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The VIGRE Program at the University of Utah
Report on the Years 2003 - 2004

Overview

The VIGRE program at the University of Utah is a department-wide program (about 2/3 of our present faculty members participate in some form of activity of the program) that addresses education and research at all levels and all areas of specialization represented in the department. Ever since the initial discussions started within the department to prepare an application for a VIGRE grant, additions have been made to our research and educational programs, which have been well received and have had considerable impact. These changes have brought forth increased activities on the instructional as well as research levels from our outreach efforts to the training of undergraduate and graduate students, as well as the training of postdoctoral assistant professors. The design of the program creates interactions between postdocs, graduate students, undergraduates, and even high school students by having each VIGRE-supported person participate in some form of VIGRE activity. There is a broad range of choices (see below) and thus each supported graduate student and/or postdoc can select the kind of program they wish to help with or lead. Occasions, of course, will arise when assignments have to be made for reasons of equity. Participation in the components of the VIGRE program is also open to all graduate students and postdocs, regardless of their VIGRE eligibility. In fact, some of the graduate students and post-docs having made outstanding contributions to our VIGRE programs are ineligible for VIGRE support.

All facets and participants of the program are evaluated at the end of each semester. These evaluations are either in the form of questionnaires (for programs that have several participants) or personal evaluations by mentors and participants. The evaluations are collected and analyzed and used to tune the program as a whole.

This past year was the third year of the program and, according to NSF practices, was the year of decision whether the program be continued for another two years. With much input from our three advisory committees, we performed an in-depth review of our accomplishments and submitted a detailed report about them to the NSF. During October, a NSF team (two program officers and a colleague from another university) site visited the department and conducted interviews with many of the VIGRE participants. We soon (December 2003) learned that the continuation of the program had been approved for another two years.

The various portions of this report have been collected, compiled, and prepared by Sarah Strong (Program Coordinator) and Klaus Schmitt (Director) of the VIGRE program. Thanks are due to many colleagues who have contributed to the program with their ideas and time.

A summary of the programs and their impact follows.

Math Circle:

This is a highly successful program for selected talented high school students.

The Circle meets on a weekly basis and is conducted by a faculty member (during the first year by Peter Trapa, then by Nick Korevaar, and last year again by Peter Trapa) assisted on a regular basis by VIGRE assistant professors, VIGRE graduate fellows, and one non-VIGRE graduate fellow. The program's emphasis is very much on problem solving and, during the past year, a total of 56 students from several junior and senior high schools along the Wasatch Front participated in all or a portion of the program. This program very much reflects vertical integration as pre-college and graduate students, as well as post-docs and faculty interact. Four of the students from the first year of the program graduated from high school and enrolled for undergraduate study at Brown (1), Cal Tech (1), and the University of Utah (2). Information is available for five of the graduating seniors from the second year of the program. They attended Utah State University (1), Brigham Young University (1), the University of Utah (1), Georgia Tech (1), and Harvey Mudd College (1). Information is unavailable from the third year of the program.
High School Summer Program:

As opposed to Math Circle, this program focuses on Number Theory and takes place during three weeks of each summer. This year was the fifth year of the program, and was the fourth year that the program has received VIGRE funding. It is open to talented high school students. During each of the past summers, approximately twenty students from schools throughout the state (but mostly from the Wasatch front) participated in the program. Several of these students, upon graduating from high school, have become students at the University of Utah with majors in mathematics. For example, Ryan Rettberg, who was in the first Summer Mathematics Program for High School Students, became an undergraduate at Utah, participated in REUs, and is now one of our VIGRE graduate students. Jim Carlson conducted the programs. At least two graduate students are chosen to assist in the program each year, and several faculty members have presented lectures on different mathematical topics.
Additional Outreach:

As in previous years, Nick Korevaar (assisted in some years by a female graduate student from the department) conducted the mathematics portion of the College of Science's ACCESS program. This program is attended each year by 21 talented entering freshman women. The program also supported (in part) the Mathematics Department's outreach efforts on the Navajo reservation by sending mathematicians there to generate interest in our subject amongst the local high school students. This is done by demonstrating the use of modern technology and mathematics in generating new geometric designs of patterns used in weaving.
Undergraduate Colloquium:

The Undergraduate Colloquium was organized just prior to the start of the VIGRE program and has been run by the Director of Student Services (Angie Gardiner) and two faculty members (Nat Smale and Gordan Savin, both members of the Steering Committee). Faculty members, as well as graduate and undergraduate students present lectures chosen to acquaint students at an early stage with research topics and present overviews of important areas of mathematics. Students may receive university credit for attending the colloquia and it is expected that undergraduate majors attend the colloquium during at least one of the years of their studies. Another purpose of the colloquium is to introduce students to possible topics for REU projects.
Modules:

Written modules on some mathematical topics have been prepared. This project is supervised by Nick Korevaar, who is assisted by one of the VIGRE assistant professors. The modules are available as supplements for course materials for both undergraduate and graduate courses. Several have been used successfully.
Research Experience for Undergraduates (REU):

Two types of REU programs take place in the department. There is the REU summer program for which a small number of students (at most a dozen) are selected to work on projects with a common theme. This program is supervised by a faculty member who is assisted by VIGRE graduate students and a VIGRE assistant professor. Such programs took place during the summers of 2001 and 2002 and were concerned with problems from knot theory and hyperbolic geometry and random walks and simulation analysis, respectively. A third REU, covering rational and integer points on elliptic curves took place during the summer of 2003 and a fourth concerned with inverse problems was held during the summer of 2004. Seven students participated during each of the first two summers, eleven participated in 2003 and ten in 2004. Two students in the 2002 program, three in the 2003 program, and three in 2004 were from institutions other than the University of Utah.

The second REU program takes place 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, mentioned above, 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. At least four of the REU students have spoken on their work at national conferences or work-shops. Should a student not be able to make satisfactory progress because of various reasons, the project may be terminated. Unfortunately, a couple of projects had to be terminated during the 2001-2002 academic year. During this past two years, the students met to discuss their research projects at a weekly seminar. Among those graduating in the 2001-2002 academic year, two chose to become mathematics graduate students and one chose computer science as a program of study. Information is available for four of the graduating seniors from 2003. One took a year off before continuing on to graduate school. The other three became mathematics graduate students at the University of Utah. Of the 2004 graduates, four went on to graduate school and one went to work in industry. One of the students who went on to graduate school went into medicine at George Washington University. The other three went into mathematics at UCLA, University of Maryland, and the University of Utah. This is a strong indicator that pipeline questions are being addressed successfully.
Expanded Graduate Recruitment and Training:

Our graduate program is advertised nationally and internationally in various publications, such as the NOTICES of the American Mathematical Society. In addition, advertisements and posters are distributed to many mathematics departments and individuals soliciting applications to graduate study. Prospective graduate students (such as those having participated in the PUTNAM competition and similar events) are contacted personally, as well. The top recruiting prospects are invited to visit our campus for a three-day weekend during March. The recruits are then provided the opportunity to become acquainted with the various programs of the department and get to know the campus and city. The current graduate student population actively participates in the recruitment process by acting as hosts to the invitees. The number of applicants during the past four years are as follows: Approximately 130 students applied in both 2001 and in 2002. In 2001, 46 of those applicants were U.S. citizens while 56 were in 2002. The 2003 recruiting season saw 225 applicants, 91 of whom were U.S. citizens (a significant increase!) and in 2004 there were 225 applicants of which 90 were US citizens or nationals. In 2001, there were fifteen offers of VIGRE fellowships to recruit six students, in 2002 there were ten offers to recruit four students. The other four VIGRE graduate students were chosen from among our present graduate student population who had chosen research areas and were scheduled to complete the requirements for the Ph.D. during the next two years. In 2003, ten VIGRE offers were made to recruit six students. The two other students were chosen from within the existing, more advanced graduate student population. In 2004, twelve VIGRE offers were made to recruit four incoming students.

