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The VIGRE Program at the University of Utah
Report on the Years 2001 - 2003

People Involved in the VIGRE Program

The following is a list of people involved in the VIGRE Program including their various activities. This list includes all VIGRE Graduate Students, Assistant Professors, people from outside the Mathematics Department who have contributed to the Program, as well as Faculty and Staff from the Department who have made contributions. We note that a large majority of our faculty and several of our graduate students are involved in some form of activity related to the VIGRE program.

Fred Adler, Associate Professor of Mathematics and Biology
VIGRE Activities: REU Mentor, Undergraduate Colloquium Lecturer, 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

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

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

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

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

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

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

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

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

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

Andrej Cherkaev, Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, VIGRE Assistant Professor Recruitment, REU Mentor

Elena Cherkaev, Research Professor of Mathematics
VIGRE Activities: REU Mentor

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

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

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

Florian Enescu, Assistant Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Math Circle Lecturer

Boas Erez, Visiting Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer

Stewart Ethier, Professor of Mathematics
VIGRE Activities: Undergraduate Colloquium Lecturer

Elisha Falbel, Professor of Mathematics, University of Paris
VIGRE Activities: Lecturer at Mini-Course on Complex Hyperbolic Geometry

Javier Fernandez, VIGRE Assistant Professor
VIGRE Activities: Lecturer at Mini-Course on Complex Hyperbolic Geometry, Graduate Colloquium Lecturer, GRE Prep Course Organizer

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, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer

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, REU Organizer, Graduate Fellow Mentor, Math Circle Lecturer, Graduate 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

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 Lecturer

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

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

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

Lajos Horvath, Professor of Mathematics
VIGRE Activities: REU Mentor

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

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

Brynja Kohler, VIGRE Graduate Fellow
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, Boot Camp Mentor

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

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

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

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

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

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

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

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

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

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

Paul Rabinowitz, Professor of Mathematics, University of Wisconsin
VIGRE Activities: External Advisory Committee

Jesse Ratzkin, VIGRE Assistant Professor
VIGRE Activities: High School Summer Program Mentor, Lecturer at Mini-Course on Variational Methods and Nonlinear PDE, Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, Math Circle Lecturer

Tom Robbins, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer

Paul Roberts, Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Graduate Fellow Mentor

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, Assistant in Organizing and Lecturer at Mini-Course on Variational Methods and Nonlinear PDE, Graduate Colloquium Lecturer, Math Circle Lecturer

Fumitoshi Sato, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer

Gordan Savin, Professor of Mathematics
VIGRE Activities: Steering Committee Member, Co-PI of VIGRE Grant, Undergraduate Colloquium Lecturer, Co-Organizer of Undergraduate Colloquium Series, REU Mentor, Graduate Fellow Mentor

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 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

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

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

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

Sylvia Wiegand, Professor of Mathematics, University of Nebraska
VIGRE Activities: External Advisory Committee Member

Jim White, University of Utah Career Services
VIGRE Activities: Undergraduate Colloquium Lecturer

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

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

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Programs for High-School Students

SUMMER MATHEMATICS PROGRAM FOR HIGH SCHOOL STUDENTS
By Angie Gardiner

The summer high school program has increased in size every year so far, and this year I believe that we will reach our goal of 22 students. We may even end up exceeding it by one or two students. Based on this, I would anticipate that, in the next year or two, we may have to turn qualified students away because the program will be full. I believe that this shows that the program is a success.

Below is a list of participants since the summer of 2000.

Participants 2000

7 participants

Assistant 2000

Darrell Poore (between undergrad and grad)

Participants 2001

19 participants

Assistants 2001

Darrell Poore (grad)
Bobby Hanson (grad)

Participants 2002

20 participants

Assistants 2002

Eric Cook (VIGRE grad student)
Bob Guy (VIGRE grad student)
Bobby Hanson (grad student)
Collin Perschon (between HS and undergrad, alumni of the program)

Also

Jennifer Taback (Guest lecturer)
Thom Pietraho (VIGRE postdoc)

Participants 2003

24 participants

Assistants 2003

Maria Bell-Scott (VIGRE grad)
Sarah Cobb (undergrad)
Chris Calaway (undergrad)
Bob Guy (VIGRE grad)
Mindy Scott (grad)

MATH CIRCLE 2002-2003
By Nick Korevaar

Summary

The Math Circle program is a wonderful, vertically integrated learning experience for the high school students, the graduate student and postdoc assistants, the core group members and the session leaders. This was our second year running Math Circle and my first year as organizer. I believe that the faculty and graduate student presenters are justifiably proud about what we tried and what we accomplished this year. The high school students who completed the surveys each semester provided very positive comments about the program. Still, Math Circle felt like a series of challenging experiments to me, and our success was not uniform. There are lessons we can learn from this year and there will be challenges to overcome as we continue this innovative program.

Participants

In late August, I sent letters to all the previous year's Math Circle students (who hadn't graduated), inviting them to return. I asked them to invite along interested friends. Marilyn Keir contacted the local high school math teachers to ask for their help in finding students who might be interested in Math Circle. In the spring of 2002 (but I fear not this past spring) State High School Math Contest participants were told about Math Circle. We are also linked on the web to University and Mathematics pages. According to the student surveys this spring, we attracted participation through each of these avenues.

The core group running Math Circle consisted of Renzo Cavalieri, David Hartenstine, Marilyn Keir, and myself. Sarah Strong provided administrative support and kept the web pages at updated. Renzo is a graduate student who played a large role in the 2001-2002 Circle. He was invaluable this year for his advice as a leader and as a facilitator. David is a VIGRE postdoc who was new to Math Circle, but became valuable in the same roles as Renzo. Marilyn is a former high school teacher who helps run our secondary math program. She was our liaison to local high schools and had useful advice about what was appropriate for Circle participants.

Session leaders were chosen from among the core group, and from graduate student and faculty volunteers. (I asked several of these people to "volunteer", others came forward on their own.) VIGRE graduate students served as assistants during the Circles, typically two for each meeting. I asked people to volunteer for particular units or topics, and this seemed to work pretty well; students could assist on topics they were interested in, and everyone contributed eventually.

Format

We organized individual sessions and grouped them into related mathematical units using the principles which evolved during the inaugural year, and which Peter Trapa summarized in last year's report.

Renzo and I thought about the first fall unit during the preceding summer. This unit was intended to introduce students to the process of mathematical thinking, proof and induction. Probably every year should start with such a unit. Renzo took responsibility for the introductory session and his source material was Ian Stewart's book, "Another Fine Math You've Got Me Into". We ended up adapting and expanding various chapters of this book throughout the first unit, and Stewart has more such material available.

We tried to come up with ideas and leaders for the subsequent units several months in advance, aiming for good leaders and relevant topics. Topic ideas came from the Berkeley Math Circle page (Rubik's Cube), Peter's recommendations from last year (contest unit), from members of the core group (knot theory) or from the leaders themselves (graph theory, number theory). After several years, we will be able to begin repeating and polishing our more successful Circle topics and the need for completely new units will become less intense.

We encouraged session leaders to think about their topics at least several weeks in advance. Renzo or I often had preliminary discussions with them. I encouraged leaders to attend a Math Circle session before the one they were going to lead. The core group met with the session leader several days before Math Circle for a preliminary run-through. Most leaders appreciated these meetings, which I believe were extremely valuable in catching potential problems and improving the actual presentations. Occasionally, there was friction when the presenter or members of the core group did not see eye to eye, but usually these disagreements resolved into a consensus for improvements. During fall semester, the preliminary meetings were on Mondays, but in the spring we moved them back to the preceding Friday. This way, the presenters had more time to modify their notes and presentation before the actual Circle.

The most effective sessions consisted of roughly equal amounts of lecture and problem solving time: A portion of Math Circle might consist of the Circle leader presenting new material for 15 - 30 minutes, then posing some problems for the students to work on. For 10 - 25 minutes the students would work on these problems, individually or in groups, with assistants circulating to listen to solutions or to propose alternate ideas. Then, for 5 - 10 minutes, student volunteers would go to the blackboard and explain their solutions. Applause was encouraged as a way to reward good work and effort. Because of the disparity in the students' backgrounds and abilities, we tried to group the problems so that everybody could solve some of them, but also so that the most advanced students would be challenged.

We occasionally ran into trouble when the lecture portions were too long or intense - the students had been in school all day, it was late in the afternoon, and they were sure to get restless if they had to sit still for a standard university math lecture.

At the end of each session, we gave the students one or two challenge problems, and we collected their written answers the following week. At the end of the semester, we awarded a prize for the best solutions. Although participation was pretty good for the first week or two, only three or four students persevered with the challenge problems for the entire semester.

