
two problems) was WeiShou Hsu, a senior mathematics major. The overall
winner of our competition and the grader (WeiShou) were given the opportunity
to attend Mathfest 2002 (held in Burlington, VT) and to participate in the
national finals of The Problem Solving Competition.
MODULES
By Nick Korevaar
In our VIGRE proposal, we envision "modules" as supplementary units for our regular courses, with the
aim of connecting course material to other areas of mathematics and
science. Modules should encourage exploration, discovery, and
research. They can be appropriate at all levels of
instruction.
David Hartenstine has made a preliminary linked list between courses
and available or proposed modules. The module descriptions need to be
expanded, and we need to figure out how to incorporate the list into the
departmental web pages and consciousness.
I have utilized and encouraged the module idea in courses which I
coordinate or teach, in particular in our sophomore
math major track, Math 22702280. Our most successful example is the
iterated function system for fractal generation. This material
originated in an undergraduate colloquium by Klaus Schmitt and has
been presented by Gordan Savin in Math 5210 as an
application of the contraction mapping theorem and an introduction to Hausdorff
measure. A different emphasis of the material has led to the module
in our linear algebra course Math 2270, and
most 2270 instructors use the fractal module in some form. (Click here for the associated Maple project.)
A version of this material has also been used successfully in the summer
ACCESS program. Instructors often present module material themselves,
but this past spring I presented fractal lectures in Mladen Bestvina's
2270 course, and in return he presented a module on hyperbolic
geometry for my Euclidean Curves and Surfaces Course, Math 4530. This
is the sort of mutually beneficial interaction we would like to
encourage.
Jim Keener is currently working with some of his graduate students to
develop a module on electrical circuits and the action potential in
nerve cells for our Differential Equations course, Math 2280. David Hartenstine has
been working on an html version of a Kepler's Laws module and I created a
module last term on minimal surfaces and complex analysis.
During the upcoming academic year we need to:
 Finish the modules which were begun last year.
 Collect more module ideas from the faculty. Many undergraduate
colloquium topics should be suitable. Demonstrations, experiments,
and commercial videos could also be useful.
 Expand and implement the linked list of courses and modules. For modules which
have been presented or which are based on colloquia it is relatively easy to scan
and link lecture notes  this would be a good resource for prospective users, and
would be much less time consuming than creating html documents. Alternately,
we could encourage the module creators or course coordinators to post
expository material on their own web pages, which we would link to.
 Encourage module experimentation, collect and incorporate
feedback.
Back to Table of Contents
At the heart of VIGRE lies the graduate program. Its purpose
is to provide a broad educational and research experience to wellchosen
graduate students and also to train them in the art of teaching, mentoring, and
organization of courses, seminars, and the like, while at the same time
reducing the time required to obtain the Ph. D. degree. We attempt to accomplish this by having
an aggressive recruitment program, providing continuous mentoring and teaching training seminars, a
colloquium series discussing important research areas, summer problem sessions
to prepare students for the necessary qualifying examinations, minicourses
presenting quick and thorough introductions to research areas, opportunities to
help mentor high school and undergraduate students in research projects as well
as becoming part of research teams early in their career.
The following describes in some detail these efforts during the past
year.
GRADUATE COLLOQUIUM
By Renzo Cavalieri
The graduate colloquium is one of the activities organized
by the Graduate Student Advisory Committee (Renzo Cavalieri and Kenneth
Chu). The speakers are either graduate students or members of the
faculty from the department. Faculty members are encouraged to speak
about their area of research at a level appropriate for beginning graduate
students. This is helpful for graduate students who are "shopping",
i.e. who still need to decide on a specialization field. These
talks provide a perspective on what types of research take place within the
department. For graduate students who are already working in a
specific area, it is a great occasion to be exposed to different kinds
of mathematics. Graduate students are also strongly encouraged to give a
talk, either on their current research or on a different topic they find
particularly interesting. The Graduate Colloquium provides an
excellent "training ground" for giving talks, a very required skill in
academia as well as in other professions, in a relatively sheltered
and friendly environment.
The complete
list of 24 talks we have organized this year is posted on the
web.
This year, the attendance has been a little less satisfactory than
usual. We hope to discuss the reasons and find solutions in the organizational GSAC meeting to
be held on April 30, 2002. One evident difference with respect to last year is the attendance
policy. In past years, the department required that all graduate
students in their first or second year attend the colloquium. This year, there is no
such attendance policy, and the attendance of first year graduate students is
particularly low. The figures are the following: the average
attendance is about 15 graduate students, of which
there's a good kernel (about 10) present at every talk; the other people
tend to only attend talks held in their own area of interest. Usually, a few post docs and faculty
members join the audience as well.
We feel it's particularly important to be able to convey to the
majority of the graduate students the importance and usefulness
of the graduate colloquium.
QUALIFYING EXAMINATION PROBLEM SESSIONS
Matthew Rudd (VIGRE Graduate Fellow) coordinated the Qualifying
Exam Problem Sessions held during the summer of 2001 in preparation for Ph.D.
preliminary exams. Students taking a particular exam met to discuss
problems, and faculty members coordinating the exams were available
for questions or met with students regularly just prior to exams.
Summer 2001 Schedule:
Algebra
 Student Organizer: Cord Erdenberger
 Faculty Advisor: Paul Roberts
 Boot Camp: Week of 1 August
Real and Complex Analysis
 Student Organizer: Kenneth Chu
 Faculty Advisor: Henryk Hecht
 Regular meetings: Fridays at 12:30 P.M., JWB 208
 Boot Camp: The weeks of 23 July and 30 July (mornings)
Applied Math
 Student Organizer: Andrew Oster
 Faculty Advisor: James Keener
 Regular meetings: Wednesdays at 1:45 P.M., INSCC
 Boot Camp: The week of 2 July
Differential Equations
 Student Organizer: Matthew Rudd
 Faculty Advisor: Klaus Schmitt
 Regular meetings: Mondays at 1:00 P.M. in JWB
 Boot Camp: The weeks of 23 July and 30 July (afternoons)
Numerical Analysis
 Student Organizer: Andrew Oster
 Faculty Advisor: Aaron Fogelson
Probability and Statistics
 Student Organizer: Chris Staskewicz
 (Chris is the only student taking the exam.)
Topology
 Faculty Advisor: Misha Kapovich
 Boot Camp: The week of 1 August
Summer 2002 Schedule:
Meagan McNulty and Ryan Stones (VIGRE Graduate Fellows)
coordinated the Qualifying Exam Problem Sessions held during the summer of 2002
in preparation for Ph.D. preliminary exams.
Unless otherwise noted, these boot camps run from May 20th
 August 9th, 2002.
Algebra
 Boot Camp: Mondays (8:30am  10:30am), Tuesdays (12:30pm  1:30pm), and Thursdays
(8:30am  10:30am)
 Location: May 9th  May 24th in JWB 240, May 28th  August 12th
in LCB 322
 Faculty Advisor: Paul Roberts
 Graduate Mentor: Greg Piepmeyer
Applied Mathematics
 Boot Camp: Mondays and Wednesdays (11:30am  2:30pm)
 Location: LCB 218
 Faculty Advisor: Paul Bressloff
 Graduate Mentor: Bob Guy
Differential Equations
 Boot Camp: Tuesdays (2:30pm  4:30pm) and Fridays (11:30am 
2:30pm)
 Location: LCB 218
 Faculty Advisor: Klaus Schmitt
 Graduate Mentor: Ken Chu
Numerical Analysis
 Boot Camp: Tuesdays and Thursdays (11:30am  2:30pm)
 Location: LCB 218
 Faculty Advisor: Jingyi Zhu
 Graduate Mentor: Bob Guy
Real and Complex Analysis
 Boot Camp: Mondays (12:30pm  1:30pm), Wednesdays (8:30am 
10:30am), and Thursdays (12:30pm  1:30pm)
 Location: May 9th  May 24th in JWB 240, May 28th  August 12th
in LCB 322
 Faculty Advisor: Hugo Rossi
Geometry and Topology
 Boot Camp: Tuesdays (8:30am  10:30am), Wednesdays (12:30pm 
1:30pm), and Fridays (8:30am  10:30am)
 Location: May 9th  May 24th in JWB 240, May 28th  August 12th
in LCB 322
 Faculty Advisors: Nathan Smale and Andrejs Treibergs
Probability
 No one is currently scheduled to take this prelim.
Statistics
 No one is currently scheduled to take this prelim.
GRANT PROPOSAL SEMINAR
"Preparing a Successful Grant Proposal"
Presentations by: Aaron Bertram, Graeme Milton, Cindy
Phillips, and Anurag Singh
The GSAC colloquium on September 4, 2001 was the setting for
a joint presentation by experienced writers of successful grants (Aaron
Bertram, Graeme Milton, Anurag Singh) and the math department grant accountant
(Cindi Phillips). The seminar was targeted at graduate students
interested in getting some perspective on the grant process, associate
professors applying for a grant for the first time,
and for other interested faculty. The focus was on applying for a regular
NSF individual investigator mathematics research grant, rather than on a large
multiinvestigator grant. Topics covered included:
 Why should I apply for a grant?
 What are my chances for success?
 How do I get started?
 What are the important things I should know about?
 What strategy should I use?
 Can I see some examples of successful grants?
 What should I put in the budget?
 How do I justify the budget?
 How will my grant be reviewed?
 What are some of the things the reviewers will be
looking for in my proposal?
 What happens after I hear from the program officer?
The talk was followed by a discussion, with input from other
faculty.
TA/TF TRAINING
The TA workshop is a twoweek training period designed to
improve communication skills of new teaching assistants. The workshop concentrates on aspects of
public speaking, effective presentation of mathematical logic, and leadership
training. The goals of the workshop are achieved by a variety of
techniques which include: case studies, contrasting presentations,
facilitator led discussions, peer, self, and
facilitator feedback on presentations given by the participants. The presentations are frequently
videotaped, and with the aid of an evaluation form, reviewed by the
student. At the end of the first week, the participants identify
goals for the second week. Trainees give a baseline (videotaped)
lecture on the first day of the workshop, and the same lecture on the last day
of the workshop. The exit lecture is also videotaped, and each
presenter reviews the complete collection of video
presentations. No first year student is given a teaching assignment
unless the facilitators agree on their preparedness. Those who are not
certified are assigned to assist one of the better teachers in the
department. Their duties include holding office hours for the class,
grading and periodically giving lectures.
TA Training Program Schedule of Events (August 6  17,
2001)
Monday, August 6, 2001
 08:30...Coffee/Tea/Treats (228 JWB)
 09:00...Introductions and Goals of Workshop  Large Group (335 JWB)
 10:00...Break
 10:15...Videotaping: Baseline Lecture  Large Group (335 JWB)
 12:00...Lunch
 13:00...Videotaping: Baseline Lecture  Large Group (335 JWB)
Homework: Prepare First Day Introduction (3  5 Minutes)
Tuesday, August 7, 2001
 08:30...Coffee/Tea/Treats (228 JWB)
 09:00...Demonstrations: Dynamic Lecturing and How to Provide
Constructive Feedback  Large Group (335 JWB)
 10:00...Break
 10:15...Practice Session: Dynamic Lecturing  Style and
Expression  Small Groups (335 JWB)
Work on presentation, style, delivery, content, clarity, and
accuracy
(First day Introduction and Baseline Lecture)
 12:00...Lunch
 13:00...Practice Session: Dynamic Lecturing  Style and
Expression  Small Groups (335 JWB)
Work on presentation, style, delivery, content, clarity, and
accuracy
(First day Introduction and Baseline Lecture)
Homework: Prepare Practice Lecture (810 minutes) and Watch
and Critique Baseline Lecture Video
Wednesday, August 8, 2001
 08:30...Coffee/Tea/Treats (228 JWB)
 09:00...Demonstrations: Blackboard Presentation  Large Group (335
JWB)
 10:00...Break
 10:15...Videotaping: Practice Lecture #2  Small Groups (335 JWB)
 12:00...Lunch
 13:00...Videotaping: Practice Lecture #2  Small Groups (335 JWB)
Homework: Prepare Practice Homework Problem (57 minutes) and Identification
of Goals for Improvement
Thursday, August 9, 2001
 08:30...Coffee/Tea/Treats (228 JWB)
 09:00...Interactive Demonstrations: Presentation of
Homework Problems  Large Group (335 JWB)
 10:00...Break
 10:15...Videotaping: Practice Homework Problem  Small Groups (335 JWB)
Work on presentation, board work, and clarity
 12:00...Lunch
 13:00...Videotaping: Practice Homework Problem  Small Groups (335 JWB)
Work on presentation, board work, and clarity
Homework:Exam Grading: Exam #1 (Due on Friday) and Watch and critique
Practice Homework Problem Video
Friday, August 10, 2001
 08:30...Coffee/Tea/Treats (228 JWB)
 09:00...Interactive Workshop: Exam Grading  Large Group (335 JWB)
 10:30...Break
 10:45...Interactive Discussion: First day of class  Large Group
(335 JWB)
Why it is Important, How to Prepare, What to Do
Leadership, Credibility, Professional Presentation and Image,
Classroom Policy
 12:00...Lunch
 13:00...Individual meetings with facilitators (335 JWB)
Make tentative course assignment, handout book
Homework: Design tentative course syllabus
Read Chapter 1 and Design Lesson Plan for Chapter 1