All new incoming graduate students participate in an intensive two-week training program, which takes place immediately before the start of the fall semester. Each graduate student is assigned a faculty mentor who closely monitors the students' progress in their program of study. Four graduate students who have been supported in part by VIGRE have now graduated with Ph.D. degrees; one is a VIGRE post-doc at the University of Texas at Austin, one is a post-doc in our department, one is an assistant professor at Utah State University, and one is a post-doc at the University of Nebraska at Lincoln.
Graduate Colloquium:

The Graduate Colloquium is organized by the Graduate Student Advisory Committee (GSAC). The speakers are either graduate students or faculty members. Faculty members are encouraged to speak about their areas of research at a level appropriate for beginning graduate students. Graduate students giving lectures will usually be advanced students who speak about their area of research. The colloquium provides an excellent training ground for giving talks, an important skill in academia as well as other professions, in a relatively sheltered and friendly environment. Additional work needs to be done to increase attendance by REU and graduate students. Part of this colloquium series is also a workshop on the writing and competing for research grants. Here, young researchers who have successfully competed for a research grant give accounts of their experiences. Our grant accountant also presents details on the more technical and administrative aspects of the process.
Preliminary Examination Study Camps:

Graduate students are encouraged to sit for the written qualifying examinations at the end of their first year of graduate study. The summer after their first two semesters of study is the time of preparation for these examinations and extensive sessions to help prepare are being conducted. The graduate students organize these sessions and each subject area has a faculty volunteer who has agreed to provide discussion time and help during the summer. The sessions have been helpful according to the students involved and have been organized by VIGRE graduate fellows. Since the autumn of 2002, each graduate course, which qualifies as a preliminary examination subject, has had an assigned graduate student volunteer, who conducts problem sessions for the particular course. This particular facet was suggested by graduate students and has been conducted on a trial basis. The Department established a committee to review our preliminary examination structure nearly two years ago; a report with recommendations will hopefully be forthcoming soon.
Mini-Courses:

During May and June of 2002, the department conducted two mini-courses, each of two weeks' duration. The intent of such courses is to introduce graduate students to research topics in a quick, efficient, and intensive way. These courses are open to students from our own university as well as a select number of U.S. graduate students from other universities. The VIGRE grant has limited funds to cover the expenses for the students from other universities who have been selected to participate as well as funds to to support an outside lecturer. Bringing these students together and exposing them to a well-chosen authority on the topic of the course furnishes a broad educational and research experience and has the double benefit of offering a student a new point of view and fostering extensive contact for our faculty and postdocs at the research level. The mini-courses further promote the concept of vertical integration by having the local graduate students and postdocs participate in the organization and running of the courses. The courses were advertised nationally via the internet as well as through regular mail to departments having graduate programs in mathematics.

There have been two mini-courses in each of the past three summers. The summer 2002 mini-courses were ``Complex Hyperbolic Geometry'' (May 13-24, 2002), and ``Variational Methods and Nonlinear PDE'' (May 28-June 8, 2002). The ``Complex Hyperbolic Geometry mini-course was run by Jim Carlson and Domingo Toledo and attended by thirteen external graduate students and one local student. The ``Variational Methods and Nonlinear PDE mini-course was run by Klaus Schmitt and attended by six external and five local graduate students. The first of the summer 2003 mini-courses was ``Mathematics Behind Biological Invasions'' (June 2-13, 2003) which was run by Fred Adler and attended by sixteen external and one local student. The second, ``Waves in Inhomogeneous Media'', took place July 28-August 8, 2003 and was organized by David Dobson. Ten external and ten internal students were in attendance. Two further mini-courses were organized for the summer of 2004; they were ``The Synthetic Geometry of the Weil-Petersson Metric'' (May 10-21, 2004) and ``Classical Problems in Commutative Algebra'' (June 7-18, 2004). The first was organized by Ken Bromberg and Mladen Bestvina while the second was run by Florian Enescu and Paul Roberts. Seven external students attended the first while the second saw fifteen external and two internal graduate students in attendance. Two courses will again take place during the early summer of 2005.
The Post-Doc Program:

The Department has had a successful postdoctoral program since the early 1970s. The program has had a broad impact on the teaching and research environment of the Department and many successful mathematicians have been part of the program and are now important voices of the national and international mathematical scene. Through VIGRE, the Department has amplified the mentoring activities of the postdocs and increased their involvement in departmental activities. VIGRE postdocs are involved in Math Circle activities (one, David Hartenstins, has co-organized the Math Circle program), participate in the organization of mini-courses, help organize seminar series (one has helped run the GRE prep course and organized this course by himself the following year), and are offered to teach topics courses in their areas of specialty. Two such one-semester graduate courses were offered by David Hartenstine (Topics in Nonlinear PDE) and Jesse Ratzkin (Geometric PDEs). One post-doc (Javier Fernandez) helped run a summer's REU program, and one has been supervising a REU project. Also, one non-VIGRE postdoc is presently supervising a REU project. Their mentors also encourage early application for research grants and special Grants Preparation Seminars are held for their benefit. Further inolvement in the mathematical life outside the department is encouraged and one of the postodcs has become a member of Project NExT. Using VIGRE funds, postdocs have had the opportunities to purchase books, journals and other educational materials and also are supported to attend research conferences in their specialties, important activities for young researchers. At no time in the past has the department had the chance to support postdocs in this manner and the above serve as indicators that an effect of the change of culture has been accomplished by the VIGRE grant. During the first year of the program there were four positions available, during the second year there were five, and during the third year there were six. While one of the first year post-docs left after the first year, the three others remained for the full three year term and have now accepted jobs at other institutions. One will be at a research institute in Argentina (Instituto Balseiro - Universidad Nacional de Cuyo - Republica Argentina), one at the University of Connecticut, and one at Western Washington University.

During the past spring we hired four new VIGRE post-docs from an applicant pool of 298 of which 107 were eligible for VIGRE support. Six VIGRE offers were made.
Summary:

As can be seen from the above, VIGRE has had a considerable impact on the Department's teaching and research activities, on the outreach efforts, and on the recruitment of students into mathematics. Participant evaluations and evaluations from our External Advisory Committee, Internal Advisory Committee, and Outreach Advisory Committee of our programs have been collected (and are available in this report). These have been used and further will be used to fine-tune and improve the various parts of the program. While the recruiting of excellent graduate students and postdocs remains the most important task, particularly of those from underrepresented groups, the grant has had a definite multiplier effect throughout the Department. Increased interaction between students and faculty is taking place at all levels.
Dissemination to the Mathematical Sciences Community:

All of our VIGRE activities (organizational structure, recruiting advertisements, reports, etc.) are posted on the web. This site is maintained by the Program Coordinator and updated in a timely fashion. Members of the Steering Committee have participated in meetings with schools that are also VIGRE sites to exchange experiences. Members of our Outreach Advisory Committee are advertising our outreach efforts to mathematics specialists at Utah school districts. All recruitment advertising is disseminated by regular mail and email notices and is posted with national sources such as the MAA and AMS REU sites. Thus, all reports filed on REU projects, descriptions of High School and Math Circle programs, mini-course lectures and the like are available to the general public. More detailed addresses for some of the individual programs are the following (each will lead to further addresses which contain additional details about the particular program, such as lecture notes, etc.):
Changes that Have Occurred:

Considerable changes have taken place in the Department's research and teaching activities since the preparation of the grant proposal commenced. These include the introduction of the graduate and undergraduate colloquia, the Math Circle, preparation of modules, the introduction of mini-courses, and two types of REU programs. In addition, we have introduced an expanded and vertically integrated mentoring program, which has been described above. The Department recently was the first department in the College to be awarded a new subject-oriented Honors program. While the University of Utah has had a general education honors program for many years, subject-oriented honors programs have been absent. Coupled with our REU program, the new Honors program will serve our outstanding undergraduate students well and students' honors theses may well be the outgrowth of REU projects. A new five year combined bachelors and masters program with a major in mathematics has recently been approved and will soon be in place. Students participating in REU projects at an early stage will be particularly suitable for such a program with REU projects leading to Masters projects. Students in this program will have a much greater opportunity to complete the requirements for the Ph.D. in a shorter time period than the five-year period we described above. Without the support of VIGRE, such a program would likely not have taken place. We have also received funding from the Eskuche Foundation and from the Math and Science Education Foundation to run the Math Circle program.

Back to Table of Contents

2003-2004 VIGRE Highlights

March 2003: Internal Advisory Committee meeting and report; Outreach Advisory Committee meeting and report; AMS-SIAM-NSF

April 2003: External Advisory Committee visit and report funding opportunities conference

June 2003: Summer REU; Summer High School program: ACCESS program; Mini-course on Biological Invasions

July 2003: Mini-course on Waves in Inhomogeneous Media

August 2003: TA-TF training

September 2003: Math Circle starts

October 2003: NSF site visit for three year review of program

December 2003: Notification that program will be continued by NSF

February 2004: Appointment of new VIGRE post-docs

March 2004: Assessment meeting with graduate students and post-docs

April 2004: New graduate students appointed

May 2004: Mini-course on Synthetic Geometry of Weil-Petersson Metric

June 2004: Mini-course on Classical Problems in Commutative Algebra; ACCESS program; Summer REU; Summer High School Program
Back to Table of Contents

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, VIGRE 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, Organizer of the Mini-Course on the Mathematics Behind Biological Invasions, Graduate Colloquium Lecturer, Assistant Professor Mentor

Nathan Albin, VIGRE Graduate Fellow
VIGRE Activities: Boot Camp Organizer, Math Circle Mentor, REU Mentor, GRE Prep Course Mentor, Senior Seminar Mentor, Summer REU Mentor

Peter Alfeld, Professor and Associate Chair of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Assistant Professor Mentor, Undergraduate Colloquium Lecturer