We grouped 3 - 5 consecutive sessions into units of related material. It usually took at least two weeks to finish a given topic, so the Circle leader usually remained the same for at least two weeks.

At the end of each unit (except the last), we had a contest day. Students worked the contest problems in the first hour. During the second hour, Renzo led a discussion of the solutions while David and I determined the contest winners. These winners chose prizes from a collection of mathematical books and games. The contest days provided a nice change of pace and the students seemed to enjoy them.

At the end of the fall term, we tried a Jeopardy-like contest with the students broken into teams and the questions taken from the fall's topics. This got a little wild, although I think it was successful. At the end of the spring term we decided not to have a contest - instead, our Chair, Graeme Milton, gave a presentation on rainbows and other light phenomena and we had a party.

Here is the 2002-2003 schedule.

Concerns and Recommendations

Crowd Control: We got to know each student and we strived for a serious yet entertaining and friendly atmosphere. We admitted several young students who were quite able mathematically, but who were disruptive when they thought they were being funny. I thought that this behavior was only a minor annoyance and talked to the offending students. We also asked particular assistants to sit near them during Circle. However, in our first semester surveys, a large number of the older students complained about the disruptive youngsters. Before Circle started back up in the spring, I called the parents of these younger kids, explained the situation, asked them to talk to their children, and said that these students would be asked to leave if their behavior did not improve. This seemed to do the trick but, in retrospect, I waited too long to act.
Diversity of Participants: We had smart 9th and 10th graders whose knowledge ended at algebra, smart 12th graders who were taking post-calculus college courses at the U, and people in every category between these two extremes. It is difficult to create presentations that will bridge such a gap. Apparently, the Berkeley Math Circle has split into "beginners" and "experts" sections, but I don't think we currently have the resources or numbers to do this. We addressed student diversity well in the Contests unit, by making two sets of problems to mirror the AMC10 and AMC12 (and up) contest formats. We split into groups when it came time to go over the contests. For the other units, we were careful to include problems with varying difficulty levels. This seemed to work pretty well.
Attendance: We were able to convince large numbers of students to try out Math Circle. Not all of these decided to continue, and this should be expected. In fact, I was overwhelmed by the number and energy of the students in the first few sessions, and felt more comfortable when participation settled into the 20 - 30 student range. We were concerned in the spring when attendance sank below 15 and are not sure what caused this drop. I spoke with at least three students who stopped coming around this time and they each said that other commitments had intruded. Apparently, spring is the time for AP test preparation and contest participation and there may be a natural diminution in scholarly interests as summer approaches. Nevertheless, I expect we misjudged the level and pacing at which to present some of the Unit 5 material. Even though the mathematical content was excellent, some student comments to me suggest that the presentation may have been at the "advanced" level. That participants struggled with material in this unit is indicated by the fact that our low point in attendance, 7, was during the Unit 5 contest. Participation rebounded somewhat during the last unit and at the final meeting, but not to the earlier levels.
Time Commitments: Math Circle is very time consuming. Many of us leaders would admit to spending around 20 hours of work preparing for a single session, partly because this experience is so different from what we usually do and partly because we are also generating web-worthy notes. As the organizer for Math Circles this past year, I also felt a certain responsibility for each presentation and once or twice I was frustrated because I sensed potential problems but didn't have the time to deal effectively with them. In the future, we should ensure that the primary organizer for Math Circle is not over-committed. I also feel that Marilyn Keir is very important to this program and that her teaching should be scheduled so that she can attend the Circles and the preliminary run-throughs. Of all the people in our department, she has had the most experience teaching smart high school students.
Session Continuity, Unit Organization, and Homework: Most topics seem to require more than a week to complete; so it would be especially helpful to have the students reinforce and work with what they've been learning. Unfortunately, both this year and last year we've had little success in encouraging outside work. Thus, when sessions build on each other, there should be enough review each week so that students who missed a session or forgot everything can be brought back up to speed.

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Programs for Undergraduate Students

SUMMER 2003 REU PROGRAM ON "RATIONAL AND INTEGER POINTS ON ELLIPTIC CURVES"
By Aaron Bertram

University of Utah, May 12 - June 20, 2003

The goal of this REU was to explore the fundamentals of elliptic curves while, at the same time, becoming familiar with some of the subtleties of the subject through computer experiments and further reading of the literature.

We had a total of eleven undergraduate participants (listed below) - eight local, two from Ohio (Case Western and Ashland) and one from Puerto Rico. The REU was run by Professors Aaron Bertram and Jim Carlson, with the assistance of VIGRE post-doc Javier Fernandez and VIGRE graduate students Nathan Albin, Matt Clay, Greg Piepmeyer, and Emily Putnam.

For the first four weeks, the schedule was two hours of lectures on the excellent book of Silverman-Tate (Rational Points on Elliptic Curves) in the mornings, followed by afternoon sessions on the use of Python (in emacs) in making elliptic curve computations. In addition, late-afternoon tutoring sessions with the graduate students on algebra, number theory and projective geometry were held four days a week to fill in some of the missing background.

The final two weeks consisted of some lectures on topics in elliptics curves, but mostly undergraduate presentations of solutions to important problems out of the book, computer projects, and papers from the literature. Some of the most interesting projects that the students prepared included:

A simple proof that Z₁₁ is not the torsion group of an elliptic curve. (This turned into an honors undergraduate thesis by Michael Woodbury.)
Computer searches for torsion groups of elliptic curves in Weierstrass normal form versus other normal forms.
Implementation of Lenstra's factorization algorithm.
Explanation of Benedict Gross' version of the Lucas-Lehmer test.
Computer searches for large integer points on elliptic curves with small discriminant.

Altogether, I think the REU was a great success. The students learned a great deal of general mathematics immediately applied to concrete elliptic curve problems. They did some very interesting computer work and several of them read and presented research papers.

List of Undergraduate Participants

Michael Giessing
Jose Gonzalez (U of Puerto Rico)
Jason Henline
Jenny Jacobs
Les Kartchner
Brian Knaeble
Joel Kramer
Collin Perschon
Eric Radke (Case Western U)
Jenise Smalley (Ashland U)
Michael Woodbury

UNDERGRADUATE COLLOQUIUM

This colloquium series is organized by Angie Gardiner, Gordan Savin, and Nathan Smale.

The following report is by Nathan Smale:

The Undergraduate Colloquium of 2002-2003 was organized by myself (Nat Smale), Gordan Savin, and Angie Gardiner. The colloquium consisted of a weekly talk on a wide variety of topics, ranging from probability and mathematial biology, to topology, geometry and number theory, and applications to industry. The speakers were regular faculty members, members of the computer staff, instructors (including VIGRE Assistant Professors), graduate students, an undergraduate student (Kree Cole-McLaughlin), and even the chairman, Graeme Milton. After the talk, typically pizza was served and informal discussions were held. The purpose of the colloquium is to expose undergraduates to a wide variety of topics in math, both pure and applied. Students may enroll in it as a course, or simply show up when a topic interests them. We had about 5 students per semester enroll in the course. The requirements for them were to attend regularly and to write a short paper on one of the topics presented. Many others attended, with typically around 15 to 20 students showing up (sometimes as many as 50, such as for Dragan Milicic's talk on the Riemann Hypothesis). Attendance should increase next year, as the colloquium will be required for those in the new Honors Program. The following is a selection of some of the speakers and the subjects of their talks:

Brandon Baker, "Boolean Algebras and Virtual Reality"
Klaus Schmitt, "Iterative vs Continuous Newton Methods: Similarities and Differences"
Hugo Rossi, "Linear Recursive Systems"
Kree Cole-McLaughlin, "Topology and Contour Trees"
Dragan Milicic, "The Riemann Hypothesis"
Fletcher Gross, "The Rubik's Cube"
Aaron Bertram, "Elliptic Curves"
John Zobitz, "Pascal Matrices and Differential Equations"
Nelson Beebe, "Pseudo-Random Numbers"
Aaron Fogelson, "Enzymes and Mathematics"
Gordan Savin, "The Banach-Tarski Paradox"
Frank Lynch, "Population Ecology"
Bobby Hanson, "Minimal Surfaces"
Graeme Milton, "The Mathematics of Rainbows"
Stew Ethier, "Paradoxes in Probability"
Brynja Kohler, "The Physiology of Movement"
Andrejs Treibergs, "The Hyperbolic Plane"
Nancy Sundell-Turner, "Mathematics of Snow Geese in the Arctic"
Bob Brooks, "Some Early Problems in Probability"

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 in recent 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 2003, assisted by VIGRE postdoc Nancy Sundell-Turner and VIGRE graduate students Emily Putnam and Maria Bell-Scott.