Monday, August 13, 2001
 08:30...Coffe/Tea/Treats (228 JWB)
 09:00...Ann Darling, Director, CTLE  Large Group (335 JWB)
Issues in Teaching and Learning
 09:30...Teaching American Students  Large Group (335 JWB)
 10:00...Break
 10:15...Interactive Workshop: Syllabus Preparation and
Class Lesson Plan  Large Group (335 JWB)
 11:15...Syllabus Design Lab (Computer Lab)
 12:00...Campus Tour: Room Visits with Practice of First Day
Introductions
Homework: Exam Grading: Exam #2 (Due on Tuesday)
Tuesday, August 14, 2001
 08:30...Coffee/Tea/Treats (228 JWB)
 09:00...Interactive Workshop: Test Construction and Preparation 
Large Group (335 JWB)
 10:00...Break
 10:15...Interactive Workshop: Student Questions and Answers 
Large Group (335 JWB)
How to Ask, How to Answer, How to Foster Discussion
 12:00...Lunch
 13:00...Interactive Workshop: Test Construction and Preparation 
Small Groups (335 JWB)
Taking and Critiquing Exams, Small Group Feedback and Iiscussion
Homework: Prepare First Day Lecture (for assigned course)(40 minutes)
Wednesday, August 15, 2001
 08:30...Coffee/Tea/Treats (228 JWB)
 09:00...Practice Session: First Day Lecture  Small Groups (335
JWB)
 10:00...Break
 10:15...Practice Session: First Day Lecture  Small Groups (335
JWB)
 12:00...Lunch
 13:00...Practice Session: First Day Lecture  Small Groups (335
JWB)
Homework: Preparation for Exit Video: First Day Introduction and
Baseline Lecture (15 minutes) and Write Exam for Chapter 1 (for assigned course) (Due
Thursday)
Thursday, August 16, 2001
 08:30...Coffee/Tea/Treats (228 JWB)
 09:00...Exit Videotaping: (no feedback)  Large Group (335
JWB)
First Day Introduction and Baseline Lecture
 12:00...Lunch
 13:00...Exit Videotaping: (no feedback)  Large Group (335
JWB)
First Day Introduction and Baseline Lecture
 15:00...Facilitators Only  Evaluation/Certification (and Exam
Design Analysis)
Friday, August 17, 2001
 08:30...Coffee/Tea/Treats (228 JWB)
 09:00...Recap Presentation by Facilitators and Certification 
Large Group (335 JWB)
 10:00...Break
 10:15...Panel Discussion with Experienced TAs  Large Group (335
JWB)
 12:00...Lunch  Group