Daniele Arcara, Assistant Professor of Matheamtics
VIGRE Activities: Undergraduate Colloquium Lecturer, Graduate 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

David Ayala, VIGRE Graduate Fellow
VIGRE Activities: Math Circle Mentor, REU Mentor

Brandon Baker, Associate Instructor of Mathematics
VIGRE Activities: Undergraduate Colloquium Lecturer

Nelson Beebe, Research Professor of Mathematics
VIGRE Activities: Undergraduate Colloquium Lecturer

Robert Bell, VIGRE Assistant Professor
VIGRE Activities: Math Circle Mentor and Lecturer, Boot Camp Mentor, Lecturer at the Mini-Course on the Synthetic Geometry of the Weil-Petersson Metric, Graduate Colloquium Lecturer

Maria Bell-Scott, VIGRE Graduate Fellow
VIGRE Activities: Math Circle Mentor, REU Mentor, Summer High School Program Mentor, ACCESS Mentor

Aaron Bertram, Professor of Mathematics
VIGRE Activities: Steering Committee Member, Co-PI of the VIGRE Grant, Graduate Colloquium Lecturer, Summer REU Organizer, Assistant Professor Mentor, Graduate Fellow Mentor, Undergraduate Colloquium Lecturer

Mladen Bestvina, Professor of Mathematics
VIGRE Activities: REU Mentor, Graduate Fellow Mentor, Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, Math Circle Lecturer, Assistant Professor Mentor, Co-Organizer of the Mini-Course on the Synthetic Geometry of the Weil-Petersson Metric

Paul Bressloff, Professor of Mathematics
VIGRE Activities: REU Mentor, Graduate Fellow Mentor, Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer

Jeffrey Brock, Associate Professor of Mathematics, Brown University
VIGRE Activities: Lecturer at the Mini-Course on the Synthetic Geometry of the Weil-Petersson Metric

Ken Bromberg, Assistant Professor of Mathematics
VIGRE Activities: Co-Organizer of the Mini-Course on the Synthetic Geometry of the Weil-Petersson Metric, REU Mentor

Robert Brooks, Professor of Mathematics
VIGRE Activities: Chair of Internal Assessment Committee, Preparation of Modules, Undergraduate Colloquium Lecturer

Gene "Drew" Butcher, VIGRE Graduate Fellow
VIGRE Activities: Math Circle Mentor, Summer High School Program Mentor

Rex Butler, VIGRE Graduate Fellow
VIGRE Activities: Math Circle Mentor, Summer High School Program Mentor

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, Summer REU Organizer, Graduate Colloquium Lecturer

Renzo Cavalieri, Graduate Student
VIGRE Activities: Math Circle Mentor and Lecturer, Graduate Colloquium Lecturer

David Chapman, Professor of Geology and Geophysics, Dean Graduate School
VIGRE Activities: Internal Advisory Committee Member

Suneal Chaudhary, VIGRE Assistant Professor

Andrej Cherkaev, Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, VIGRE Assistant Professor Recruitment, REU Mentor, Co-organizer and Lecturer for Mini-course on Waves in Inhomogeneous Media

Elena Cherkaev, Research Professor of Mathematics
VIGRE Activities: REU Mentor, Co-organizer and Lecturer for Mini-course on Waves in Inhomogeneous Media

Kenneth Chu, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, Colloquium Organizer

Matthew Clay, VIGRE Graduate Fellow
VIGRE Activities: Graduate Colloquium Lecturer, Boot Camp Mentor, Math Circle Mentor, REU Mentor, Summer REU Mentor

Kree Cole-McLaughlin, REU Student
VIGRE Activities: 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, Graduate Colloquium Lecturer

Scott Crofts, VIGRE Graduate Fellow
VIGRE Activities: GRE Prep Course Mentor, Senior Seminar Mentor

Eric Cytrynbaum, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer

Martin Deraux, Associate Instructor
VIGRE Activities: Lecturer at Mini-Course on Complex Hyperbolic Geometry

David Dobson, Professor of Mathematics
VIGRE Activities: Steering Committee Member, Organizer of the Mini-Course on Waves in Inhomogeneous Media, Graduate Fellow Mentor, Co-Organizer of the Summer REU Program on Inverse Problems and Applications, Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer

Elizabeth Doman, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer

Sankar Dutta, Professor of Mathematics, University of Illinois at Urbana-Champaign
VIGRE Activities: Lecturer at the Mini-Course on Classical Problems in Commutative Algebra

Berton Earnshaw, VIGRE Graduate Fellow

Florian Enescu, Assistant Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Math Circle Lecturer, Co-Organizer of and Lecturer at the Mini-Course on Classical Problems in Commutative Algebra, REU Mentor

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, GRE Prep Course Mentor and Organizer, Senior Seminar Mentor, Boot Camp Mentor, Summer REU Mentor

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, Undergraduate Colloquium Lecturer, REU Mentor

Stefanos Folias, VIGRE Graduate Fellow
VIGRE Activities: Graduate Colloquium Lecturer, REU Mentor, Boot Camp Organizer

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, Coordinator of REU Program, Graduate Fellow Mentor, Math Circle Lecturer, Graduate Colloquium Lecturer, Co-Organizer of the Summer REU Program on Inverse Problems and Applications, Undergraduate Colloquium Lecturer

Fletcher Gross, Professor of Mathematics
VIGRE Activities: Undergraduate Colloquium Lecturer, Math Circle Lecturer, Honors Program Director, Graduate Fellow Mentor

Robert Guy, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Undergraduate Mentor, High School Summer Program Mentor, Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, Math Circle Lecturer, Boot Camp Mentor, Math Biology Journal Club Co-Organizer

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, Math Circle Mentor and Lecturer, PDE/Geometry Seminar Co-Organizer, REU Mentor, Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer

Evan Haskell, Assistant Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer

Henryk Hecht, Professor of Mathematics
VIGRE Activities: REU Mentor, Graduate Fellow Mentor, Undergraduate Colloquium Lecturer

Ray Heitmann, Professor of Mathematics, University of Texas
VIGRE Activities: Lecturer at the Mini-Course on Classical Problems in Commutative Algebra

Scott Hendrickson, Mathematics Specialist, Alpine School District
VIGRE Activities: Outreach Advisory Committee Member

Lajos Horvath, Professor of Mathematics
VIGRE Activities: REU Mentor

Melvin Hochster, Distinguished Professor of Mathematics, University of Michigan
VIGRE Activities: Lecturer at the Mini-Course on Classical Problems in Commutative Algebra

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

Michael Kapovich, Professor of Mathematics
VIGRE Activities: Graduate Fellow Mentor, VIGRE Assistant Professor Recruitment, REU Mentor

James Keener, Professor of Mathematics
VIGRE Activities: Graduate Fellow Mentor, Undergraduate Colloquium Lecturer, Graduate 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, REU Mentor

Sarah Kitchen, VIGRE Graduate Fellow

Brynja Kohler, VIGRE Graduate Fellow
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, Boot Camp Mentor, Math Circle Mentor, Math Biology Journal Club Co-Organizer

Piotr Kokoszka, Professor of Mathematics, Utah State University
VIGRE Activities: 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, Coordinator of and Lecturer at Math Circle, Graduate Fellow Mentor

Robert Lazarsfeld, Professor of Mathematics, University of Michigan
VIGRE Activities: Undergraduate Colloquium Lecturer

An Le, 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

Mark Lewis, Professor of Mathematics at the University of Alberta
VIGRE Activities: Lecturer at the Mini-Course on the Mathematics Behind Biological Invasions

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

Frank Lynch, VIGRE Graduate Fellow
VIGRE Activities: Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer, Math Circle Mentor, Summer REU Mentor

Pejman Mahboubi, VIGRE Graduate Fellow

Dan Margalit, VIGRE Assistant Professor
VIGRE Activities: Math Circle Mentor and Lecturer, Boot Camp Mentor, Lecturer at the Mini-Course on the Synthetic Geometry of the Weil-Petersson Metric

Jean Mawhin, Professor of Mathematics, Universite Catholique de Louvain
VIGRE Activities: Principal Lecturer at Mini-Course on Variational Methods and Nonlinear PDE

Aaron McDonald, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer

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

Grigory Mikhalkin, Associate Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer

Dragan Milicic, Professor of Mathematics
VIGRE Activities: Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer

Graeme Milton, Professor and Chair of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, Math Circle Lecturer

Claudia Miller, Professor of Mathematics, Syracuse University
VIGRE Activites: Lecturer at the Mini-Course on Classical Problems in Commutative Algebra

Michael Neubert, Associate Scientist at Woods Hole Oceanographic Institution
VIGRE Activities: Lecturer at the Mini-Course on the Mathematics Behind Biological Invasions

Wieslawa Niziol, Associate Professor of Mathematics
VIGRE Activities: REU Mentor

Andrew Oster, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer

Robert Palais, Research Associate Professor of Mathematics
VIGRE Activities: REU Mentor