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. Emily presented the ideas of frequency analysis for solving substitution ciphers. Each group decrypted successive 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 some of the history about how it was deciphered, as well as recent developments and modifications, such as the discovery that in some strange organisms, one of the universal "stop" codons has evolved to encode a novel amino acid. 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 study different ways in which space can be distorted, with a focus on the geometry of affine transformations in the plane. Nancy gave a presentation on ant allometry, and its relationship to ant colony dynamics. We observed that fern leaves, broccoli, and circulatory systems have scaling properties which are more complicated than what one studies classically. This led to the notion of fractals and a discussion of some historical fractals such as the Cantor set and Sierpinski's triangle. We discussed the more recent realization that many fractals can be obtained as limits of iterated set mappings, often using affine transformations. For their projects, students created original fractals using affine contractions 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, and discovered that its origins go back to the 1800s. Some groups even found original source material from that same time which gives a more correct power law, consistent with their own work from the class and national data.

During the second week, Angie Gardiner led an advising session about math classes, the math major and minor, and honors in mathematics. Nancy gave a lecture about her research modeling Arctic Snow Geese foraging habits. In addition to the mathematical content of these two weeks, we hope that the contact with female mathematicians has been an eye opening experience for the ACCESS women. Several of them indicated an interest in becoming math majors, and a large fraction indicated an interest in at least minoring in math.

For more information on the ACCESS program in the College of Science, please click here. For more details about this year's mathematics component, please click here.

INTERNSHIP PROGRAM
By David Dobson

The VIGRE Internship Program has not been changed significantly since 2001 - 2002. I took over the program from Nat Smale this year. The function of the program so far has been to act as a "clearing house". When a firm contacts the department seeking to fill an internship position, we try to locate appropriate student candidates by contacting faculty members working in areas related to the position. The scale of this activity has been limited to date, since very few companies call seeking candidates. Our primary goal for the coming year will be to actively seek industrial partners and to get the word out that talented mathematics students are available for internships.

SENIOR SEMINAR
by Hugo Rossi

As part of the VIGRE program at the University of Utah, a senior seminar was started in the academic year 2002 - 2003. This provides an opportunity for students who are working on undergraduate research projects to report on their work. The seminar also includes students writing Senior theses as part of the Honors program.

The seminar was held on Monday afternoons, starting at 3:00 pm. Students were asked to prepare about a 40 minute report, after which there were discussions. Sometimes, the student's prepared 40 minutes actually took 90 minutes and at other times, lively discussions kept the group together for as long. It was interesting to watch how the students in the audience became interested in the work being presented; and in at least two cases, the interest continued into closer collaboration. These were between Ronald McKay and Gary Crum, and Michael Woodbury and Nathan Hancock.

The seminar was run by Hugo Rossi with the assistance of VIGRE graduate assistants Nathan Albin and Emily Putnam. The first few talks were given by faculty and graduate students, so that the participants could get an idea what kind of a presentation was expected. 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.

Rex Butler: Representations of Finite Groups
Faculty Mentor: Henryk Hecht
Kree Cole-McLaughlin: Computational Morse Theory
Faculty Mentor: Mladen Bestvina
Joshua Coon: Algorithms for Moving Large Numbers of Objects Through Small Openings
Faculty Mentor: Andrej Cherkaev
Gary Crum: Angle Inequalities for Spherical Triangles
Faculty Mentor: Misha Kapovich
Nathan Hancock: Platelet Distributions in the Blood
Faculty Mentor: Aaron Fogelson
Tara Henriksen: Optimal Intervention Time for Cystic Fibrosis
Faculty Mentor: Fred Adler
Michael Hofmann: Elliptic Functions
Faculty Mentor: Gordan Savin
Ronald McKay: Diffusion Processes
Faculty Mentor: Davar Khoshnevisan
Michael Woodbury: Fibrin Network Conformations
Faculty Mentor: Aaron Fogelson

PROBLEM SOLVING COMPETITION
By David Hartenstine

I was the faculty advisor this year for the Undergraduate Problem Solving Competition. This is a national program, run by Dr. Richard Neal. The contest is open to all University undergraduates. The problems, which are sent to us by Dr. Neal, are posted about once a month. The participants have approximately two weeks to work on the problems before they must be turned in. Brian Knaeble, a junior math major, selected the problems and corrected the entries. The person with the best solution to the problem was selected as the winner. If there was no solution better than the rest, the winner was the first person with a correct entry. The winner of each monthly contest was allowed to choose a mathematically-themed book as a prize. Batdorj Lhaajav, a senior math major, was declared the overall winner for the year.

Participation could have been better. We typically had about seven entries. We could do a better job advertising the contest in our undergraduate classes. One problem is that the problems are not very challenging: many of our best students find them to be too easy and don't bother submitting a solution. On the one hand, the problems should be hard enough to be interesting, but on the other, to maximize participation, they should be at a level that the average math major will be able to solve them in a reasonable amount of time. We have, on occasion, used our own problems. Both Brian and Batdorj have been given the opportunity to attend MathFest this Summer in Boulder, CO, with department support, to compete in the national finals of the Problem Solving Competition. Last year at MathFest, Wei-shou Hsu, last year's grader, was the national winner.

Back to Table of Contents

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.

The first year that the graduate colloquium was held, it was a required "class" for first and second year graduate students. Attendance was tracked, and it was required that each student either give a talk or write up a report of any single talk given during that semester. Though the attendance was good that year, in the years that followed, these requirements were removed and attendance has greatly dropped! In fact, we regularly only have between 15 and 20 graduate students and faculty attending, with very few of those as first and second year graduate students. It has been discussed in the annual GSAC end-of-the-year organizational meeting, as well as with many graduate students in private, and most agree that mandatory attendance is necessary in order to improve attendance. There is a major issue with the fact that we are restricting the types of talks given at the Graduate Colloquium, while the target audience is not in attendance.

Although the first and second years are targeted, the audience is truly the graduate student body as a whole. Though there is a core group attending all colloquia, there are others who choose only to attend talks within their field of interest. In general, this is fine if the core group attending were larger than the usual 10 people. It is of importance to the success of the Graduate Colloquium that we find a solution to the problem of poor attendance. One major fear is that, if someone does not regularly attend during the first or second year, then there is a good chance that they will not attend in the future. For a first and second year, we understand that time is a serious issue since there are many deadlines and due-dates in classes. It seems that simply offering the colloquium for credit does not ensure that students will attend. This is another fact suggesting that the requirement for first and second year graduate students be instated. We believe that the Graduate Colloquium is not only an important part of the graduate education but also is beneficial to all first and second year graduate students, as it provides a stepping stone for the numerous seminars, departmental colloquia, and conferences that they most likely will be attending in the future.

Another issue - one problem that is difficult to tame - is providing a consistency to the level of the talks presented at the graduate colloquium. Since different people talk on a regular basis and each person has their own idea about what level of a talk is appropriate, there often is a grave inconsistency from talk to talk. Mathematics is an amazingly large field that is composed of many subfields, many of which are unable to effectively communicate with each other about advanced topics. Hopefully, we all have some common ground on which we can connect. However, there are many methods and tools developed in each area of mathematics to analyze and understand problems and ideas. This tends to decrease the accessibility of a field to those who are not familiar with those tools and techniques and affects people at all levels, including those at the graduate level.

Two simple examples, suppose someone gives a talk relating to algebra and uses the term group. This person may feel that all graduate students in mathematics should know what a group is and, consequently, that it should be accessible to everyone. However this is a mistake: though it may be true that each student should know what a group is, and suppose that each does, it does not follow that each person is familiar with how groups are used within the context of the problem, since it is not required for all mathematics students to delve deeply into algebra or any related field. A group is a fundamental object in mathematics and provides an example of how sensitive we must be about the accessibility of what we are talking about.

Care should be taken in explaining, for example, how and why using the group helps us to better understand the problem: this provides accessibility to those unfamiliar while reinforcing and improving the understanding of those who are familiar. Similarly, someone interested in applied mathematics or differential equations may want to casually talk about phase-plane analysis. Again, though most students should know this from undergraduate differential equations, not every graduate student is familiar with the techniques. This issue is a problem for both a graduate student and a faculty member alike; however, it may be more of a concern for a faculty member, as their notion of accessibility tends to differ from that of a graduate student, i.e., the standard for a professor may be higher than that of a graduate student. We have, in the past, made it a goal to discuss, in person, these issues with the presenter, but we feel that it may be more effective in writing. As it is difficult to quantify accessibility, instead we ask that the presenter think about the ideas and techniques presented in the talk and tone down the talk for the sake of accessibility and be more verbose about the material. This is NOT a topics seminar, and we ask that one errs on the side of being more easily understood than more difficult to understand.