GRADUATE STUDENT RECRUITING
Recruiting Weekend:
The top recruiting prospects are invited to visit campus for
a threeday weekend in midMarch. They are housed in the guest
housing on upper campus. Those who are interested can take
advantage of a Saturday outing of skiing, snow shoeing, or getting acquainted
with the city. On Sunday, the recruits are given an overview of the department,
city, and state. After lunch they are given a tour of campus followed
by a general reception in the departmental common room. All faculty are
invited to attend and some formal presentations on research areas are
given. The remainder of the afternoon is dedicated to informal
discussions with faculty. The current graduate students then host
a dinner for the guests at a local restaurant. On Monday, recruits
attend some classes and visit with current graduate students.
Graduate Recruitment Weekend Schedule of Events (March 25
 26, 2001)
Sunday, March 25, 2001
 10:00  11:30 am
Meet at University Guest House Conference Room
 10:00  10:20 am
Welcome: Jim Carlson and Graduate Advisory Committee (GSAC
Chairs)
 10:20  10:40 am
Overview of the Graduate program: Peter Trombi
 10:40  11:00 am
Life in Salt Lake City
 11:30 am  1:00 pm Lunch
(Conference Room, University Guest House)
 1:00  3:00 pm
Tour of Campus, Math Building, etc.
 3:00  6:00 pm
Mathematics Commons Room (228 JWB)
 3:00  4:00 pm
Overview of Mathematics Research Programs
 4:00  5:00 pm
Informal discussions in small groups
 5:00  6:00 pm
Reception with faculty and graduate students
 Dinner arranged by GSAC
Monday, March 26, 2001
 12:45  2:00 pm
Visits to Classes and Graduate Colloquium
(lunch
with graduate students and visiting graduate students)
 3:00 pm
Open House at INSCC Building (kitchen area) hosted by math biology
faculty and students.
Graduate Recruitment Weekend (March 31  April 1, 2002)
By Peter Trombi
The goals of the recruiting weekend are to bring the top
applicants to campus as a group so they get a sense of the cohort that will
comprise the incoming graduate class.
The recruits were invited to visit campus for a threeday
weekend on March 31, 2002 through April 1, 2002. They were housed in
the University Guest House on upper campus.
Those who were interested took advantage of a Saturday outing of
skiing, snow shoeing, cultural events, or getting acquainted with the
city.
On Sunday, the recruits were given an overview of the
department, city, and state. After lunch, they were given a tour of
campus followed by formal presentations on research areas in the
department. This was followed by a general reception attended by most faculty and
graduate students. The remainder of the afternoon was dedicated to
informal discussions with faculty. The current graduate students then
hosted dinner for the guests at a local restaurant.
On Monday, the recruits attended some classes and visited
with current graduate students.
The responses from some of the attendees of the recruitment
weekend were very positive. Some of them were: "I would like
to thank you for putting together such a great weekend for our visit.
I really think the quality of the department was evident in
everything that we did." and "I had such
a wonderful time visiting Utah this past weekend. Thanks for all your
hard work organizing and preparing everything that you did offer.
Please thank the graduate students who were involved as well, they were
terrific!"
Schedule of Events:
Sunday, March 31, 2002
 9:00  10:00 am
Meet at the University Guest House  Continental Breakfast
 10:00  10:30 am Drive
or Walk to Mathematics Building
 10:30  10:45 am Welcome: Graeme Milton and Graduate Advisory
Committee (GSAC Chairs)  LCB 222
 10:45  11:15 am Overview
of the Graduate Program: Peter Trombi
 11:15  11:45 am Life
in Salt Lake City
 11:45 am  1:00 pm
Lunch
 1:00  3:00 pm
Tour of Campus, Mathematics Buildings, etc.
 2:30  3:00 pm
Mathematical Biology Open House (Hosted by Mathematical Biology
Faculty)  LCB 322
 3:00  4:00 pm
Overview of Mathematics Research Programs  LCB 222
 4:00  5:00 pm
Informal Discussions in Small Groups  LCB 222
 5:00  6:00 pm
Reception with Faculty and Graduate Students  JWB 228
 6:00pm Dinner
Arranged by GSAC
Monday, April 1, 2002
 Visits to Classes and...
 12:45  2:00 pm Graduate
Colloquium as well as Lunch with Graduate Students and Visiting
Graduate Students  JWB 208
Name 
Attended Recruiting Weekend 
VIGRE 
Male/Female 
Accepted Offer 
Declined Offer 
BS/BA University 
Max Aeschbacher 
Yes 
Yes 
Male 