George Papanicolaou, Professor of Mathematics at Stanford University
VIGRE Activities: Lecturer at the Mini-Course on Waves in Inhomogeneous Media

Brad Peercy, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer

Cindi Phillips, Mathematics Department Accountant
VIGRE Activities: VIGRE Grant Accountant, Graduate Colloquium Lecturer

Gregory Piepmeyer, VIGRE Graduate Fellow
VIGRE Activities: Graduate Colloquium Lecturer, Boot Camp Mentor, Math Circle Mentor, REU Mentor, Summer REU Mentor

Thomas Pietraho, VIGRE Assistant Professor
VIGRE Activities: Math Circle Assistant and Lecturer, Assistant in Summer High School Program

Emily Putnam, VIGRE Graduate Fellow
VIGRE Activities: Math Circle Mentor, GRE Prep Course Mentor, Senior Seminar Mentor, Summer REU Mentor, ACCESS Mentor

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, Math Circle Mentor and Lecturer, Boot Camp Mentor, PDE/Geometry Seminar Co-Organizer

Ian Renner, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer

Ryan Rettberg, VIGRE Graduate Fellow
VIGRE Activities: Math Circle Mentor, Boot Camp Mentor, Graduate Colloquium Lecturer

Russell Richins, VIGRE Graduate Fellow

Tom Robbins, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer

Paul Roberts, Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Graduate Fellow Mentor, Co-Organizer of and Lecturer at the Mini-Course on Classical Problems in Commutative Algebra

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, Math Circle Lecturer

Matthew Rudd, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, Prelim Boot Camp Organizer and Mentor, Assistant in Organizing and Lecturer at Mini-Course on Variational Methods and Nonlinear PDE, Graduate Colloquium Lecturer, Math Circle Lecturer, PDE Seminar Co-Organizer

Sean Sather-Wagstaff, Postdoctoral Fellow, University of Illinois at Urbana-Champaign
VIGRE Activites: Lecturer at the Mini-Course on Classical Problems in Commutative Algebra

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, REU Mentor, Graduate Fellow Mentor, Graduate Colloquium Lecturer

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 Modules, 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

Inbo Sim, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer

Anurag Singh, Assistant Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer

Nathan Smale, Professor and Associate Chair of Mathematics
VIGRE Activities: Steering Committee Member, Undergraduate Colloquium Lecturer, Co-Organizer of Undergraduate Colloquium, Internship Organizer, Lecturer at the Mini-Course on Variational Methods and Nonlinear PDE, Assistant Professor Mentor, REU Mentor

Sandra Spiroff, VIGRE Assistant Professor
VIGRE Activities: Lecturer at the Mini-Course on Classical Problems in Commutative Algebra, Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer

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)

Nancy Sundell-Turner, VIGRE Assistant Professor
VIGRE Activities: Math Circle Lecturer, Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer, Boot Camp Mentor, Math Biology Journal Club Organizer, Lecturer at the Mini-Course on the Mathematics Behind Biological Invasions, ACCESS Mentor

William Symes, Professor of Mathematics at Rice University
VIGRE Activities: Lecturer at the Mini-Course on Waves in Inhomogeneous Media

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)

Joshua Thompson, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer

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, Graduate Fellow Mentor, REU Mentor

Andrejs Treibergs, Professor of Mathematics
VIGRE Activities: REU Mentor, Undergraduate Colloquium Lecturer, Lecturer at Mini-Course on Variational Methods and Nonlinear PDE, Graduate Colloquium Lecturer

Peter Trombi, Professor of Mathematics
VIGRE Activities: Steering Committee Member, Co-PI of VIGRE Grant, Graduate Recruitment, Participant in VIGRE Conferences

Don Tucker, Professor of Mathematics
VIGRE Activities: Undergraduate Colloquium Lecturer

Michael van Opstall, VIGRE Assistant Professor

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

Michael Woodbury, VIGRE Graduate Fellow
VIGRE Activities: REU Mentor, GRE Prep Course Mentor, Senior Seminar Mentor, Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer

Grady Wright, VIGRE Assistant Professor
VIGRE Activities: Boot Camp Mentor, Numerical Analysis Seminar Organizer, Summer REU Mentor, Graduate Colloquium Lecturer

Jingyi Zhu, Associate Professor of Mathematics
VIGRE Activities: REU Mentor, Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer

John Zobitz, Graduate Student
VIGRE Activities: Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer

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Programs for High-School Students

MATH CIRCLE 2003-2004
By Peter Trapa

The purpose of these notes is to document the activities of the Math Circle during the 2003--2004 academic year.

Summary:

The 2003-2004 installment of the Math Circle represented its third year of existence. The program is healthy and successful and I anticipate its continued success in the 2004-2005 academic year. Nonetheless there is room to grow and improve. My most immediate concern is participation, especially among women and minorities, and this is discussed in greater detail below.

Format:

This year, the Circle began September 27, 2003, and met from 4-6pm each subsequent Wednesday of the Fall and Spring terms; it finished on April 28, 2004. As in previous years, two consecutive weeks were devoted to the same topic and were typically led by the same person. A typical session consisted of about 45 minutes of the leader lecturing at the board and an hour of problem solving. (15 minutes were usually reserved for breaks.) It worked best when the lecturing and problem solving were intermingled.

The focus continued to be enrichment, as is evidenced from the list of topics given below.

Topics:

Topics, in chronological order, were as follows:

Magic Squares and Modular Arithmetic (Peter Trapa, 2 weeks)
Algebraic Curves (Renzo Cavalieri, 2 weeks)
Infinity and Induction (Peter Trapa, 2 weeks)
What is Symmetry? (Bob Bell, 2 weeks)
Four-Dimensional Cubes (Dan Margalit, 2 weeks)
Permutations and the 15-puzzle (Peter Trapa, 3 weeks)
Unique Factorization (Sandra Spiroff, 2 weeks)
Topological Constructs (Eric Cook, 2 weeks)
Distance and Metric Spaces (David Hartenstine, 2 weeks)
Genetic Selection (Nancy Sundell-Turner, 2 weeks)
Five weeks were devoted to contests

Homework:

In past years, assigning any kind of homework was usually a disaster. Virtually none was assigned this year.

What makes a good session?:

This is documented carefully in the 2001-2002 year-end report. My only comment here is that we were again able to achieve a friendly, respectful atmosphere that engendered creativity and cooperation.

Contests:

Contests continued to be an important and successful feature of the program. All were administered "in class"; there were no take-home contests. (Previous years have had poor response rates.)

Personnel:

Eric Cook was my assistant. He did an excellent job, despite being busy with many other commitments. Additionally I got quite a bit of support from the VIGRE postdocs assigned to the program, Dan Margalit and Bob Bell. Both were outstanding. The graduate students who rotated through the program did a nice job - nothing spectacular, but generally competent.

Apart from the sessions I led, all others were either led by graduate students or postdocs. Of course, there is nothing wrong with that; uniformly they took their responsibilities seriously and produced well-prepared and thoughtful presentations. The lack of permanent faculty this year only points to an excellent untapped source for next year.

Beyond those charged with Math Circle responsibilities through VIGRE, I would like to point out the exceptional - and purely voluntary - contributions of Frank Lynch (a graduate student) who attended and helped with nearly every session. David Hartenstine was also very helpful in a volunteer capacity. Additionally, Bell and Margalit both went above and beyond their official responsibilities.

Finally, and perhaps most importantly, it was a pleasure to work with Sarah Strong. Her efficiency and careful attention to detail were extremely valuable and ensured that the program ran smoothly.

Participation:

One constant concern is the fall-off in attendance that we (over the past three years) have witnessed near the end of each term, as well as in the middle of the Spring term. This year was no exception. We started strong in the Fall, and through natural attrition, arrived at a good core group of 15-20 students by the end of October. That core group stayed reasonably constant throughout the Fall. In the Spring, the numbers were lower and dropped even lower near Spring Break before rebounding at the end.

Most of the attendance fluctuations are inevitable. In the beginning, some naturally find that the program is not for them and stop attending. As for the Spring, there seem to be more extracurricular activities that eat into our core of serious participants. My only recommendation is to continue to step up phoning and emailing during these extra-busy times. (Sarah and Kathleen Kerr were very helpful with phoning this Spring.)

Outlook and Suggestions:

For next year, I propose targeting more women and minority participation. It seems that the program is well-established with certain area high schools - principally West, Skyline, Alta, and Highland - as perhaps 80% of our participants hailed from them. West provides the most the most diverse crowd, both in terms of the number of females and minorities. It may make sense to make extra advertising allowances to other traditionally diverse schools next year. Perhaps I should visit math classes in these schools next Fall before the program starts.

On a related issue, a principal means to augment the interest of current female and minority participants is through sessions led by (surprise) females and minorities. We did an OK job with women this year (with sessions led by Spiroff and Sundell-Turner). The demographic reality of the department always makes finding women to lead sessions tough. But it's important, and energy should be devoted in this direction next year.

