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The VIGRE Program at the University of Utah
Report on the Year 2001 - 2002

Prologue

The Department of Mathematics at the University of Utah successfully competed for a National Science Foundation five-year 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 post-doctoral 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 year-long 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 three-week 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 boot-camps held during the summer 2001. Other VIGRE events that took place during the 2001 - 2002 academic year were two mini-courses (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.

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Award Notification

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 (Co-Principal Investigator current) Hugo Rossi (Co-Principal Investigator current) Gordan Savin (Co-Principal Investigator current) James A. Carlson (Co-Principal 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 year-round 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

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VIGRE Highlights July, 2000 - July, 2002

July, 2000

Submission of Proposal

November, 2000

Site Visit by NSF Team

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

Math Circle Starts

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

Mini-Course on Complex Hyperbolic Geometry

June, 2002

Mini-Course 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

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People Involved in the VIGRE Program

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, Co-PI 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, Co-Organizer of and Lecturer at Mini-Course on Complex Hyperbolic Geometry, Undergraduate Colloquium Lecturer, Steering Committee Member, Co-PI 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 Mini-Course 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 Mini-Course on Complex Hyperbolic Geometry

Javier Fernandez, VIGRE Assistant Professor
VIGRE Activities: Lecturer at Mini-Course 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 Co-Organizer of Mini-Course 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 Mini-Course 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, Co-PI of VIGRE Grant, Undergraduate Colloquium Lecturer, Preparation of Modules, Co-Organizer of ACCESS Summer Program, Participant in VIGRE Conference, Lecturer in Mini-Course 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 Mini-Course 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 Mini-Course on Variational Methods and Nonlinear PDE

Meagan McNulty, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Undergraduate Mentor, Math Circle Mentor, Prelim Boot Camp Co-Organizer

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 Mini-Course 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, Co-PI of VIGRE Grant, Coordinator of REU Program, Undergraduate Colloquium Lecturer, Co-Organizer 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 Mini-Course 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, Co-PI of VIGRE Grant, Undergraduate Colloquium Lecturer, Co-Organizer 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 Mini-Course on Variational Methods and Nonlinear PDE

Richard Schwartz, Professor of Mathematics, University of Maryland
VIGRE Activities: Lecturer at the Mini-Course 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, Co-Organizer of Undergraduate Colloquium, Internship Organizer, Lecturer in Mini-Course on Variational Methods and Nonlinear PDE

Ryan Stones, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Undergraduate Mentor, Math Circle Mentor, Prelim Boot Camp Co-Organizer

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: Co-Organizer of and Lecturer at the Mini-Course 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 Mini-Course on Variational Methods and Nonlinear PDE

Peter Trombi, Professor of Mathematics
VIGRE Activities: Steering Committee Member, Co-PI 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 mini-courses, 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

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Programs for High-School Students

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 2001-2002 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, post-doctoral 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 half-hour 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 in-class 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 week-long afternoon workshop in knot theory.

Angie Gardiner, Director of Undergraduate Services, a full-time 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 full-time 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 math-physics 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 year-long 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

7 participants

Assistant 2000

Darrell Poore (between undergrad and grad)

Participants 2001

19 participants

Assistants 2001:

Darrell Poore (grad)
Bobby Hanson (grad)

Participants 2002

20 participants

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 2001-2002
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 year-end 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 4-6pm 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 contest-type 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)
Inclusion-Exclusion principle (Fletcher Gross, 2 weeks)
Catalan number, bijective proofs (Mladen Bestvina, 2 weeks)
The game of 16, length and sign of a permutation, Robinson-Schested-Knuth 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 5-7 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 student-to-teacher than simply friend-to-friend. 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 20-30 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 head-off 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 non-issue, 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 one-on-one 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 in-class 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 inclusion-exclusion, 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 year-end surveys, meeting once a week for 2 hours was preferable to twice-weekly meetings. Many of these kids are over-programmed 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 head-to-head 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

Programs for Undergraduate Students

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 free-wheeling 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 n-colorable 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 n-colorability and related matters. In addition, and in addition to solving many problems in Adams as a warm-up, 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 integro-differential 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 non-colorability of pretzel knots. He gave an if-and-only 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 semi-rural 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 2001-2002 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) = S₀ F(S₀) = S₁... F(S_N-1) = 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 non-linear 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 activation-inhibition systems. I will begin by studying the classical Turing instability in diffusion-driven 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 well-known "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 two-phase (or two-grain) 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 afore-mentioned 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 micro-structural 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 Cimarron-Memorial 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 patient�s 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 one-year 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 Black-Scholes model and the formula II. Application of the Black-Scholes 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. Day-to-day 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

Home-schooled
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 eight-week, 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 college-level 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 3/4-power 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 well-known 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 Wei-Shou Hsu, a senior mathematics major. The overall winner of our competition and the grader (Wei-Shou) 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 2270-2280. 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

Programs for Graduate Students

At the heart of VIGRE lies the graduate program. Its purpose is to provide a broad educational and research experience to well-chosen 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, mini-courses 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 multi-investigator 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 two-week 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 (8-10 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 (5-7 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 three-day weekend in mid-March. 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 (G-SAC 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 G-SAC

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 three-day 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 (G-SAC 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 G-SAC

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

MINI-COURSE ON COMPLEX HYPERBOLIC GEOMETRY (MAY 13 - 24, 2002)
By Jim Carlson

A mini-course on complex hyperbolic geometry was held May 13-24, 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 (non-VIGRE 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, e-mail, 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 mini-course, and several students were not VIGRE-eligible.

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 mini-course 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 Goldman-Parker 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 3-manifolds, 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 first-hand 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 discussion-problem 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 2-space.

Elisha Falbel gave two lectures on his work with Parker on the moduli space of type-preserving 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 mini-course instructive and helpful. It introduced them to the ideas and techniques of an active, problem-rich research field, and gave them a personal view into how research is conducted.

MINI-COURSE ON VARIATIONAL METHODS AND NONLINEAR PDE (MAY 28 - JUNE 7, 2002)
By Klaus Schmitt

The mini-course, 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 mini-course 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 mini-course. 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.

2001-2002 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: Mini-course (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), Southeastern-Atlantic Regional Conference on Differential Equations at Wake Forest University (talk in November, 2001), VIGRE Mini-Course 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 Mini-Course 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

2002-2003 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")

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The Post-Doctoral Program

The post-doctoral 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 post-doctoral program is viewed and only candidates with exceptional promise are appointed to these positions. Each post-doc (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 post-doc is assigned a faculty mentor who shares the same or similar research specialty. The mentor supervises the post-doc'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: Mini-course
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 "A-model 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 Mini-Course 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: Mini-course (with Klaus Schmitt)
Current Research Interests: Partial Differential Equations, specifically concerning the Monge-Ampere equation
Papers Submitted for Publication: "Regularity properties of weak solution to the Monge-Ampere 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
Post-Docs
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 Mini-Course	Schmitt’s Mini-Course	REU Mentor	Summer High School Program	Summer REU Program
Post-Docs
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

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VIGRE Steering Committee
Department of Mathematics
University of Utah
155 South 1400 East; Room 233
Salt Lake City, UT 84112
email: viscom@math.utah.edu

The VIGRE Program at the University of Utah Report on the Year 2001 - 2002

Integrated Program for Training in Mathematics

Abstract

The VIGRE Program at the University of Utah
Report on the Year 2001 - 2002