High School: Math Circle State Math Contest Summer High School Program Undergraduate: GRE Prep Course Undergraduate Colloquium Research Experience for Undergraduates Graduate: Mini-Courses Qualifying Exam Problem Sessions Graduate Fellowships Committees: Steering Internal Advisory External Advisory Outreach Advisory Other Information: People Master Calendar VIGRE Award Publications Undergraduates Graduates Postdocs 04-05 AR |
## 2004-2005 VIGRE Annual Report |
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## Table of ContentsOverview2004-2005 VIGRE HighlightsPeople Involved in the VIGRE
ProgramPrograms for High School Students- Math Circle 2004 - 2005
- Summer High School Program
Programs for Undergraduate Students- Academic Year REU Program
- Summer 2005 REU Program on "The Mathematics of Games of Chance"
- Undergraduate Colloquium
- Summer ACCESS Program
- Senior Seminar
- Problem Solving Competition
Programs for Graduate Students- Graduate Colloquium
- Mini-Course on "Arc Spaces & Motivic Integration"
- Mini-Course on "Nonconvex Variational Problems & Applications"
## OverviewThe VIGRE program at the University of Utah is a department-wide program to which many of our present faculty members contribute; it addresses education and research at all levels and all areas of specialization represented in the department (see http://www.math.utah.edu/vigre/). The program just completed its fourth year of operation and now enters the final year of the grant period. 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, have arisen when assignments had 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 were ineligible for VIGRE support; here we want to particularly point out the contributions made to the operation of the Math Circle by Renzo Cavalieri who graduated this past spring and is now at the University of Michigan.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 and are part of our detailed annual report. Most of these evaluations contain material that should be treated confidentially and hence is not made available to the general public. Sarah Strong, our program coordinator for some time, left the University during the year to move to Boston. She did an outstanding job and helped enormously in creating a sound operating structure for our program. She was succeeded by Kathleen Moore who collected, compiled, and prepared this report and who is now in charge of coordinating the various parts of the program. The program was directed by Klaus Schmitt. 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 was conducted for the third time by our colleague Peter Trapa. He was assisted on a regular basis by VIGRE assistant professors, VIGRE graduate fellows, and two non-VIGRE graduate fellows (Renzo Cavalieri and Scott Crofts). The program's emphasis is very much on problem solving and, during the past year, more than 50 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 postdocs 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 on years three and four is still being collected.**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 sixth year of the program, and was the fifth 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. Sixteen students participated this past summer with four of the coming from outside the State. 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 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.**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 summer program for 2005 was conducted by Stewart Ethier and concentrated for six weeks on the Mathematics of Games of Chance. A total of ten studentds participated with five coming from outside 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 four years and also some of the REU students have spoken on their work at national conferences or work-shops and have had their work accepted for publication. Sevearl alumni of the program have chosen to become mathematics graduate students and one chose computer science as a program of study. For example, one student took a year off before continuing on to graduate school, several became mathematics graduate students at the University of Utah, UCLA, Washington University, and comparable schools. 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. In 2005 we hired 6 new graduate students and appointed two of our advanced graduate students as VIGRE fellows. 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 postdoc at the University of Texas at Austin, one is a postdoc in our department, one is an assistant professor at Utah State University, and one is a postdoc 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. The 2005 mini-courses were devoted to "Arc Spaces and Motivic Integration", organized by Aaron bertram and Chris Hacon and "Nonconvex variational problems" organized by Elena and Abdrej Cherkaev. Both courses were well attended and had several guest lecturers, as well as lecturers from our faculty. The 2006 courses are being organized by Dragan Milicic, Peter Trapa, and davar Khoshnevisan.