Unlike last year (under Korevaar's direction), we did not devote any time to state and national contest problems. We chose to do this based on the seemingly tepid response evident on last year's evaluations. Nonetheless, I think I made a mistake by not pursuing contest preparation this year. I would like to give it another try next year, perhaps by slightly modifying Korevaar's original approach.

With a modicum of effort based on the suggestions above, we can add to the momentum of this established and successful program.

SUMMER HIGH SCHOOL PROGRAM
By Jim Carlson

Summary:

The Summer Mathematics Program for High School Students at the University of Utah provides outstanding students an opportunity to develop their talents to the fullest. By presenting intriguing puzzles, challenging problems and powerful ideas, the program stimulates curiosity, develops the intellect, and lays a strong foundation for future work in mathematics, the sciences, or science related careers.

Participants:

This year we had twenty students participate in our summer program: fifteen from the Salt Lake City area, one from Vernal, two from Cedar City, one from Ferron, and one from Florida. Three were between their freshman and sophomore years, six were between their sophomore and junior years, and eleven were between their junior and senior years. Five of the participants were female.

Jim Carlson returned from Cambridge, Massachusetts to direct the program, and he was assisted by two graduate students funded through the VIGRE grant (Drew Butcher and Rex Butler), and one graduate student funded through the department (Maria Bell). Angie Gardiner also helped organize the program, and several faculty members participated in the colloquia.

Format:

The program ran for three weeks (June 14 - July 1), four days a week, 8:30 a.m. to 4:00 p.m. In the morning students worked on number theory, learning about topics such as Diophantine Equations, modular arithmetic, properties of the primes, and continued fractions. There were also two contests. The first was to break secret messages sent using RSA cryptography. The second was to find the parameter N for Pell's equation x² - Ny² = 1 with the "best" ratio R = (digits of x)/(digits of N), where (x,y) is the smallest solution with positive coordinates. The students particularly enjoyed these contests.

After lunch students attended a colloquium whose topics ranged widely indeed: Peter Alfeld, "Infinity is Different"; Aaron Bertram, "Pythagoras vs the Elliptic Curve"; Klaus Schmitt, "Fractals"; Jim Carlson, "The Mathematics of Google"; Fred Adler, "Cicadas"; David Dobson, "Inverse Problems"; Peter Trapa, "It's a Small World"; Davar Khoshnevisan, "Normal Numbers", Sandra Spiroff, "Unique Factorization"; Jim Carlson, "Some Unsolved Problems in Mathematics."

Each day ended with a 90-minute computer lab in which the students learned to program in Python and do experimental number theory with it. They solved problems such as: find a 100-digit "industrial prime"; solve the equation 123456789x - 235711y = 1; let p = 10¹⁰⁰ + 267; compute 2 to the power N mod p, where N = 3¹⁰⁰ + 7¹⁰⁰.

Resources:

Problem sets, handouts, a Python tutorilal, etc. are available on the web.

Concerns/Recommendations:

We would like to see more participants come from outside the Salt Lake City area. Next year we plan to advertise in neighboring states.
It has worked well to have at least one of the graduate assistants return the next year. This provides continuity and experience, and we would like to continue this.
A year ago we used "alumni assistants," undergraduate students who were former participants of the program. We would like to be able to do this again in the future.

NDAHOO'AH PROGRAM
By Kelly MacArthur

The teachers we sent down taught two two-hour courses per day with each class consisting of 12-16 Navajo students. The ages ranged from 12 to 17 years old, which covered quite a diverse skill level. The classes mainly taught Logo programming to enable the students to represent their Navajo craft design graphically on the computer. The students themselves spent another two hours per day in class with Navajo elders learning how to make a traditional craft. In addition to Logo, our teachers taught geometry and other math skills needed for the students to be successful with their Logo projects.

The classes were fairly balanced when it came to gender. When asked on the last day of class whether or not they were planning on attending college, about half of them said yes. Many more said they didn't have any plans yet.

The VIGRE money you gave us went to pay for two trips for myself down to Monument Valley. I went once in April to meet with Pat Seltzer, the principal at Monument Valley High School (MVHS). During that visit, I was introduced to the program's history and goals. Pat also showed me around the school so I could understand the setup of the classes, etc. I also went down again in June to see how the teachers were doing and observe the program in progress. The rest of the money you gave us went toward David Seal's travel expenses. He was one of our teachers. We all drove down. I stayed in a motel when I went, but David and Chris (our two teachers) stayed on campus in an extra apartment.

The main overall goal of the program itself is to teach the Navajo crafts to the students in order to keep those traditions alive. Our main goal is to support that process with an infusion of modern technology and mathematics. It is the blend of the craft with mathematics that makes this program most beneficial. Eventually, we'd like to see the program grow to serve more students and perhaps serve as a model for other American Indian programs. An additional goal is to keep the U of U interested and committed to the betterment of their math instruction and learning, in other ways besides just the Ndahoo'ah program.

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Programs for Undergraduate Students

ACADEMIC YEAR REU PROGRAM
By Kenneth Golden

The undergraduate participants of the REU program have engaged in a broad range of exciting mathematical projects and begun to produce substantial results that are being reported in professional venues.

Over the past year we have had 18 individual research projects, including those supported by VIGRE and NSF REU Supplements. The topics have included neuronal modeling, Ito diffusions, binary quadratic forms, resistor networks, social networks, the visual cortex, optimal design, Fourier analysis, continued fractions, sea ice, DNA melting curves, biomedical imaging, and statistical models of time series. The participants ranged from freshmen to seniors, and six of these projects were conducted by women undergraduates. One of these students was recruited directly from the ACCESS summer program for scientifically talented women entering the University. Many of our students have given lectures on their projects in a wide range of venues, including local seminars and national undergraduate conferences. One of our students presented her research to world experts in her field at Victoria University in New Zealand, and a paper on her project is written and will be submitted for publication shortly. At least two other REU projects are being prepared for publication in professional journals. Five of our students have journeyed to the Arctic for their research projects over the past two years. Since the inception of the REU program in 2001, about 55 students have participated, some of whom are still in the program. Of those who have graduated and for whom we have information, at least 22 have entered graduate or professional schools, most of them in mathematics or closely related areas. Finally, while many factors have played a role, it is apparent that the REU program has certainly helped to raise the level of interest in undergraduate mathematics at the University of Utah. Let M be the combined number of declared majors and pre-majors in Mathematics. Over the last four years from 2000 to 2003, the values of M have been 160, 157, 206, and 223.

SUMMER 2004 REU PROGRAM ON "INVERSE PROBLEMS AND APPLICATIONS"
By David Dobson

The Summer 2004 REU Program on "Inverse Problems and Applications" was held during the six-week period June 1 through July 9, 2004. The goal of this REU was to introduce participating students to some of the basic ideas underlying inverse problems and to quickly transition to work on individual research projects. The program was conducted by David Dobson and Ken Golden, with assistance from postoc Grady Wright, and graduate student Frank Lynch.

A total of ten students participated in the program. Six students were from the University of Utah and the remaining four were from other institutions across the country (UC Berkeley, Rose-Hulman, SUNY Geneseo, and Colby College). Students ranged widely in rank from freshmen to finishing seniors, and just as widely in backgrounds and interests.

The basic format of the program was to meet as a group twice daily, Monday through Friday: two hours in the computer lab each morning, and two hours in the classroom each afternoon. The first two weeks of classroom time were devoted to background lectures covering relevant concepts from linear algebra, basic functional analysis, differential equations, and a variety of examples of inverse problems in applications. Initially, the morning sessions in the computer lab were devoted to introductory projects in Matlab and LaTeX, and to familiarization with internet-based research resources. These labs were run by Grady Wright and Frank Lynch. After the first two weeks, focus of the program turned gradually to individual student mentoring as they began to work on their research projects. Each student was provided with help, references, and direction each day. Parts of the morning and afternoon meetings were also devoted to student presentations.

Two milestones were set for the students. First, after the first three weeks, each student was to have chosen a research problem, and prepared a short oral presentation describing the problem and background material. Second, at the end of the program, students were to have prepared final oral and written reports. All students met the first milestone, although a few did not turn in a final written report.

Some students entered the program with good ideas for research topics, and chose projects right away. Several other students were able to identify appropriate problems after some nudging in the right direction. And several other students chose problems which were presented in class as possible course projects. The program appears to have been a success for all involved. Lack of time was a problem. Some student projects were showing promise for developing interesting (publishable) results, but the six weeks were over too quickly (on the other hand, most participants were exhausted after six weeks). Some students planned to continue working on the projects. In retrospect, some of the time pressure may have been alleviated by focusing more on group projects. Student surveys were collected at the end of the program. Overall, responses were nearly uniformly positive. One point we could improve upon in the future would be to provide a meal plan and more social/recreational activities for the out-of- state students.

Much of the material from the Summer 2004 REU program can be found on the website.