We are NOT asking that the entire talk be accessible to everyone. We encourage that more advanced topics and techniques enter these talks for those familiar with those areas. Instead, we request that the majority of the talk be accessible to everyone.

The Graduate Colloquium fills an important niche within the department, lying somewhere between the departmental and undergraduate colloquia. It can serve as a mode for professors to describe their research to the graduate student body and as a precursor to the abundant topics seminars offered by the department. Most importantly, it provides a forum for graduate students to meet once a week and share mathematics.

QUALIFYING EXAMINATION PROBLEM SESSIONS

Nathan Albin (VIGRE Graduate Fellow) coordinated the Qualifying Exam Problem Sessions held during the summer of 2003 in preparation for Ph.D. preliminary exams. These "boot camps" ran from May 19 - August 8, 2003.

Real and Complex Analysis

Boot Camp: Mondays and Wednesdays 2-4
Location: LCB 322
Advisor: Joe Taylor
Mentor: Matthew Clay

Differential Equations

Boot Camp: Tuesdays 11-1, Thursdays 2-4
Location: LCB 322
Advisor: Andrejs Treibergs

Algebra

Boot Camp: Tuesdays and Thursdays 11-1
Location: LCB 218 (Tuesday), LCB 322 (Thursday)
Advisor: Fletcher Gross
Mentor: Greg Piepmeyer

Applied Mathematics

Boot Camp: Tuesdays 2-4, Fridays 11-1
Location: LCB 322
Advisors: Paul Bressloff, Jim Keener
Mentor: Brynja Kohler

Geometry and Topology

Boot Camp: Tuesdays and Thursdays 2-4
Location: LCB 218

Numerical Analysis

Boot Camp: Wednesdays 11-1, Fridays 2-4
Location: LCB 322
Advisor: Peter Alfeld

Probability

No boot camp

Statistics

No boot camp

TA/TF TRAINING
By Peter Trombi

Last fall, the department ran its TA workshop for all new funded graduate students. Fourteen students attended, ten of whom were males and four females. Of the twelve U.S. students who attended, three were VIGRE students.

TA Training Program Schedule of Events (August 4 - 15, 2003)

Monday, August 4, 2003

08:30...Coffee/Tea/Treats
09:00...Introductions and Goals of Workshop - Large Group
10:00...Videotaping: Baseline Lecture #1 - Large Group
12:00...Lunch
13:00...Videotaping: Baseline Lecture #1 - Large Group

Homework: Prepare Mini Lecture: Self Introduction (3 - 5 min)

Tuesday, August 5, 2003

08:30...Coffee/Tea/Treats
09:00...Demonstrations: Dynamic Lecturing and How to Provide Constructive Feedback - Large Group
10:00...Break
10:15...Practice Session: Self Introduction (3 - 5 min)
Dynamic Lecturing - Style and Expression - Small Groups
12:00...Lunch
13:00...Practice Session: Why You Like Math (3 - 5 min)
Dynamic Lecturing - Style and Expression - Small Groups

Homework: Prepare Practice Lecture #2 (8 - 10 min)
Watch and Critique Baseline Lecture #1 Video

Wednesday, August 6, 2003

11:00...Demonstration: Blackboard Presentation - Large Group
11:45...Videotaping: Practice Lecture #2 (Written and Oral Feedback from Faculty and Students) - Small Groups

Homework: Watch and Critique Practice Lecture #2 Video
Prepare Practice Homework Problem (5 - 7 min)

Thursday, August 7, 2003

11:00...Interactive Demonstration: Presentation of Homework Problems - Large Group
11:45...Practice Session: Practice Homework Problem
Work on Presentation, Board Work, and Clarity - Small Groups

Homework: Identification of Goals for Improvement

Friday, August 8, 2003

11:00...Interactive Discussion: First day of class - Large Group
Why it is Important, How to Prepare, What to Do
Leadership, Credibility, Professional Presentation and Image, Classroom Policy
11:45...Individual Meetings with Facilitators
Make Tentative Course Assignment
Distribute Text Books

Homework: Read Chapter 1 of Course Text
Draft Lesson Plan for Chapter 1

Monday, August 13, 2001

08:30...Coffe/Tea/Treats
09:00...Interactive Workshop: Syllabus Preparation - Large Group
11:00...Break
11:15...Campus Tour - Small Groups
Room Visitations, Practice: Self Introduction
12:00...Lunch
13:00...Interactive Workshop: Syllabus Preparation - Large Group
(Syllabus Complete by Wednesday)

Homework: Prepare First Day Lecture (20min)
(Motivation for Course Content for Assigned Course)

Tuesday, August 12, 2003

08:30...Coffee/Tea/Treats
09:00...Videotaping: First Day Lecture (Motivation) - Small Groups
(Written Evaluations)
10:15...Break
10:30...Videotaping: First Day Lecture (Motivation) - Small Groups
(Written Evaluations)
12:00...Lunch
13:00...Videotaping: First Day Lecture (Motivation) - Small Groups
(Written Evaluations)
14:30...Break
14:45...Interactive Workshop: Student Questions and Answers - Large Group
How to Ask, Answer, and Foster Discussion

Homework: Watch and Critique First Day Lecture (30 min)
(Teach Course Content for Assigned Course)

Wednesday, August 13, 2003

08:30...Coffee/Tea/Treats
09:00...Final Videotaping: Second Day Lecture - Large Group
10:15...Break
10:30...Final Videotaping: Second Day Lecture - Large Group
12:00...Lunch
13:00...Final Videotaping: Second Day Lecture - Large Group

Homework: Write Quiz on Chapter 1 (Actual Course Content)
(Quiz should take about 20 mins to complete.)

Thursday, August 14, 2003

08:30...Coffee/Tea/Treats
09:00...Interactive Workshop: Test Construction and Writing Quizzes - Large Group
10:00...Break
10:15...Interactive Workshop: Quizzes
15:00...Facilitators Only - Evaluation/Certification

Friday, August 15, 2003

08:30...Coffee/Tea/Treats
09:00...Recap Presentation by Facilitators and Certification - Large Group
10:00...Break
10:15...Panel Discussion with Experienced TAs - Large Group
12:00...Lunch as a Group

GRADUATE STUDENT RECRUITING
By Peter Trombi

The goals of the recruiting weekend are to bring the top applicants to campus as a group so they get a sense of the cohort that will comprise the incoming graduate class.

The recruits were invited to visit campus for a three-day weekend from March 29, 2003 through March 31, 2003. They were housed in the University Guest House on upper campus.

Those who were interested took advantage of a Saturday outing of skiing, snow shoeing, cultural events, or getting acquainted with the city.

On Sunday, the recruits were given an overview of the department, city, and state. After lunch, they were given a tour of campus followed by formal presentations on research areas in the department. This was followed by a general reception attended by most faculty and graduate students. The remainder of the afternoon was dedicated to informal discussions with faculty. The current graduate students then hosted dinner for the guests at a local restaurant.

On Monday, the recruits attended some classes and visited with current graduate students.

The responses from those who attended the recruitment weekend were very positive. Most felt that the faculty presentations were extremely helpful and informative.

The results of this year's recruiting are as follows:

Number of Male Applicants: 160
Number of Female Applicants: 65
Number of International Applicants: 134
Number of U.S. Applicants: 91
Number of Offers Made: 45
Number of Offers to Males: 32
Number of Offers to Females: 13
Number of Offers to U.S. Citizens: 32
Number of VIGRE Offers to Males: 8
Number of VIGRE Offers to Females: 1
Number of VIGRE Acceptances: 6 (all males)
Number of Current Students Supported by VIGRE: 2 (both males)

Recruiting Weekend Schedule

Saturday, March 29, 2003
	Skiing, Snow Shoeing, Cultural Event, etc.
Sunday, March 30, 2003
9:00 - 10:00	Continental Breakfast at University Guest House
10:00 - 10:30	Drive or Walk to Mathematics Building
10:30 - 10:45	Welcome from Graeme Milton and GSAC Chairs
10:45 - 11:15	Overview of Graduate Program by Peter Trombi
11:15 - 11:45	Life in Salt Lake City
11:45 - 13:00	Lunch
13:00 - 14:00	Tour of Campus and Math Buildings
14:00 - 15:00	Math Biology Open House
15:00 - 16:00	Overview of Mathematics Research Programs
16:00 - 17:00	Informal Discussions in Small Groups
17:00 - 18:00	Reception with Faculty and Graudate Students
18:00	Dinner Arranged by GSAC
Monday, March 31, 2003
	Visit Classes and...
12:45 - 14:00	Graduate Colloquium

MINI-COURSE ON THE MATHEMATICS BEHIND BIOLOGICAL INVASIONS
By Fred Adler

The VIGRE mini-course entitled "The Mathematics Behind Biological Invasions" was held from June 2 - 13, 2003. There were 20 participants from around the country and the world. The primary lecturers were Mark Lewis (University of Alberta) and Mike Neubert (Woods Hole Oceanographic Institution), who each contributed approximately 9 hours of lectures. Additional speakers, all from the University of Utah, were Fred Adler, Nancy Sundell-Turner, and Jim Keener (Department of Mathematics) and Don Feener (Department of Biology). The course also included a field trip, led by Lynn Bohs (Department of Biology), to study invasive (non-native) plants of the Wasatch foothills.