X 
University of Utah 
Nathan Albin 
No 
Yes 
Male 
X 

University of Hawaii 
Phillip Caroll 
Yes 
Yes 
Male 

X 
High Point University, NC 
Topaz Dent 
Yes 
No 
Female 

X 
UC Davis 
Matina Donaldson 
No 

Female 

X 
Reed College, OR 
Elisa Gomez (International) 
Yes 
No 
Female 

X (declined funding but will be attending as unfunded) 
University of Jaen, Spain 
William Koppelman 
Yes 
No 
Male 
X 

University of Wyoming 
Aaron McDonald 
Yes 
No 
Male 
X 

Rockhurst University, MO 
Emily Putnam 
Yes 
Yes 
Female 
X 

San Francisco State Univeristy 
Thomas Putnam 
No 
Yes 
Male 

X 
Rice University, TX 
Ian Renner 
Yes 
No 
Male 
X 

Valparaiso University, IN 
Dennis Rice 
No 
No 
Male 

X 
Northern Arizona University 
Christopher Robinson 
Yes 
No 
Male 
X 

Murray State University, KY 
Mindy Scott 
Yes 
No 
Female 
X 

University of Utah 
Richard Smith 
Yes 
No 
Male 

X 
Hope College, MI 
Nessy Tania (International) 
Yes 
No 
Female 

X 
UC Davis 
Joshua Thompson 
Yes 
No 
Male 
X 

Wofford College, SC (BS) Wake Forest University (MS) 
John Zobitz 
Yes 
No 
Male 
X 