UNDERGRADUATE COLLOQUIUM
By Gordan Savin

The Undergraduate Colloquium was organized by Angie Gardiner and Gordan Savin. The purpose of the colloquium is to popularize our undergraduate program and to introduce students to a variety of ideas and problems in mathematics and its applications. The colloquium is open to everyone, but students my enroll and earn one university credit, provided that they attend regularly and write a paper on one of the colloquium topics. We had five and four students formally enrolled in the Fall and Spring semesters, respectively. The general attendance was well over twenty during the Fall term, but it tapered off, especially as the school year was approaching its end. The speakers were our regular faculty, instructors, two visitors, and two graduate students. (Unfortunately, we did not have any speakers coming from industry, rather than academia.) We had a total of 27 lectures. The following is a selection of talks:

Graeme Milton, "Bubbly Fluids and Stealthy Submarines"
Fletcher Gross, "Counting with Groups"
Jingyi Zhu, "From Parts Failure in a Car to Enron's Default"
Stewart Ethier, "Seven Shuffles Suffice"
Fred Adler, "Can Ants Do Calculus?"
Henryk Hecht, "Regular Polyhedra"
Jim Carlson, "The Mathematics of Google"
Mike Woodbury, "Congruent Numbers and Elliptic Curves"
David Dobson, "Smelborp Esrevni: Backward Thinking and Its Applications"

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 has been directed for quite a few years by Professor Sid Rudolph of the Physics Department. Each summer, 21 bright and energetic students arrive on campus and spend different weeks in the various science departments. 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. Each week the women are divided into seven fresh groups of three students each and, after learning about the week's topic in detail, they use the following week to complete group projects. Nick Korevaar led the two Math weeks in 2004. In 2003 he was assisted by VIGRE postdoc Nancy Sundell-Turner and VIGRE graduate students Emily Putnam and Maria Bell. This year there were no female VIGRE graduate students, and we did not succeed in recruiting an alternate female student from within the Department.

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. Nick presented the ideas of frequency analysis for solving substitution ciphers, having each group decrypt portions of what turned out to be an interesting historical account of Sophie Germain's struggles to become a mathematician. Jim Carlson gave two guest presentations on number theory and RSA security, and these were built around sessions in which the women were led to anticipate and follow up on the mathematical ideas that Jim introduced. Towards the end of the week, and because cryptography can be thought of as an analogy for most scientific research, Biology Professor Jon Seger spoke on the genetic code. He presented the history and details about how it was deciphered, and the ACCESS women appreciated the analogies with their cryptography work. For their group projects, the ACCESS women created a moderately scaled RSA cryptosystem, tested it by sending encrypted messages to each other, and wrote papers explaining what they had done.

The second math week was devoted to classical and fractional scaling laws in mathematics and science. The week began with classical scaling of lengths, areas and volumes when space is dilated. This led us to different ways in which space can be distorted, and a focus on the geometry of affine transformations in the plane. We observed that fern leaves, broccoli, and circulatory systems seem to have scaling properties which are more complicated than what one studies classically. This led to a review of some historical fractals such as the Cantor set and Sierpinski's triangle, and to the more recent realization that many fractals can be obtained as the limit of iterated set mappings, often using affine contractions. Fred Adler gave a guest presentation on a paper of West, Brown, and Enquist which attempts to use a branching, fractal-like model of circulatory systems, to explain a famous scaling law in biology, that animal metabolism scales like mass to the 3/4 power. For their projects, students used affine contractions to create original fractals, and explained how they did it. They also used class and national data to deduce that there is an empirical power law relating human heights to weights, but that the power one obtains is not the one used in the well-known body mass index (BMI). They wrote a research paper on the origins and uses of BMI. It turns out that there is a better power law, consistent with their own work from the class data, and that this correct power was actually known to Verhulst in the early 1800s.

During the second week, Angie Gardiner led an advising session about math classes, the math major and minor, and honors in mathematics. Ken Golden gave a lecture on his sea ice experiments and modeling, and since he is also our Director of Undergraduate Studies, he spoke about research opportunities for undergraduates in our Department. In particular, he highlighted REU work he has mentored, and the fact that an ACCESS woman from last year is now working on a sea ice imaging project under his supervision.

For more information on the ACCESS program, go to the College of Science's webpage. Click here for more details about this year's mathematics component.

SENIOR SEMINAR
By Nick Korevaar

The Senior Seminar, begun in 2002-2003, was continued in 2003-2004. The seminar provides an opportunity for students who are working on undergraduate research projects to hear about the research of other students, to observe ways in which to make such research presentations, and to prepare and make reports of their own. This year, the seminar was organized by Klaus Schmitt and Nick Korevaar. VIGRE Assistant Professor Javier Fernandez and VIGRE graduate students Mike Woodbury and Scott Crofts assisted.

The seminar was held on Monday afternoons of spring semester, starting at 3:00 pm and continuing for about an hour. Initial presentations were by former and experienced REU students, beginning with an introductory session by Mike Woodbury, who was an REU student in 2002-2003. In addition to talking about his work, he gave pointers to the students about making research presentations. As the semester continued we had current, less-experienced REU students present their work. These talks tried to set a model for informality and presentation of ideas rather than computations; the model was not always followed, but usually so. Following are the titles of presentations with the names of the presenter and mentor.

Mike Woodbury (2/2/04): "Presenting Research to Your Peers, and my Explorations of Rational and Integers Points on Elliptic Curves"
Faculty Mentor: Aaron Bertram
Rex Butler (2/8/04): "Simulation of the Nonlinear Voter Model"
Faculty Mentor: Davar Khoshnevisan
Mike Hofman (2/23/04): "Continued Fractions and Number Theory"
Faculty Mentor: Gordan Savin
David Groulx (3/1/04): "Modeling the Folding of Cloth"
Faculty Mentor: David Hartenstine
Ryan Behunin (3/8/04): "Optimization for Unknown Loads"
Faculty Mentor: Andrej Cherkaev
John Faust (3/22/04): "Mathematical Models of Orientation and Direction Selectivity in Primary Visual Cortex"
Faculty Mentor: Paul Bressloff
Zsuzsanna Horvath (3/29/04): "Asymptotic Properties of GARCH"
Faculty Mentor: Davar Khoshnevisan
Pejman Mahboubi (4/5/04): "Constructing a Continuous Function for which the Fourier Series does not Converge"
Faculty Mentor: Nat Smale

The seminar met with mixed success. Students who presented felt that the experience was quite valuable. The organizers and VIGRE assistants tried to create in informal atmosphere in which questions and suggestions were encouraged, and this seems to have been successful. Still, several of the audience students said that they felt overwhelmed by the math being presented. Also, some presenters indicated that they could have used more mentoring on how to make the presentation, before actually making it. It should be possible to address these shortcomings by using our VIGRE personnel more effectively, instead of just having them attend the seminar and make comments.

Student attendance was on the low side; we could do a better job of making sure that all REU participants and mentors are aware of the seminar and its potential value. If we run the seminar in the spring of 2005, we should take care of organizational details in fall 2004, so that people can plan their schedules accordingly.

PROBLEM SOLVING COMPETITION
By Dan Margalit

I have been helping with the Undergraduate Problem Solving Competition since March. In that time, I have found this job to be a pleasant experience.

Overall, the competition seemed to be somewhat of a success. Approximately fifteen different students turned in correct solutions to the six problems posted over the year (somehow, six doesn't seem like a lot). There were four or five different first place winners. I believe that most participants were undergraduates.

One disappointment is that the overall winner has declined the invitation to compete in the national contest at Mathfest. I have emailed the second place winner, and have not heard back.

I enjoyed talking to Mike Hofmann, as we discussed possible problems for posting. He has agreed to go to MathFest. (This is one of the perks for posting and grading the problems).

I'm not sure how much impact this contest has on anybody. The problems tended to be straighforward. I had little interaction with the students, aside for a few meetings with Mike. I think Angie gave books to the winners.

There are at least three different contest organizations: Putnam, Calculus Challenge, and Problem Solving Competition. I wonder if more could be accomplished by combining forces, whatever that means.

I hope to help with this again next year, and I hope we can think of ways to make this a more engaging and fruitful endeavor.

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Programs for Graduate Students

GRADUATE COLLOQUIUM
By Stefanos Folias

The graduate colloquium is one of the activities organized by the Graduate Student Advisory Committee. Both graduate students and faculty members feature as speakers in the colloquium. Faculty members are invited to present, in a fairly elementary and possibly broad way, their area of research. This is helpful for graduate students in that it shows in what research individual faculty members are interested, and it helps students who are "shopping", i.e., who still need to decide on a field of specialization. The reason for an elementary talk is to ensure that it will not only be accessible to them, but also to ensure that they may understand and appreciate the field or topic, which is particularly important for those students who are deciding on a professor, area of research, and what not. We definitely wish to encourage, rather than discourage, and talking at a more advanced level tends to have the latter effect.