In addition to listening to and participating in lectures, students worked on problems both individually and in groups. During the second week, students broke into seven groups to work on more extended projects, with results being presented to the entire group on the last day. The topics ranged from sea otter invasions in California to a comparison of different methods for estimating spread rates from dispersal data. At least one group is planning to submit a revised version of their project for publication. The principle lecturers are also having their notes typed up for possible publication.

MINI-COURSE ON WAVES IN INHOMOGENEOUS MEDIA
By David Dobson

July 28th through August 7th, 2003, the Department of Mathematics presented a summer mini-course for graduate students on "Waves in Inhomogeneous Media". The mini-course was funded by the Department's NSF VIGRE grant. The two-week course featured principal speakers Prof. George Papanicolaou of Stanford University and Prof. William Symes of Rice University. Other speakers included Utah Math faculty members Alexander Balk, Andrej Cherkaev, Elena Cherkaev, David Dobson, Ken Golden, and Graeme Milton, as well as Jerry Schuster from the Geophysics Department. Jesse Ratzkin assisted and coordinated discussion sessions. An exciting and broad range of topics was covered, including seismic imaging, waves in random media, water waves, inverse problems, waves in chains and lattices, waves in periodic media, properties of sea ice, rainbows, and wave behavior in composite media. The mini-course concluded with a one-day "mini-symposium" on current research topics on waves in inhomogeneous media, which featured six speakers from research institutions across the U.S. and Europe, as well as Tom Robbins from our own Mathematics Department. Many University of Utah students attended the mini-course, including several from other departments, and a few Mathematics undergraduates. Eight graduate students from Universities across the country traveled to Utah to participate in the mini-course. Three postdocs also participated. This event was an unusual opportunity to learn first-hand from top experts in wave behavior. The involvement and successful interaction of such a broad range of people - undergraduates, graduate students, postdocs, and faculty members - truly embodied the VIGRE concept. A schedule of the mini-course, including abstracts of talks, electronic versions of several presentations, and computer exercises, is available here.

VIGRE GRADUATE FELLOWS

Nathan Albin (VIGRE Term: 2002 - 2003)

B.S. 2001, University of Hawaii
Faculty Mentor: Klaus Schmitt
Ph.D. Qualifying Exams: Real and Complex Analysis, Differential Equations, Applied Mathematics
VIGRE Duties: Math Circle rotation, REU mentor, GRE prep course, Senior Seminar, Boot Camp organizer
Fall 2002 Class Schedule: Ordinary Differential Equations, Real Analysis, Applied Math
Spring 2003 Class Schedule: Partial Differential Equations, Complex Analysis, Applied Math
Conferences Attended: 51st Midwest PDE Seminar, April 2003, UIC, Chicago, IL

David Ayala (VIGRE Term: 2003 - 2004)

B.S. 2003, University of Utah
Faculty Mentor: Nick Korevaar

Maria Bell-Scott (VIGRE Term: 2002 - 2003)

B.S. 2002, University of Utah
Faculty Mentor: Aaron Bertram
Ph.D. Qualifying Exams: Numerical Analysis, Applied Mathematics
VIGRE Duties: Math Circle rotation, Summer High School Program, ACCESS
Area of Interest: Applied Mathematics
2002 - 2003 Classes Taken: MATH 5210 (Introduction to Real Analysis), MATH 6710 (Applied Linear Operators and Spectral Methods), MATH 6610 (Analysis of Numerical Methods I), MATH 5740 (Mathematical Modeling), MATH 6220 (Complex Analysis), MATH 6620 (Analysis of Numerical Methods II)

Gene Butcher (VIGRE Term: 2003 - 2004)

B.S. 2003, University of Kentucky
Faculty Mentor: Peter Trapa

Rex Butler (VIGRE Term: 2003 - 2004)

B.S. 2003, University of Utah
Faculty Mentor: Henryk Hecht

Matthew Clay (VIGRE Term: 2002 - 2003)

B.S. 2001, University of Oregon
Faculty Mentor: Michael Kapovich
Ph.D. Qualifying Exams: Geometry/Topology, Algebra, Real and Complex Analysis
VIGRE Duties: Math Circle rotation, Summer REU mentor, Boot Camp mentor, Graduate Colloquium Lecturer
Area of Interest: Geometric Group Theory
Fall 2002 Schedule: Math 6130 (Algebraic Geometry), Math 6240 (Lie Groups/Lie Algebras), Math 7810 (Student Geometry Seminar)
Spring 2003 Schedule: Math 6140 (Algebraic Geometry), Math 6250 (Lie Groups/Lie Algebras), Math 6910 (Reading Course � Cohomology of Groups, Automorphisms of Surfaces), Math 7850 (Topology of Real Algebraic Varieties)
Lectures Given: "Ends of a Group", "Hyperbolic Groups and Isometries of CAT(0) Spaces", and "Finite Subgroups of Hyperbolic Groups" (all at the Student Geometry Seminar, University of Utah); "Topological Methods in Group Theory � Grusko's Theorem and Kuros' Theorem", "Topological Methods in Group Theory � Ends of a Group" (both at the Max Dehn Seminar, University of Utah); "Coxeter Groups", "Introduction to Geometric Group Theory for Student Recruitment Weekend" (both at the Graduate Colloquium, University of Utah)
Conferences Attended: Wasatch Topology Conference, Park City, UT, June 2003

Eric Cook (VIGRE Term: 2001 - 2002)

B.S. 1999, Colby College
Hometown: Atkinson, NH
Faculty Mentor: Henryk Hecht
VIGRE Duties: REU mentor, Math Circle rotation, HS Summer Program
Area of Interest: Pure Mathematics
Fall 2001 Schedule: Math 5110 (Mathematical Biology), Math 6210 (Real Analysis), Math 6310 (Modern Algebra I), Math 6710 (Applied Linear Operator and Spectral Methods)
Spring 2002 Schedule: Math 5520 (Introduction to Algebraic Topology), Math 6220 (Complex Analysis), Math 6320 (Modern Algebra II)

Scott Crofts (VIGRE Term: 2003 - 2004)

B.S. 2003, University of Illinois
Faculty Mentor: David Dobson

Stefanos Folias (VIGRE Term: 2003 - 2004)

B.S. 1997, University of California - San Diego; M.S. 2000, University of Utah
Hometown: Salt Lake City, UT
Faculty Mentor: Paul Bressloff
Area of Interest: Mathematical Neuroscience

Sarah Geneser (VIGRE Term: 2001 - 2002)

B.A. 2001, Rice University
Hometown: Houston, TX
Faculty Mentor: Jim Keener
VIGRE Duties: REU mentor, Math Circle rotation
Area of Interest: Neural Modeling and Medical Imaging
Fall 2001 Schedule: Math 6410 (Ordinary Differential Equations), Math 6710 (Applied Linear Operators and Spectral Methods), Math 6770 (Mathematical Biology I), Math 6910 (Neuroscience Supervised Reading)
Spring 2002 Schedule: CS 6220 (Scientific Computing II), Math 6620 (Analysis of Numerical Methods II), Math 6720 (Applied Complex Variables and Asymptotic Methods), Math 6780 (Mathematical Biology II)
Seminars: Math Biology Seminar, GSAC Colloquium, Neuroscience Group Meeting, Dr. Keener's Math Biology Group Meeting

Robert Guy (VIGRE Term: 2001 - 2003)