St. John's University, MN 
MINICOURSE ON COMPLEX HYPERBOLIC GEOMETRY (MAY 13  24, 2002)
By Jim Carlson
A minicourse on complex hyperbolic geometry was held May 1324, 2001
as part of the University of Utah's VIGRE program. The
course had three aims:
 introduce graduate students to
fundamental ideas and basic techniques in complex hyperbolic geometry,
 introduce them to recent research in the area, and
 introduce them to open problems.
Personnel:
 Organizers: Domingo Toledo and Jim Carlson
 Invited Speakers: Richard Schwartz, University of Maryland, and
Elisha Falbel, University of Paris VI (visiting Johns Hopkins)
 Postdoctoral fellows: Javier Fernandez (VIGRE funded) and Martin
Deraux (nonVIGRE funded)
Outside Participants, with their affiliations and source of
support:
 Matthew Bainbridge, Harvard University, VIGRE
 David Dumas, Harvard University, funded entirely by Harvard
 Samuel Grushevsky, Harvard University, VIGRE
 W. Patrick Hooper, SUNY Stony Brook, VIGRE
 Ryan Hutchinson, Notre Dame, VIGRE
 Philip Jacobs, University of Houston, VIGRE
 Cathy Jones, University of Maryland, partial VIGRE & partial
Univ. of Maryland through Bill Goldman's NSF grant
 Nikolai Krylov, University of Illinois at Chicago, partial support
from his university and partial support from the University of Utah
through Carlson and Toledo's NSF grant
 Maryam Mirzakhani, Harvard University, funded entirely by Harvard
 Blake Pelzer, University of Maryland, VIGRE
 Natasa Sesum, Massachusetts Institute of Technology, lodging and
airfare paid through the University of Utah by Carlson and Toledo's
NSF grant
 Stephen Wang, University of Chicago, VIGRE
 Kevin Wortman, University of Chicago, VIGRE
Preparation:
Domingo Toledo recruited the invited speaker, Richard Schwartz, a
leader in the field of complex hyperbolic geometry. Richard Schwartz
suggested that Elisha Falbel also be invited to speak. The program was advertised nationally
by mail, email, and the web. Toledo also contacted a number of mathematicians across the country to
see if their graduate students would be interested in attending. The
response was extremely good. So much so that we, together with others
(Bill Goldman at Maryland, Curt McMullen at Harvard) supported several students
from our research grants. We had reached the limit of our VIGRE
budget for the minicourse, and several students were not VIGREeligible.
Program:
In the first week Carlson, Deraux, and Toledo gave lectures on the basics of real and complex hyperbolic
geometry. The aim was to develop sufficient background for Schwartz's
talks the following week. Fernandez and Deraux led problem and
discussion sessions. A schedule of the lecture topics can be seen at
the minicourse website.
On the weekend, a group of about eight students rented cars and
visited southern Utah. A hike and picnic were organized for those who remained
here, and for the invited speakers who arrived during the weekend.
In the second week, Richard Schwartz discussed results of Goldman and Parker on deformations of the ideal
triangle group in the complex hyperbolic plane, the conjecture of Goldman and
Parker as to the precise interval of discreteness of these deformations, and
his solution of the GoldmanParker conjecture. These were the
subjects of six of his eight lectures. The remaining two lectures were devoted
to other deformation problems, to the construction of CR structures on certain
real hyperbolic 3manifolds, and to open problems. Schwartz's lectures were distinguished by their clarity,
enthusiasm, depth, and level of engagement by the students. He not only presented a beautiful
circle of results, but gave students great insight into how they were found and
into what the thought process leading up to them was. Students received a firsthand account of how
experimentation with the computer can lead to results, and how the
computer can be used to actually *prove* results. Some of the afternoon
discussionproblem sessions were held in the Department's new computer teaching
lab. There Richard demonstrated how software he had written could be
used to visualize the action of a group on the ball in complex 2space.
Elisha Falbel gave two lectures on his work with Parker on the moduli
space of typepreserving representations of the modular group in the
complex hyperbolic plane. This was a nice and natural complement to the lectures of
Schwartz. Software used for visualization was also demonstrated.
A party was given at Toledo's house on May 23rd.
Evaluation:
 The quality of student participants was superb.
 The level of esprit de corps among the students was very good.
 The participants found the minicourse instructive and helpful.
It introduced them to the ideas and techniques of an active,
problemrich research field, and gave them a personal view into how research is
conducted.
MINICOURSE ON VARIATIONAL METHODS AND NONLINEAR PDE (MAY 28 
JUNE 7, 2002)
By Klaus Schmitt
The minicourse, as its title suggests, was intended to provide an introduction to the use of modern
variational methods in the study of nonlinear PDE. The course was
organized by David Hartenstine (a VIGRE Assistant Professor), Matthew
Rudd (a VIGRE Graduate Fellow), and Klaus Schmitt (PI of
the VIGRE grant). Professor Jean Mawhin of Université
Catholique de Louvain, a world renowned expert in the subject and
known as an excellent lecturer, was invited as the principal
lecturer. Others (from outside the University of Utah) invited to
lecture were, Jon Jacobsen (a VIGRE postdoctoral assistant professor at Pennsylvania State
University) and Vy Le of the University of Missouri. The Geometry/PDE
group (Nick Korevaar, Jesse Ratzkin (a VIGRE Assistant
Professor), Nat Smale, and Andrejs Treibergs), as well as the
organizers of the course, gave lectures, also.
The course was advertised nationally via the internet as well as regular mail to departments having
graduate programs in mathematics. The number of inquiries from
graduate students was small and six outside
graduate students were chosen to receive financial support from the VIGRE grant
to attend the course (the proposal's intention is to invite five students from
universities other than Utah to attend the course). Five students
from the University of Utah attended the course as well.
Besides the lectures
already mentioned, there were discussion
sessions for each lecture (except the last) which were organized and conducted
by the student participants. The students were also
assigned to four working groups, each of which was assigned a project to be
worked on during the first week of the course. The projects' findings were then presented during the
second week of the course.
To provide the attendees some leisure time, Thursday afternoon of the
first week and Wednesday afternoon of the second week were free of
minicourse activities. A hike in the Wasatch mountains followed by a picnic at one
of the organizers' homes took place on Sunday. There was also a "farewell picnic" held at the
end of the minicourse. Some pictures of the hike, the picnics, and
the lectures may be seen by clicking here.
The costs for the picnics and some other incidental expenses were
carried by the Department.