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 an interesting topic of their choice. This provides an excellent form of "training" for giving talks (which is a required skill in academia or any other professional setting) in a relatively sheltered and friendly environment. Again, the goal is to encourage rather than discourage. We are not trying to teach one how to give a good talk, rather to provide for graduate students the chance to give a talk in a less stressful forum.

The complete list of talks we have organized this year is posted on the web.

This report is an update to the last letter which discusses the background and previous state of the following issues. The current state of affairs is both positive and negative. In the past, problems have primarily included the accessibility of the talks, the number of students participating by giving talks, and, most of all, the attendance by the graduate student body for whom the colloquium was created.

We see these issues as being the most important for the success of the graduate colloquium. On the positive side in general, the talks are tending towards the desired level of accessibility, with the occasional talk deviating from this level. This has most likely been accomplished by the continual mentioning of the idea of what is the right level of accessibility and the subsequent discretion of the speaker. We only expect that this will continue to improve in the future, but it is clear that the idea of accessibility should continue to be discussed with the speaker to ensure its maintenance. We have fairly well achieved our goal to have fairly equal representation of pure and applied mathematics, especially since our department is divided so. Often is the case that the colloquia alternate consistently between the two.

Another important goal is having the majority of the talks be given by graduate students, a goal which was achieved during the spring semester but continues to be a problem during the fall. One idea to aid with this problem is the idea of a monetary gift as an added incentive to the speaker, say a gift certificate of $15 dollars to the bookstore on campus. This would come out to be roughly $500 for two semesters. The major problem, on the other hand, is the generally low attendance by the graduate student body. The general trend is that there is a group of graduate students who attend regularly, a number of subgroups who attend only talks they are interested in, and another major group of students who do not attend at all. Two stated problems of attending are the late time in the afternoon (4:30pm) and the number of obligations that plague graduate students, i.e. homework and project deadlines, other seminars, teaching, and what not. The time has now been moved back to 4:00pm, any earlier and we risk conflict with many other classes, teaching, and seminars.

One novel proposal has been to initiate a social organization committee whose purpose is to generate more social functions among the graduate students: if the graduate students know each other better, then hopefully it follows that they may be more inclined to hear and support their giving a talk. The committee has been selected for the following year (2004-2005). Maybe this combined with the monetary gift may motivate students enough that we really improve the attendance.

It was also suggested by a professor that we could modify the colloquium by moving the time to precede that of the departmental colloquium and to have occasionally an invited speaker to the departmental colloquium give, instead, two talks, one in the first hour to graduate students which is more accessible and another higher level talk to the departmental colloquium. We have decided, rather than change the colloquium time all together, simply to reserve the time before the departmental colloquium and include additional colloquia as the situations arise. One important point is that we still want to have ample time for graduate students to give colloquia. It is not clear at the moment how many invited speakers will wish to give two such talks, but an such occasion will be very welcomed as it is often the case the departmental colloquia can be very inaccessible to graduate students in different fields from that of the talk.

In all, our goal is to strive to bring the colloquium to a point where it seems healthy enough that it will continually be a successful program for the graduate student body. This is the reason that we focus on its problems, whether or not they have improved, and what is being done to improve them.

One thing that remains clear is that the coordinators of the colloquium need to assume a VERY active role in choosing and seeking speakers, discussing with those speakers the ultimate goals of the colloquium and the audience to whom it speaks, and doing what they can to ensure its success. At the present point the graduate colloquium is very sensitive and the support for it needs to grow for it to become the colloquium we hope it will become. The highest attendance ever was recorded consistently during the first year of its existence during the 1999-2000 school year. However attendance was required for all first and second years, a requirement that was rescinded the following year marking a dramatic decline in attendance. We would rather not reinstitute the requirement of attendance and instead find a different approach to making the colloquium appealing enough that graduate students wish to attend regularly. It seems the lure of food, which is provided regularly in the 15 minutes prior, is not enough to persuade the majority of the graduate students. The new approaches hopefully will help to gain support. It would seem that once the colloquium attains a large regular attendance, new students might continually feel as though it is the "place to be". This means that graduate students of all years must regularly attend. As it has been repetitively stated in this report, attendance is our major concern.

MINI-COURSE ON THE "SYNTHETIC GEOMETRY OF THE WEIL-PETERSSON METRIC"
By Kenneth Bromberg

This spring, through the support of the departments VIGRE grant, the Unversity of Utah held a mini-course on the "Synthetic Geometry of the Weil-Petersson Metric". The course was designed to introduce graduate students to the Weil-Petersson metric on Teichmulller space. The main speaker was Jeff Brock of the University of Texas. Brock gave twelve lectures discussing topics such as the behavior of geodesics, the visual sphere and connections with hyperbolic 3-manifolds. Before Brock's talks, introductory lectures where given by Bob Bell, Mladen Bestvina, Ken Bromberg and Dan Margalit (all from the University of Utah). These lectures introduced students to Teichmuller space and the mapping class group. At the end of the course, lectures were given on topics related to the course by Martin Bridgeman (Boston College), Maryam Mirzakhani (Harvard) and Pete Storm (University of Chicago).

The course was well attended. The local students were: Josh Thompson, Adam Keenan, Lars Louder, David Ayala, Matt Clay, Zrinka Despotovitch, and Renzo Cavalieri. Students also attended from other institutions through the support of the VIGRE grant: David McReynolds (Texas), Richard Kent (Texas), Jason Deblois (Texas), Matt Bainbridge (Harvard), Moon Duchin (Chicago), PJ Lamberson (Columbia), Chris Leininger (Columbia) and Ilesanmi Adeboye (Michigan). Other non-local attendees included Kasra Rafi (UCSB) and Zeno Huang (Oklahoma).

For a number of different reasons the course was a great success. First and most obviously, the students learned about this very interesting topic The Weil-Petersson metric is a very active area of current research and Brock did a fantastic job of introducing students to the subject. Second, the size of the course was relatively small compared to a standard conference, with most of the attendees graduate students. This gave the students the opportunity to meet faculty and students at other institutions and to learn about what they are doing. Students not only spent time discussing material from the course, but they also talked with each other about their own research. This is extremely useful, especially for the students here at Utah, which is relatively geographically isolated. These kind of interactions will hopefully lead to future collaborations.

MINI-COURSE ON "CLASSICAL PROBLEMS IN COMMUTATIVE ALGEBRA"
By Paul Roberts

This summer, from June 7-18, 2004, Florian Enescu and I ran a mini-course on Classical Problems in Commutative Algebra. The aim of the course was to introduce graduate students to a set of conjectures in the field that have been in the forefront of research for the past thirty years or so. Many of these conjectures originated from Serre's algebraic theory of intersection multiplicities, and their status was summarized in a set of notes by Mel Hochster in 1975. Since then there has been a lot of progress, and a second aim of the minicourse was to give an up to date account of what has been happening since that date.

The course was organized by having an introductory week with background talks given by young mathematicians. The speakers were:

Florian Enescu, University of Utah
Sandy Spiroff, University of Utah
Sean Sather-Wagstaff, University of Illinois at Urbana-Champaign
Claudia Miller, Syracuse University

The idea behind the introductory talks was to give the students the necessary background as well as to introduce them to some of the questions we would be discussing later. The second week was devoted to a more advanced program on the current state of many of the problems. We had four speakers:

Sankar Dutta, University of Illinois at Urbana-Champaign
Ray Heitmann, University of Texas at Austin
Mel Hochster, University of Michigan
Paul Roberts, University of Utah

There were 17 students who participated in the minicourse. In addition to those supported by the VIGRE grant, there were several others who obtained support from other sources. Most of the students were close to finishing their Ph.D., but a few were in their second or third year. The students were:

Ibrahim Al-Ayyoub, New Mexico State University
Nicholas Baeth, University of Nebraska at Lincoln
Olgur Celikbas, University of Nebraska at Lincoln
Erin Chamberlain, University of Utah
Andrew Crabbe, University of Nebraska at Lincoln
Christine Cumming, Purdue University
Hailong Dao, University of Michigan
Trung Dinh, New Mexico State University
Bahman Engheta, University of Kansas
Neil Epstein, University of Kansas
Ananthnaravan Hariharan, University of Kansas
Jinjia Li, University of Illinois at Urbana-Champaign
Frank Moore, University of Nebraska at Lincoln
Kazuma Shimomoto, University of Utah
Bart Snapp, University of Illinois at Urbana-Champaign
Brent Strunk, Purdue University
Diana White, University of Illinois at Urbana-Champaign

There was one more participant. Jan Strooker, a senior mathematician from the University of Utrecht who has worked on these problems for many years, decided that the program was of sufficient interest that he paid his own way to come for the two weeks.

The program was quite ambitious but, from the reactions of the students, it appears that they enjoyed the mini-course and got a lot out of it. We believe that we fulfilled our aim of introducing graduate students to this important area of Commutative Algebra.