B.S. 1997, University of North Carolina; M.S. 1999, University of Utah
Ph.D. 2003, University of Utah (Topic: Model of aggregating blood platelets, modeled as a fluid with variable material properties); Accepted a post doctoral position at the University of Utah
Hometown: Greenville, NC
Faculty Mentor: Aaron Fogelson
Ph.D. Qualifying Exams: Numerical Analysis, Applied Mathematics, Real and Complex Analysis
VIGRE Duties: REU mentor, Summer High School Program mentor and lecturer, Math Circle mentor and lecturer, Boot Camp mentor, Math Biology Journal Club organizer
Areas of Interest: Mathematical Modeling, Mathematical Biology, Fluid Dynamics, Numerical Analysis
Fall 2001 Schedule: Math 7970 (Thesis Research)
Spring 2002 Schedule: Math 6630 (Numerical PDE), Math 7970 (Thesis Research)
Fall 2002 Schedule: Thesis Research
Spring 2003 Schedule: Thesis Research, Math 6780 (Mathematical Biology II)
Seminars: Applied Math, GSAC Colloquium, Undergraduate Colloquium, Math Biology, Math Physiology group meeting, Fluid Dynamics group meeting, helps lead the Math Biology Journal Club
Presentations: "A Continuum Approach to Modeling Platelet Aggregation", Society for Mathematical Biology Annual Meeting, Knoxville, TN, July 2002 (poster presentation); "A Probabilistic Model of Platelet Aggregation", Society for Mathematical Biology Annual Meeting, Knoxville, TN, July 2002; "Comparing closures for a multiple scale, continuum model of platelet aggregation", University of Utah Mathematical Biology Seminar, April 2003; "A Continuum Approach to Modeling Platelet Aggregation", SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May 2003; "A Continuum Model of Platelet Aggregation: Closure Models and Simulations", Seventh US National Congress on Computational Mechanics, Albuquerque, NM, July 2003
Papers Published: "Probabilistic modeling of platelet aggregation: Effects of activation time and receptor occupancy" (with A. Fogelson), Journal of Theoretical Biology, Vol. 219, 33-53 (2002)
Papers in Preparation: "Asymptotic analysis of shear thinning for a PTT fluid and non-equilibrium network model"; "A continuum model of platelet aggregation: closures and simulations" (with A. Fogelson); "A fully second order accurate projection method for inflow/outflow boundary conditions" (with A. Fogelson)
Conferences Attended: Society of Mathematical Biology Conference in Knoxville, TN, July 2002; SIAM Conference on Applications of Dynamical Systems in Snowbird, UT May 2003; Seventh US National Congress on Computational Mechanics, Albuquerque, NM, July 2003

Brynja Kohler (VIGRE Term: 2002 - 2003)

M.S. 1998, New York University
Hometown: Boston, MA
Faculty Mentor: James Keener
Ph.D. Qualifying Exams: Complex Analysis, Advanced Calculus, and Linear Algebra (all taken at NYU)
VIGRE Duties: Math Circle rotation, Boot Camp mentor, Math Biology Journal Club organizer
Fall 2002 Class Schedule: MATH 6730 (Asym. Perturbation Models), MATH 6910 (Supervised Reading), MATH 7875 (Seminar on Applied Mathematics), MATH 7970 (Thesis Research)
Spring 2003 Class Schedule: MATH 6740 (Bifurcation Theory), MATH 7970 (Thesis Research)
Papers in Preparation: "Population Dynamics of Regulatory T-Lymphocytes" (with J. Keener); "A Mathematical Model of the Stretch Reflex and Clonus" (with D. Levine and C. S. Peskin)
Conferences Attended: Program for Women in Mathmatics, Institute for Advanced Study, Princeton NJ, May 12 - 22, 2003; Annual Meeting, Society for Mathematical Biology, Dundee, Scotland, August 6 - 9, 2003
Talks Given: "Muscle Physiology and Dynamics in the Stretch Reflex" October 8, 2002 and "Modeling Regulatory T Cells" March 31, 2003 (both at GSAC); "A Mathematical Look at the Physiology of Movement" March 11, 2003 (Undergraduate Colloquium); "A Survey of Population Models of T Lymphocytes" May 16, 2003, Program for Women in Mathematics, Institute for Advanced Study, Princeton, NJ

Larsen Louder (VIGRE Term: 2001 - 2002)

B.S. 2001, University of Utah
Hometown: Twin Falls, ID
Faculty Mentor: Mladen Bestvina
VIGRE Duties: REU mentor, Math Circle rotation
Areas of Interest: Topology, Geometry
Fall 2001 Schedule: Math 6310 (Modern Algebra I), Math 6210 (Real Analysis), Math 6170 (Riemannian Geometry), Math 7853 (Topics in Geometric Topology)
Spring 2002 Schedule: Math 6150 (Kahler Manifolds), Math 6220 (Complex Analysis), Math 6320 (Modern Algebra II)
Seminars: GSAC Colloquium
Conferences Attended: Wasatch Topology Conference in the Fall, 2001

Frank Lynch (VIGRE Term: 2003 - 2004)

B.A. 1999, Linfield College; M.S. 2001 University of Utah
Hometown: Ritzville, WA
Faculty Mentor: James Keener
Area of Interest: Mathematical Biology

Meagan McNulty (VIGRE Term: 2001 - 2002)

B.S. 1998, Metro State College
Hometown: Wheatridge, CO
Faculty Mentor: Ken Golden
VIGRE Duties: REU mentor, Math Circle rotation
Fall 2001 Schedule: Math 6410 (Ordinary Differential Equations), Math 6610 (Analysis of Numerical Methods I), Math 6710 (Applied Linear Operator and Spectral Methods), Math 5110 - Audit (Mathematical Biology I), Bio 5910 � Audit (Mathematical Models in Biology)
Spring 2002 Schedule: Math 5210 (Introduction to Real Analysis), Math 6620 (Analysis of Numerical Methods II), Math 6720 (Applied Complex Variables, Asymptotic Methods), Math 6910, Math 5110 � Audit, Math 6920 � Audit, Biol 2020 - Audit
Seminars: GSAC Colloquium, Math Biology Journal Club, SLAM Meeting, Biology Group Meeting

Greg Piepmeyer (VIGRE Term: 2002 - 2003)

B.A. 1998, University of Utah
Ph.D. 2003, University of Utah (Topic: Finding examples of modules of finite projective dimension and finite length with unusual intersection properties)
Hometown: Reno, NV
Faculty Mentor: Paul Roberts
Ph.D. Qualifying Exams: Algebra, Analysis, Topology
VIGRE Duties: Math Circle rotation, REU mentor, Boot Camp mentor, Graduate Colloquium Lecturer
Area of Interest: Applications of homological algebra within commutative algebra
Lectures Given: Commutative Algebra Seminar, Utah
Papers Published: Paper jointly written with Roger Horn appeared in Linear Algebra and its Applications 361 (pages 99 � 106)
Conferences Attended: Three conferences in conjunction with the Special Year in Commutative Algebra held at MSRI, Computational Commutative Algebra Mini-Course held at Texas A\&Min the Summer of 2002, Algebra and Number Theory talks at the AMS meeting held in Utah

Emily Putnam (VIGRE Term: 2002 - 2003)

B.A. 2002, San Francisco State University
Hometown: Berkeley, CA
Faculty Mentor: Aaron Bertram
Ph.D. Qualifying Exams: Algebra, Analysis
VIGRE Duties: Math Circle rotation, GRE Prep, Senior Seminar, REU mentor, ACCESS
Area of Interest: Commutative Algebra
Fall 2002 Schedule: Math 4510 (Topology), Math 6210 (Real Analysis), Math 6310 (Algebra I)
Spring 2003 Schedule: Math 5520 (Introduction to Algebraic Topology), Math 6220 (Complex Analysis), Math 6320 (Algebra II), Math 6350 (Commutative Algebra)
Conferences Attended: Joint AMS/MAA Meeting in Baltimore, MD � January, 2003; Western Sectional Meeting of the AMS, University of Utah � October 2002; Contemporary Algebra and Algebraic Geometry Red-Raider Symposium, Texas Tech University � November 2002; Western Sectional Meeting of the AMS, San Francisco State University � May 2003
Lectures Given: "Munshi's Proof of the Hilbert Nullstellansatz" for the University of Utah Commutative Algebra Seminar, April 2003

Ryan Rettberg (VIGRE Term: 2003 - 2004)

B.S. 2003, University of Utah
Faculty Mentor: Fletcher Gross

Matthew Rudd (VIGRE Term: 2001 - 2003)