All participants were asked to complete a questionnaire and a summary
of the responses are available here.
In summary, we feel that the course was a success both in its format
and presentations.
20012002 VIGRE GRADUATE FELLOWS
Eric Cook
 B.S. 1999, Colby College
 Hometown: Atkinson, NH
 Faculty Mentor: Henryk Hecht
 VIGRE Duties: REU mentor, Math Circle rotation, HS
Summer Program
 Area of Interest: Pure Mathematics
 Fall 2001 Schedule: Math 5110 (Mathematical Biology), Math 6210 (Real Analysis),
Math 6310 (Modern Algebra I), Math 6710 (Applied Linear Operator and Spectral
Methods)
 Spring 2002 Schedule: Math 5520 (Introduction to Algebraic Topology), Math 6220
(Complex Analysis), Math 6320 (Modern Algebra II)
Sarah Geneser
 B.A. 2001, Rice University
 Hometown: Houston, TX
 Faculty Mentor: Jim Keener
 VIGRE Duties: REU mentor, Math Circle rotation
 Area of Interest: Neural Modeling and Medical Imaging
 Fall 2001 Schedule: Math 6410 (Ordinary Differential
Equations), Math 6710 (Applied Linear Operators and Spectral Methods), Math
6770 (Mathematical Biology I), Math 6910 (Neuroscience Supervised
Reading)
 Spring 2002 Schedule: CS 6220 (Scientific Computing II), Math 6620 (Analysis of
Numerical Methods II), Math 6720 (Applied Complex Variables and Asymptotic
Methods), Math 6780 (Mathematical Biology II)
 Seminars: Math Biology Seminar, GSAC Colloquium, Neuroscience Group Meeting, Dr.
Keener's Math Biology Group Meeting
Robert Guy
 M.S. 1999, University of Utah
 Hometown: Greenville, NC
 Faculty Mentor: Aaron Fogelson
 Ph.D. Qualifying Exams: Numerical Analysis, Applied Mathematics, Real and Complex
Analysis
 VIGRE Duties: REU mentor, HS summer program
 Areas of Interest: Applied Math, Fluid Dynamics,
Mathematical Modeling, Math Biology, Numerical Analysis
 Fall 2001 Schedule: Math 7970 (Thesis Research)
 Spring 2002 Schedule: Math 6630 (Numerical PDE), Math 7970
(Thesis Research)
 Seminars: Applied Math, GSAC Colloquium, Undergraduate Colloquium, Math Biology,
Math Physiology group meeting, Fluid Dynamics group meeting, helps lead the
Math Biology Journal Club
 Papers Published: "Probabilistic modeling of platelet aggregation:
Effects of activation time and receptor occupancy" by Robert Guy and
Aaron Fogelson, Journal of Theoretical Biology (accepted but not yet
published)
 Papers in Preparation: Thesis
 Conferences Attended: Society of Mathematical Biology Conference in Knoxville, TN
in early July, 2002 (also a speaker at this conference)
Larsen Louder
 B.S. 2001, University of Utah
 Hometown: Twin Falls, ID
 Faculty Mentor: Mladen Bestvina
 VIGRE Duties: REU mentor, Math Circle rotation
 Areas of Interest: Topology, Geometry
 Fall 2001 Schedule: Math 6310 (Modern Algebra I), Math 6210 (Real Analysis),
Math 6170 (Riemannian Geometry), Math 7853 (Topics in Geometric
Topology)
 Spring 2002 Schedule: Math 6150 (Kahler Manifolds), Math 6220 (Complex Analysis),
Math 6320 (Modern Algebra II)
 Seminars: GSAC Colloquium
 Conferences Attended: Wasatch Topology Conference in the Fall,
2001
Meagan McNulty
 B.S. 1998, Metro State College
 Hometown: Wheatridge, CO
 Faculty Mentor: Ken Golden
 VIGRE Duties: REU mentor, Math Circle rotation
 Fall 2001 Schedule: Math 6410 (Ordinary Differential Equations), Math 6610
(Analysis of Numerical Methods I), Math 6710 (Applied Linear Operator and
Spectral Methods), Math 5110  Audit (Mathematical Biology I), Bio 5910 
Audit (Mathematical Models in Biology)
 Spring 2002 Schedule: Math 5210 (Introduction to Real Analysis), Math 6620
(Analysis of Numerical Methods II), Math 6720 (Applied Complex Variables,
Asymptotic Methods), Math 6910, Math 5110  Audit, Math 6920 
Audit, Biol 2020  Audit
 Seminars: GSAC Colloquium, Math Biology Journal Club,
SLAM Meeting, Biology Group Meeting
Matthew Rudd
 M.S. 1996, University of Chicago
 Hometown: Rome, GA
 Faculty Mentor: Klaus Schmitt
 Ph.D. Qualifying Exams: Applied Mathematics, Differential Equations, Real and
Complex Analysis
 VIGRE Duties: Minicourse (with Dr. Schmitt), REU mentor
 Area of Interest: Partial Differential Equations
 Fall 2001 Schedule: Math 6430 (Advanced Partial Differential Equations), Math
6170 (Introduction to Riemannian Geometry), Math 7970 (Thesis
Research)
 Spring 2002 Schedule: Math 6630 (Numerical Methods for PDE), Math 7840 (Topics in
PDE), Math 7970 (Thesis Research), CS 6950 – Reading Course (Finite
Element Methods)
 Seminars: GSAC Seminar (talks on October 16, 2001 and in March, 2002), PDE Seminar
(talk on October 24, 2001), Wake Forest University Math Department Colloquium
(talk on October 31, 2001), SoutheasternAtlantic Regional Conference on
Differential Equations at Wake Forest University (talk in November, 2001),
VIGRE MiniCourse on Variational Methods and Nonlinear PDE
 Papers Submitted for Publication: Variational inequalities of
elliptic and parabolic type” with Klaus Schmitt to the Taiwanese Journal
of Mathematics (will be published in fall, 2002)
 Papers in Preparation: Thesis ("Nonlinear constrained evolution
in Banach spaces")
 Conferences Attended: SEARCDE Conference at Wake Forest University in November,
2001 (lectured at this conference), VIGRE MiniCourse on Variational Methods
and Nonlinear PDE in May – June, 2002 (lectured at this
conference)
Ryan Stones
 B.S. 2001, Brigham Young University
 Hometown: Salt Lake City, UT
 Faculty Mentor: Misha Kapovich
 VIGRE Duties: REU mentor, Math Circle rotation
 Area of interest: Pure Mathematics
 Fall 2001 Schedule: Math 6210 (Real Analysis), Math 6310 (Modern Algebra I), Math
6510 (Differential Manifolds)
 Spring 2002 Schedule: Math 6220 (Complex Analysis), Math 6320
(Modern Algebra II), Math 6520 (Introduction to Algebraic Topology)
Robert Thorn
 B.S. 2001, University of Utah
 Hometown: Salt Lake City, UT
 Faculty Mentor: Paul Bressloff
 VIGRE Duties: REU mentor, Math Circle rotation
 Area of Interest: Math Biology
 Fall 2001 Schedule: Math 5310 (Introduction to Modern Algebra I), Math 5410
(Introduction to Ordinary Differential Equations), Math 6710 (Applied Linear
Operator and Spectral Methods)
 Spring 2002 Schedule: Math 5210 (Introduction to Real Analysis), Math 5320
(Introduction to Modern Algebra II), Math 6720 (Applied Complex Variables,
Asymptotic Methods)
 Seminars: Neuroscience, Math Biology
20022003 VIGRE GRADUATE FELLOWS
Nathan Albin
 B.A. 2001, University of Hawaii
 Faculty Mentor: Klaus Schmitt
 VIGRE Duties: Math Circle Mentor, REU Mentor, GRE Prep, Senior
Seminar, Boot Camp Organizer
Maria Bell
 B.S. 2002, University of Utah
 Hometown: Provo, UT
 Faculty Mentor: Aaron Bertram
 VIGRE Duties: Math Circle Mentor, REU Mentor, ACCESS Mentor
Matthew Clay
 B.S. 2001, University of Oregon
 Hometown: Enumclaw, WA
 Faculty Mentor: Misha Kapovich
 VIGRE Duties: Math Circle Mentor, REU Mentor, Boot Camp Mentor
 Area of Interest: Algebra
 Fall 2002 Schedule: Math 6040 (Mathematical Probability), Math
6130 (Introduction to Algebraic Geometry), Math 6240 (Lie
Groups/Lie Algebras)
Robert Guy
 M.S. 1999, University of Utah
 Hometown: Greenville, NC
 Faculty Mentor: Aaron Fogelson
 Ph.D. Qualifying Exams: Numerical Analysis, Applied Mathematics, Real and Complex
Analysis