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Committee on Diversity

The following report is by David Dobson:

A Committee on Diversity was formed in 2003 to promote diversity issues within the department. The initial committee consisted of David Dobson (Chair), Ken Golden, Nick Korevaar, Emily Putnam, and Sarah Strong.

The first initiative of the Committee was to establish a chapter of the Association for Women in Mathematics (AWM) at the University of Utah. This was accomplished in the early spring of 2004. Elena Cherkaev serves as faculty mentor to the group, with financial support provided by the Department. Students Emily Putnam, Erin Chamberlain, and Brynja Kohler served as President, Vice President, and Secretary/Treasurer, respectively for 2003-2004. The group sponsored two chapter meetings in Spring 2004, with plans for an enhanced program in 2004-2005. Student response toward the group has been uniformly positive, and it appears that this will be a growing, positive influence in the years to come.

The Chair of the Diversity Committee met with the University's Vice President for Diversity, Karen Dace. Dr. Dace provided a wealth of information about diversity resources on campus, including the Women's Resource Center, the MESA Society, Summer Research Opportunities through the Graduate School, and contacts in other departments on campus who have been particularly successful with diversity efforts over the past few years. Most of these resources are aimed at student recruitment and retention, as opposed to faculty issues. Dr. Dace suggested that two departments on campus (Psychology and Communications) have recently been successful with diverse faculty recruitment and would probably have good ideas for us.

Although perhaps not directly attributable to Diversity Committee efforts, the Department was successful in increasing diversity over the past year. Successes include the appointment of Elena Cherkaev to full Professor (our only regular faculty hire for the year), the hiring of six (46%) female postdoctoral associates, and six (38%) female graduate students.

In summary, the Committee on Diversity has seen some success in its first year of existence. Plans for the coming year include expanding the discussion of diversity issues across the department, more collaboration with on-campus diversity resource centers and working with the hiring and graduate committees to recruit more women and minority candidates.

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VIGRE 3rd-Year Assessment Report

The following report is by the NSF Site Visit Team:

A site visit team consisting of Hans Kaper (NSF), Abigail Thompson (University of California, Davis) and Richard Millman (NSF), visited the Mathematics Department of the University of Utah on October 15, 2003 for the required 3rd-year assessment of their VIGRE project. The PIs had been given a list of eight questions addressing VIGRE issues. The Department Chair (Dr. Graeme Milton) and members of the VIGRE Management Team were present at the first meeting of the day. We also met with the graduate students (about 25), VIGRE postdocs (7), undergraduate students who did research projects (10), and Dr. David Chapman, Dean of the Graduate School. What follows are observations of the site visit team.

The University of Utah project is quite different from most VIGRE sites. Whereas the basis for most VIGRE sites revolves around vertical integration in research groups, the University of Utah's revolves around a sequence of educational activities for all levels, from 10-year olds through postdoctoral fellows. This approach has worked quite well except as noted below. The various communities, especially graduate students and postdoctoral fellows, feel very much a part of the process, part of the University, well mentored, and much involved. All said that they are benefiting from the University of Utah approach.

How has the integration of research and education been achieved at all levels?

The VIGRE program was designed to create interactions between postdocs, graduate students, undergraduates and even high school students, and it does, with efforts revolving around the Math Circle, High School Summer Program, Undergraduate Colloquia, research experiences for undergraduates, minicourses (including some given by faculty of other institutions), and modules. These efforts are well and accurately described in the self assessment.

How has the VIGRE program broadened education?

There is much broadening by colloquia, seminars and courses. The relevant point here is that the graduate students have a voice in designing the courses, including those mentioned above. The fact that the graduate students and postdocs are very much a part of the undergraduate seminar enables them to enhance their communication skills and broaden their background. The self-assessment shows the broadening of the postdocs. In addition, the postdocs talked about how they were encouraged to go to other departments (sometimes by being given names of faculty, etc.) to look for areas of common interest. There are very pleased with these interactions.

In what ways has the VIGRE program improved instructional and communication skills of students and postdocs?

The primary mechanisms identified by the project to achieve this goal are through the educational mechanisms above. In addition, we found uniformly that the faculty was working with the postdocs and the graduate students on grant proposals (including a grants seminar), papers, future job-related issues, and of course the individual theses of doctoral students. The attention to the undergraduates and the high school students has forced graduate students and postdocs to pay attention to the level of their audience in their professional communications.

What has been the effect of the mentoring programs that have been developed?

The Mathematics Department appears to have a very positive atmosphere to promote faculty-student and student-student mentoring. There are formal reviews of the postdocs, an excellent approach. As mentioned above, faculty work with students and postdocs on their written work.

One area that could be improved is for the Department to come to a uniform understanding (if not agreement) of what mentoring means to the Mathematics Department at the University of Utah. There is certainly no "correct" answer, but a careful and purposeful discussion of the subject would add much to the experience of the various constituencies of the Department. We certainly recognize that mentoring is quite different depending on who is mentoring and the level of the person being mentored.

How has the VIGRE program promoted recruitment into the mathematical sciences?

We were pleased to see that the goal of 50 graduate students had been achieved and that the faculty is confident about reaching the goal of 300 undergraduate math majors by the end of the VIGRE grant. The number of women undergraduate majors is in line with national trends, but the number of minority and women graduate student isn't and the number of women postdocs (only 1 or 2 a year out of 11 or 14) most certainly isn't. We recognize the possible difficulty of attracting minority faculty and graduate students to Utah. On the other hand, it is a department that recruits the prospective faculty, not just the location or demography of the area.

We urge the Department to think carefully about its recruitment plans for women faculty, postdocs, and graduate students. We are requesting a plan to be sent to the site visit team by November 15. This issue, which was already brought up during the original site visit (Nov. 20,2000), is most in need of improvement in the project. As we mentioned during the site visit, there are institutions that recruit well for women even though they do not currently have tenured woman faculty members. The Utah VIGRE management team could, for example, explore what is done at other campuses, so that they could increase the number of talented women at all levels.

We also hope that careful thought will be given to the reasons why the number of REU experiences for women is so low compared to that of men. There are many ways to approach this issue, but the absence of a clear solution path does not mean that the status quo should be accepted. We look forward to hearing how the Department will address the women in REU issue also.

How has the interaction of the several levels of students and faculty been enhanced?

Education issues have played a central role in these interactions. There has been much layered interaction in which the various projects have played a role. This is well described in their self-assessment.

How has the VIGRE program affected time to degree?

It is really too early to determine the impact on time to degree. However, it seems clear that providing students fellowship support in their first year is very effective in getting students off to a good start.

What has been the dissemination to the mathematical sciences community of the results of the VIGRE program?

Dissemination has been primarily through the Web and through presentations at meetings organized by the NSF and professional societies. There was no evidence that more pro-active dissemination strategies are being considered. The Department did reach out to the local mathematical community in the Utah schools, which is excellent. We hope that they will find other opportunities at the national level (e.g. AMS, MAA or SIAM meetings) to show off the unique program they run.

What other changes has the VIGRE program made possible?

The change that was most often cited during the site visit is the increase in both the numbers and the quality of the educational outreach efforts to the Salt Lake City educational community. In addition, there will soon be a five-year cohort of individuals (the Utah graduate students and postdocs) who have experience in substantive educational issues at the high school and college level. We feel that the Utah VIGRE program will have a significant effect on the relationship between mathematics and K-12 education as these individuals move into their mathematical careers.

Summary and Recommendation

In summary, the visiting team was favorably impressed by many of the advances of the project. The impression of the Site Visit Team can be best described by the way in which the postdocs responded when asked whether they felt like a part of the Department. In contrast to the postdocs at the initial site visit, they answered "yes, absolutely" almost in unison.

The atmosphere in the Mathematics Department is clearly very conducive to promoting mentoring and faculty-student and student-student interactions. Given that, the general approach in the Department is to let mentoring occur naturally. As mentioned above, we urge the Department to think globally about the issue of mentoring, but they are clearly doing it well now.

The leadership of the Mathematics Department, both past and present, appears to have a very good working relationship with the members of the Department, exchanging ideas and working out agreeable allocations of project resources. (The postdocs commented on how well this works for them also.) We applaud the dedication and enthusiasm of the VIGRE management team for their successful efforts and especially cite Dr. Klaus Schmitt for the care and efficiency in the Department's preparations for the site visit and for the clarity of the documents sent to us prior to, during, and after the visit. We have no concerns about the quality of the program, even though two key players are on leave or in the process of leaving the University through retirement. We look forward to seeing their recruitment plans.

Recommendation: The site visit team recommends that the project be funded for the remaining two years of the five-year award.

Hans Kaper, NSF
Richard Millman, NSF
Abigail Thompson, University of California, Davis

10/23/03 FINAL

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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 Years 2003 - 2004

The VIGRE Program at the University of Utah
Report on the Years 2003 - 2004