M.S. 1996, University of Chicago
Ph.D. 2003, University of Utah (Topic: Nonlinear constrained evolution in Banach spaces); Accepted a post doctoral position at the University of Texas at Austin
Hometown: Rome, GA
Faculty Mentor: Klaus Schmitt
Ph.D. Qualifying Exams: Applied Mathematics, Differential Equations, Real and Complex Analysis
VIGRE Duties: Mini-Course on Variational Methods and Nonlinear PDE, REU mentor, Math Circle mentor and lecturer, Boot Camp mentor, PDE Seminar
Areas of Interest: Nonlinear Partial Differential Equations, Nonlinear Analysis, Scientific Computing
Fall 2001 Schedule: Math 6430 (Advanced Partial Differential Equations), Math 6170 (Introduction to Riemannian Geometry), Math 7970 (Thesis Research)
Spring 2002 Schedule: Math 6630 (Numerical Methods for PDE), Math 7840 (Topics in PDE), Math 7970 (Thesis Research), CS 6950 � Reading Course (Finite Element Methods)
Fall 2002 Schedule: Math 7840 (Topics in PDEs), Thesis Research
Spring 2003 Schedule: Thesis Research
Lectures Given: GSAC Seminar (talks on October 16, 2001 and in March, 2002); PDE Seminar (talk on October 24, 2001); Wake Forest University Math Department Colloquium (talk on October 31, 2001)
Papers Published: "Variational inequalities of elliptic and parabolic type" (with K. Schmitt) Taiwanese Journal of Mathematics, 6 (2002), 287 - 322
Papers Submitted for Publication: "Weak and strong solvability of parabolic variational inequalities on Banach spaces" submitted to the Journal of Functional Analysis; Thesis ("Nonlinear constrained evolution in Banach spaces") submitted to the Journal of Functional Analysis
Papers in Preparation: "Fine properties of Orlicz-Sobolev functions"
Conferences Attended: SEARCDE Conference at Wake Forest University in November, 2001 (lectured at this conference); VIGRE Mini-Course on Variational Methods and Nonlinear PDE in May � June, 2002 (lectured at this conference); Midwest PDE Seminar, Chicago, IL, April 2003; Sectional Meeting of the AMS, Salt Lake City, UT, October 2002 (lectured at this conference)

Ryan Stones (VIGRE Term: 2001 - 2002)

B.S. 2001, Brigham Young University
Hometown: Salt Lake City, UT
Faculty Mentor: Michael Kapovich
VIGRE Duties: REU mentor, Math Circle rotation
Area of interest: Pure Mathematics
Fall 2001 Schedule: Math 6210 (Real Analysis), Math 6310 (Modern Algebra I), Math 6510 (Differential Manifolds)
Spring 2002 Schedule: Math 6220 (Complex Analysis), Math 6320 (Modern Algebra II), Math 6520 (Introduction to Algebraic Topology)

Robert Thorn (VIGRE Term: 2001 - 2002)

B.S. 2001, University of Utah
Hometown: Salt Lake City, UT
Faculty Mentor: Paul Bressloff
VIGRE Duties: REU mentor, Math Circle rotation
Area of Interest: Math Biology
Fall 2001 Schedule: Math 5310 (Introduction to Modern Algebra I), Math 5410 (Introduction to Ordinary Differential Equations), Math 6710 (Applied Linear Operator and Spectral Methods)
Seminars: Neuroscience, Math Biology

Michael Woodbury (VIGRE Term: 2003 - 2004)

B.S. 2003, University of Utah
Faculty Mentor: Gordan Savin

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The Post-Doctoral Program

The post-doctoral program in mathematics at the University of Utah was started during the early seventies. Its members include many prominent research mathematicians who occupy academic positions at leading mathematics departments. It is in this spirit that the VIGRE post-doctoral program is viewed and only candidates with exceptional promise are appointed to these positions. Each post-doc (VIGRE assistant professor) is appointed for a three year period, has a teaching load of one course per semester and is expected to participate in the other VIGRE programs of the department. When joining the faculty, each post-doc is assigned a faculty mentor who shares the same or similar research specialty. The mentor supervises the post-doc's academic activities and is responsible for evaluating his or her performance in teaching, research, and service.

The department graduated nine Ph.D. students this year. Of the nine Ph.D.'s conferred, two were women and six were U.S. citizens. Two of the six U.S. students were partially supported by VIGRE.

The recruiting season for the 2003 - 2004 academic year saw the following results:

Applicants: 250(35 women)
U.S. Citizens: 83(10)
Offers Made: 14(2)
VIGRE Offers Made: 7(1)

The following list provides the names and activities of people appointed from the first year of the grant (2001 - 2002) to the 2003 - 2004 academic year as VIGRE Assistant Professors.

Robert Bell (VIGRE Funded Fall 2003 - Spring 2006)

Ph.D. 2003, The Ohio State University
Topology (Geometric Group Theory)
Hometown: Coral Springs, Florida
Faculty Mentor: Mladen Bestvina
Teaching Duties Fall 2003: Math 3210, Foundations of Analysis I
VIGRE Duties: Math Circle Mentor and Lecturer, Mini-Course Mentor
Current Research Interests: CAT(0) spaces, Artin groups, Coxeter groups
Papers in Preparation: "Three dimensional FC Artin groups are CAT(0)" (thesis)
Lectures Given: University of Utah Max Dehn Seminar 9/15/03 "Three dimensional FC Artin groups are CAT(0)"
Conferences Attended: Albany Group Theory Conference, 10/03

Javier Fernandez (VIGRE Funded Fall 2001 - Spring 2004)

Ph.D. 2001, University of Massachusetts
Algebraic Geometry, Hodge Theory
Hometown: Buenos Aires, Argentina
Faculty Mentor: Jim Carlson
Teaching Duties Fall 2001: Math 1090, Business Algebra
Teaching Duties Spring 2002: Math 1100, Quantitative Analysis
Teaching Duties Fall 2002: Math 3160, Applied Complex Variables
Teaching Duties Spring 2003: Math 2270, Linear Algebra
Teaching Duties Fall 2003: Math 1090, Business Algebra
VIGRE Duties: Mini-Course on Complex Hyperbolic Geometry, GRE Prep Course Assistant and Organizer, Senior Seminar Assistant, Boot Camp Mentor, Rational and Integer Points on Elliptic Curves REU Mentor
Current Research Interests: Hodge Theory and its applications to the understanding of mirror symmetry (for instance, the relation between variations of Hodge structure and quantum products); dimensional bounds of variations of Hodge structures with prescribed degenerating behavior; the relationship between geometry and physics
Papers Published: "Frobenius modules and Hodge asymptotics" (with E. Cattani) submitted to Comm. Math. Phys.; "Opposite filtrations, variations of Hodge structures and Frobenius modules" (with G. Pearlstein) was accepted in Aspects of Mathematics, Vieweg Publ. (2003)
Papers in Preparation: "Infinitesimal variations of Hodge structure at infinity"; "Hodge structures for orbifold cohomology"; "Variation of Hodge structures for quantum orbifold cohomology"
Lectures Given: Algebraic Geometry Seminar at the University of Utah "A-model variation of Hodge structure, an application of asymptotic Hodge theory" September, 2001 and "Hodge structures for orbifold cohomology" September, 2003; Mathematical Physics Seminar "Perturbation theory and Feynman diagrams" March, 2002; Graduate Colloquium at the University of Utah "A window into mirror symmetry" April, 2002; lead problem sessions (with Martin Deraux) on Mini-Course on Complex Hyperbolic Geometry May, 2002; Western Algebraic Geometry Seminar at Stanford University "Hodge theoretic constructions of Frobenius manifolds" April, 2003; String Geometry Seminar at the University of Utah "Introduction to Calabi-Yau manifolds" October, 2002; Max Planck Institut in Bonn, Germany "Frobenius modules and Hodge asymptotics" July, 2002
Conferences Attended: Park City Math Institute July, 2001; Arizona Winter School 2001, Tucson, AZ, March, 2002; Workshop on Frobenius manifolds at the Max Planck Institute of Mathematics, July, 2002; Western Algebraic Geometry Seminar, Vancouver, September, 2003; Von Neumann Symposium and Conference, MSRI, Berkeley, CA, August, 2003; Western Algebraic Geometry Seminar, Stanford, CA, April, 2003

David Hartenstine (VIGRE Funded Fall 2001 - Spring 2004)