 VIGRE Duties: Math Circle Mentor, Boot Camp Mentor, Math Biology
Journal Club Organizer, Summer High School Program Mentor
Areas of Interest: Applied Math, Fluid Dynamics, Mathematical
Modeling, Math Biology, Numerical Analysis
 Papers Published: "Probabilistic modeling of platelet aggregation:
Effects of activation time and receptor occupancy" by Robert Guy and
Aaron Fogelson, Journal of Theoretical Biology (accepted but not yet
published)
 Papers in Preparation: Thesis
Brynja Kohler
 M.S. 1998, New York University
 Hometown: Boston, MA
 Faculty Mentor: Jim Keener
 VIGRE Duties: Math Circle Mentor, Boot Camp Mentor, Math Biology
Journal Club Organizer, ACCESS Program Mentor
 Area of Interest: Mathematical Biology
Greg Piepmeyer
 B.A. 1998, University of Utah
 Hometown: Reno, NV
 Faculty Mentor: Paul Roberts
 VIGRE Duties: Math Circle Mentor, REU Mentor, Boot Camp Mentor,
Summer High School Program Mentor
 Area of Interest: Commutative Algebra
 Fall 2002 Schedule: Math 7800 (Toric Varieties), Thesis Hours
Emily Putnam
 B.A. 2002, San Francisco State University
 Hometown: Berkeley, CA
 Faculty Mentor: Aaron Bertram
 VIGRE Duties: Math Circle Mentor, GRE Prep, Senior Seminar, REU
Mentor, ACCESS Program Mentor
 Area of Interest: Algebra
Matthew Rudd
 M.S. 1996, University of Chicago
 Hometown: Rome, GA
 Faculty Mentor: Klaus Schmitt
 Ph.D. Qualifying Exams: Applied Mathematics, Differential Equations, Real and
Complex Analysis
 VIGRE Duties: Math Circle Mentor, REU Mentor, Boot Camp Mentor,
PDE Seminar
 Area of Interest: Partial Differential Equations
 Fall 2002 Schedule: Math 7840 (Topics in PDE), Math 7970 (Thesis
Research)
 Papers Submitted for Publication: "Variational inequalities of
elliptic and parabolic type" with Klaus Schmitt to the Taiwanese Journal
of Mathematics (will be published in fall, 2002)
 Papers in Preparation: Thesis ("Nonlinear constrained evolution in Banach
spaces")
Back to Table of Contents
The postdoctoral program in mathematics at the University
of Utah was started during the early seventies. Its members include many
prominent research mathematicians who occupy academic positions at leading
mathematics departments. It is in this spirit that the VIGRE postdoctoral
program is viewed and only candidates with exceptional promise are appointed to
these positions. Each postdoc (VIGRE assistant professor) is appointed
for a three year period, has a teaching load of one course per semester and is
expected to participate in the other VIGRE programs of the
department. When joining the faculty, each postdoc is assigned a faculty mentor who
shares the same or similar research specialty. The mentor supervises the
postdoc's academic activities and is responsible for evaluating his or
her performance in teaching, research, and service.
The following list provides the names and activities of
people appointed during the years 2001 and 2002 as VIGRE
Assistant Professors.
VIGRE ASSISTANT PROFESSORS
Javier A. Fernandez
 Ph.D. 2001, University of Massachusetts
 Algebraic Geometry, Hodge Theory
 Hometown: Buenos Aires, Argentina
 Faculty Mentor: Jim Carlson
 Teaching Duties Fall 2001: Math 1090, Business Algebra
 Teaching Duties Spring 2002: Math 1100, Quantitative Analysis
 VIGRE Duties: Minicourse
 Current Research Interests: Hodge Theory and its applications to the understanding of
mirror symmetry (for instance, the relation between variations of Hodge
structure and quantum products); dimensional bounds of variations of Hodge
structures with prescribed degenerating behavior; the relationship between
geometry and physics.
 Papers Submitted for Publication: "Frobenius modules and Hodge
asymptotics" (with E. Cattani) submitted to Comm. Math. Phys.
 Papers in Preparation: "Infinitesimal variations of Hodge structure at
infinity"
 Lectures Given: Algebraic Geometry Seminar "Amodel variation of Hodge structure,
an application of asymptotic Hodge theory" September, 2001; Mathematical
Physics Seminar "Perturbation theory and Feynman diagrams" March,
2002; Graduate Colloquium "A window into mirror symmetry" April,
2002; lead problem sessions (with Martin Deraux) on MiniCourse on Complex
Hyperbolic Geometry May, 2002
 Conferences Attended: Park City Math Institute July, 2001; Arizona Winter School
2001, Tucson, AZ, March, 2002; Workshop on Frobenius manifolds at the Max
Planck Institute of Mathematics, July, 2002
David A. Hartenstine
 Ph.D. 2001, Temple University
 Partial Differential Equations
 Hometown: Allentown, Pennsylvania
 Faculty Mentor: Klaus Schmitt
 Teaching Duties Fall 2001: Math 1210, Calculus I
 Teaching Duties Spring 2002: Math 1220
 VIGRE Duties: Minicourse (with Klaus Schmitt)
 Current Research Interests: Partial Differential
Equations, specifically concerning the MongeAmpere equation
 Papers Submitted for Publication: "Regularity
properties of weak solution to the MongeAmpere equation" (with C. E.
Gutierrez), to Trans. AMS
 Lectures Given: Two PDE Seminar lectures, Univ. of Utah, 8/29/01 and 9/5/01; AMS Session
on Nonlinear Elliptic PDE, San Diego, January, 2002
 Conferences Attended: Symposium for 75th Birthday of James Serrin,
University of Minnesota, November, 2001; AMS/MAA Joint National Meeting, San
Diego, January, 2002; AMS/UMI Joint International Meeting, Pisa, Italy, June,
2002
Thomas Pietraho
 Ph.D. 2001, MIT
 Representation Theory
 Hometown: Middlebury, Vermont
 Faculty Mentor: Peter Trapa
 Teaching Duties Fall 2001: Math 1220, Calculus II
 VIGRE Duties: Math Circle, Summer High School Program
Lecturer
 Current Research Interests: Representation Theory of Lie Groups, Combinatorics of
Representation Theory
Jesse L. Ratzkin
 Ph.D. 2001, University of Washington
 Differential Geometry, Geometric PDE
 Hometown: Berkeley, California
 Faculty Mentor: Nat Smale
 Teaching Duties Fall 2001: Math 2280, Introduction to
Differential Equations
 Teaching Duties Spring 2002: Math 2270, Introduction to Linear
Algebra
 VIGRE Duties: Summer Mathematics Program for High
School Students 2002
 Current Research Interests: Geometric Analysis and Riemannian
Geometry
 Papers Submitted for Publication: "An end to end gluing
construction for metrics of positive scalar curvature", to appear in Ind.
Univ. J. Math.
 Papers in Preparation: Something with many gluing constructions for constant mean
curvature surfaces, joint with Rafe Mazzeo, Frank Pacard, and Dan
Pollack
 Lectures Given: Gang seminar at U Mass Amherst: CMC Surfaces of Higher Genus, 2/15/02;
Graduate Colloquium: Introduction to CMC Surfaces, 3/12/02; Undergraduate
Colloquium: Crystal growth; Differential Geometry Seminar: Gluing special
Lagrangian submanifolds, 4/18/02
 Conferences Attended: Annual Meeting of the Canadian
Mathematics Society, 12/7/01  12/10/01, Toronto; Spring 2002 PNGS,
5/11/02  5/12/02, Seattle, WA
The above people will be VIGRE Assistant Professors in the
2002  2003 academic year except for Thomas Pietraho. The new person
will be:
Nancy Sundell
 Ph.D. 2002, Cornell University
 Faculty Mentor: Fred Adler
 Current Research Interests: Theoretical Ecology with an Emphasis on the Application of
Mathematics to Topics in Population and Conservation Biology
2001 RECRUITMENT STATISTICS