Ph.D. 2001, Temple University
Partial Differential Equations
Hometown: Allentown, Pennsylvania
Faculty Mentor: Klaus Schmitt
Teaching Duties Fall 2001: Math 1210, Calculus I
Teaching Duties Spring 2002: Math 1220
Teaching Duties Fall 2002: Math 7840, Topics in Partial Differential Equations
Teaching Duties Spring 2003: Math 2210, Calculus III
Teaching Duties Fall 2003: Math 5410, Introduction to Ordinary Differential Equations
VIGRE Duties: Mini-Course in Variational Methods and Nonlinear PDE, Math Circle Lecturer and Mentor, PDE/Geometry Seminar Co-Coordinator, Modules Coordinator, Calculus Challenge Coordinator, Undergraduate Problem Solving Contest Faculty Advisor
Current Research Interests: Partial Differential Equations, more specifically, nonlinear elliptic equations
Papers Published: "Regularity properties of weak solution to the Monge-Ampere equation" (with C. E. Gutierrez) in Transactions of the AMS, Volume 355, Number 6, 2003, 2477 - 2500
Papers Submitted for Publication: "An Aleksandrov-type estimate for a parabolic Monge-Ampere equation" to Proceedings of the AMS
Papers in Preparation: "The solvability of the Dirichlet problem for the Monge-Ampere equation in domains that are not strictly convex"; "Viscosity subsolutions, the subfunctions of Beckenbach and Jackson, and applications to nonlinear elliptic equations" (with K. Schmitt); "On quasilinear elliptic equations of minimal surface type"; "Math Circle, an outreach program at the University of Utah" (with R. Cavalieri)
Lectures Given: Two PDE Seminar lectures, Univ. of Utah, 8/29/01 and 9/5/01; AMS Session on Nonlinear Elliptic PDE, San Diego, January, 2002 and Salt Lake City, October, 2002; University of Utah PDE/Differential Geometry Seminar, October, 2003; AMS Meeting, Phoenix, January, 2004; Talk about Math Circle at the MAA Meeting, Boulder, August 2003; University of Utah Graduate Colloquium, September, 2003; University of Utah Undergraduate Colloquium, October, 2003
Conferences Attended: Symposium for 75th Birthday of James Serrin, University of Minnesota, November, 2001; AMS/MAA Joint National Meeting, San Diego, January, 2002; AMS/UMI Joint International Meeting, Pisa, Italy, June, 2002; MAA MathFest, Burlington, VT, July 2002; AMS Meeting, Salt Lake City, October 2002; AMS/MAA Joint National Meetings, Baltimore, January 2003; Legacy of R. L. Moore Conference, Austin, March 2003; CBMS Conference "Fully Nonlinear Equations in Geometry", Notre Dame, June 2003; MAA MathFest, Boulder, July--August 2003; Project NExT Fellow 2002 - 2003

Dan Margalit (VIGRE Funded Fall 2003 - Spring 2006)

Ph.D. 2003, University of Chicago
Topology
Hometown: Flanders, New Jersey
Faculty Mentor: Mladen Bestvina
Teaching Duties Fall 2003: Math 4510, Introduction to Topology
VIGRE Duties: Math Circle Mentor and Lecturer, Mini-Course Mentor
Current Research Interests: Mapping class groups
Papers Published: "A lantern lemma" in Algebraic and Geometric Topology 2 (2002), paper no. 46, pages 1179 - 1195; "Automorphisms of the pants complex" to appear in Duke Mathematical Journal
Paper in Preparation: "A primer on mapping class groups" (with B. Farb)
Lectures Given: University of Utah Max Dehn Seminar 9/8/03
Conferences Attended: Albany, NY Geometric Group Theory 10/17/03; AMS Special Session on Cohomology of Groups 10/24/03

Thomas Pietraho (VIGRE Funded Fall 2001 - Spring 2002)

Ph.D. 2001, MIT
Representation Theory
Hometown: Middlebury, Vermont
Faculty Mentor: Peter Trapa
Teaching Duties Fall 2001: Math 1220, Calculus II
VIGRE Duties: Math Circle, Summer High School Program Lecturer
Current Research Interests: Representation Theory of Lie Groups, Combinatorics of Representation Theory

Jesse Ratzkin (VIGRE Funded Fall 2001 - Spring 2004)

Ph.D. 2001, University of Washington
Differential Geometry, Geometric PDE
Hometown: Berkeley, California
Faculty Mentor: Nat Smale
Teaching Duties Fall 2001: Math 2280, Introduction to Differential Equations
Teaching Duties Spring 2002: Math 2270, Introduction to Linear Algebra
Teaching Duties Fall 2002: Math 1060, Trigonometry
Teaching Duties Spring 2003: Math 7810, Topics in Riemannian Geometry
Teaching Duties Fall 2003: Math 3150, PDE for Engineers
VIGRE Duties: Math Circle Lecturer and Mentor, REU Mentor, Boot Camp Mentor, Mini-Courseon Variational Methods and Nonlinear PDE, Mini-Course on Waves in Inhomogeneous Media, PDE/Geometry Seminar Co-Coordinator
Current Research Interests: Geometric Analysis and Riemannian Geometry
Papers Published: "An end to end gluing construction for metrics of positive scalar curvature", in Ind. Univ. J. Math., Vol. 52 #3, pg 703 - 726
Papers in Preparation: Something with many gluing constructions for constant mean curvature surfaces, joint with Rafe Mazzeo, Frank Pacard, and Dan Pollack; "Necksize bounds for singular Yamabe metrics with symmetry" (with R. Kusner)
Lectures Given: Gang seminar at U Mass Amherst: CMC Surfaces of Higher Genus, 2/15/02; Graduate Colloquium: Introduction to CMC Surfaces, 3/12/02; Undergraduate Colloquium: Crystal growth; The roundness of bubbles, 9/16/03; Differential Geometry Seminar: Gluing special Lagrangian submanifolds, 4/18/02; Gluing constructions for CMC surfaces and aplications to moduli spaces, I and II, 8/31/01 and 9/7/01; Moduli spaces of CMC surfaces I, II, and III, 11/2/01, 11/16/01, and 11/30/01; PDE Seminar: Periodic operators on cylinders, 11/26/02; PDE/Geometry Seminar: What is Ricci flow?, 9/10/03; Seminar at Georgia Tech: Gluing constructions for CMC surfaces and moduli spaces, 12/02
Conferences Attended: Annual Meeting of the Canadian Mathematics Society, 12/7/01 � 12/10/01, Toronto; Spring 2002 PNGS, 5/11/02 � 5/12/02, Seattle, WA; Meeting in Brest on harmonic maps, minimal surfaces, and geometric evolution equations, Summer 2002; AMS Sectional Meeting in Bloomington, IN, April 2003; Southeastern Geometry Seminar in Atlanta, GA, December 2002

Nancy Sundell-Turner (VIGRE Funded Fall 2002 - Spring 2004)

Ph.D. 2002, Cornell University
Mathematical Ecology
Hometown: Clifton Park, New York
Faculty Mentor: Fred Adler
Teaching Duties Fall 2002: Math 1210, Calculus I
Teaching Duties Spring 2003: Honors 2202, Honors Calculus for Students in Non-Technical Majors II
Teaching Duties Fall 2003: Honors 2201, Honors Calculus for Students in Non-Technical Majors I
VIGRE Duties: Math Circle Lecturer, Mini-Course on the Mathematics Behind Biological Invasions, ACCESS Mentor, Boot Camp Mentor, Math Biology Journal Club Co-Coordinator
Current Research Interests: Theoretical Ecology with an Emphasis on the Application of Mathematics to Topics in Population and Conservation Biology
Papers in Preparation: "Dynamics of a spatial herbivory system: Herbivore enhancement, adaptive behavior and trophic cascades" for the Journal of Ecology
Lectures Given: Math Biology Colloquium, Fall 2002; Graduate Student Math Colloquium, Fall 2002; Undergraduate Math Colloquium, Spring 2003
Conferences Attended: Ecological Society of America, August, 2003

Grady Wright (VIGRE Funded Fall 2003 - Spring 2006)

Ph.D. 2003, University of Colorado at Boulder
Numerical/Computational Mathematics
Hometown: Salt Lake City, Utah
Faculty Mentor: Peter Alfeld
Teaching Duties Fall 2003: Math 5610, Introduction to Numerical Analysis
VIGRE Duties: Boot Camp Mentor, Numerical Analysis Seminar Coordinator, Summer REU Mentor
Current Research Interests: Radial Basis Functions (RBFs); High-order methods for PDEs (spectral, finite difference, and RBF methods); Numerical methods for ODEs
Papers Published: B. Fornberg and G. Wright, "Stable computation of multiquadric interpolants for all values of the shape parameter", to appear in Computers and Mathematics with Applications; B. Fornberg, G. Wright, and E. Larsson, "Some observations regarding interpolants in the limit of flat radial basis functions", to appear in Computers and Mathematics with Applications
Papers in Preparation: G. Wright and B. Fornberg, "Scattered node finite difference formulas generated by radial basis functions"; B. Fornberg, E. Larsson, and G. Wright, "On RBF interpolation with a class of oscillatory radial functions"
Lectures Given: University of Utah Numerical Analysis Seminar 9/8/03 "An introduction to the radial basis function methods"

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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 2001 - 2003

Table of Contents:

People Involved in the VIGRE Program

Programs for High-School Students

Programs for Undergraduate Students

Programs for Graduate Students

The Post-Doctoral Program

The VIGRE Program at the University of Utah
Report on the Years 2001 - 2003