Graduate Fellows

Assistant Professors

Number of Applicants

132

141

•
Number of U.S. Applicants *

46

33

• Number of U.S. Female Applicants

14

20




Number of Offers Made

35


•
Number of U.S. Offers Made

21


• Number of VIGRE Offers

15

7

•
Number of Offers to Females

14


• Number of VIGRE Female Offers

4

1




Number of Acceptances

18


•
Number of VIGRE Acceptances

6

4

• Number of VIGRE Female Acceptances

2

0




Number of Internal People Recruited for VIGRE

2





Total Number of VIGRE People

8

4

*U.S. citizens, nationals, or permanent residents, as far as
could be determined.
2002 RECRUITMENT STATISTICS

Graduate Fellows

Assistant Professors

Number of Applicants

130

210

•
Number of U.S. Applicants *

56

61

• Number of U.S. Female Applicants

18

13




Number of Offers Made

30

9

•
Number of U.S. Offers Made

23


• Number of VIGRE Offers

10

6

•
Number of Offers to Females

11

4

• Number of VIGRE Offers to Females

4





Number of Acceptances

15


•
Number of VIGRE Acceptances

4

1

• Number of VIGRE Female Acceptances

2

1




Number of Internal People Recruited for VIGRE

5





Total Number of VIGRE People

8


*U.S. citizens, nationals, or permanent residents, as far as
could be determined
2001  2002 VIGRE DUTIES
Academic Year


REU Mentor

Math Circle

PDE Seminar

Modules

PostDocs





Fernandez





Hartenstine



X

X

Pietraho


X



Ratzkin





Graduate Fellows





Cook


X



Geneser


X



Guy

X




Louder


X



McNulty

X

X



Rudd

X




Stones


X



Thorn


X



Summer


Boot Camp Organizer

Carlson &
Toledo’s MiniCourse

Schmitt’s MiniCourse

REU Mentor

Summer
High School Program

Summer REU Program

PostDocs







Fernandez


X





Hartenstine



X




Pietraho





X


Ratzkin




X

X


Graduate Fellows







Cook





X


Geneser






X

Guy





X


Louder






X

McNulty

X






Rudd



X




Stones

X






Thorn






X

Back to Table of Contents