**The Postdoc 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 Hartenstine, 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 postdoc (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 postdocs left after the first year, one after the second, the others remained for the full three year term. Three 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. At present there are six postdocs supported in part by the grant with their remaining support coming from Department funds.**Summary:** As can be seen from the report below, 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. As this is the last year of the program, a committee appointed by the executive committee has prepared a proposal to NSF to continue our program for another five years under the NSF's EMSW21 initiative. The proposal was recently submitted with Aaron Bertram and David Dobson as principal investigators. The other members of Committee are: Fred Adler, Elena Cherkaev, Nick Korevaar, Ken Golden, Gordan Savin, Zhingyi Zhu, and Klaus Schmitt. The Committee was assisted by Kathleen Moore, the present Program Coordinator.**Dissemination to the Mathematical Sciences Community:** All of our VIGRE activities (organizational structure, recruiting advertisements, reports, etc.) are posted on the web at http://www.math.utah.edu/vigre. 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.):
- Math Circle:
http://www.math.utah.edu/mathcircle - REU:
http://www.math.utah.edu/vigre/reu/index.html - Mini-Courses:
http://www.math.utah.edu/vigre/minicourses/index.html - Undergraduate Colloquium:
http://www.math.utah.edu/a/ugrad/colloquia/ http://www.math.utah.edu/vigre/annual-report/undergrad-colloq01-02.html - Graduate Colloquium:
http://www.math.utah.edu/a/gsac/colloq.html http://www.math.utah.edu/vigre/annual-report/grad-colloq01-02.html - Graduate Fellowships:
http://www.math.utah.edu/vigre/gradfellowships.html - Postdoc Positions:
http://www.math.utah.edu/vigre/postdocs.html - Grant Proposals:
http://www.math.utah.edu/gsac/grant-index.html - Outreach:
http://www.math.utah.edu/mathcircle/ http://www.math.utah.edu/hsp/ - Annual Report:
http://www.math.utah.edu/vigre/annual-report/01-02.html
- Math Circle:
**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. Our five year combined bachelors and masters program with a major in mathematics now has some students enrolled; students participating in REU projects at an early stage are 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 still have some funding from the Eskuche Foundation and from the Math and Science Education Foundation to run the Math Circle program. And last but very importantly, our NUMBER of MAJORS has increased to over 300, which was one our original VIGRE goals.
Departmental enrollment figures - 1994-2005 Back to Table of Contents ## 2004-2005 VIGRE HighlightsAugust 2004: TA-TF trainingSeptember 2004: Math Circle startsMarch 2005: Assessment meeting with graduate students and
postdocsApril 2005: New graduate students appointedMay 2005: Mini-courses on Nonconvex Variational Problems and Applications, and Arc Spaces and Motivic IntegrationJune 2005: Summer REU; Summer High School program: ACCESS
programBack to Table of Contents ## People Involved in the VIGRE ProgramThe 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, Boot Camp 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 Jason Behrstock, VIGRE Assistant Professor
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, Max Dehn Seminar Organizer, Undergraduate 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, Co-Organizer of the Mini-course on Arc Spaces and Motivic Integration 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 Manuel Blickle, Professor of Mathematics, University of Essen
VIGRE Activities: Lecturer at the Mini-course on Arc Spaces and Motivic Integration Marian Bocea, Assistant Professor
VIGRE Activities: Undergraduate Colloquium Lecturer, Assistant for the Mini-course on Nonconvex Variational Problems and Applications Andrea Braides, Professor of Mathematics, University of Rome tor Vergata
VIGRE Activities: Lecturer at the Mini-course on Nonconvex Variational Problems and Applications 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 Erin Chamberlin, VIGRE Graduate Fellow
Julian Chan, VIGRE Graduate Fellow
David Chapman, Professor of Geology and Geophysics,
Dean Graduate School
VIGRE Activities: Internal Advisory Committee Member Suneal Chaudhary, VIGRE Assistant Professor
VIGRE Activities: GRE Preparation Course Organizer, Boot Camp Mentor Andrej Cherkaev, Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, VIGRE Assistant Professor Recruitment, REU Mentor, Co-Organizer and Lecturer for the Mini-course on Waves in Inhomogeneous Media, Co-Organizer of the Mini-course on Nonconvex Variational Problems and Applications Elena Cherkaev, Research Professor of Mathematics
VIGRE Activities: REU Mentor, Co-Organizer of the Mini-course on Waves in Inhomogeneous Media, Co-Organizer and Lecturer for the Mini-course on Nonconvex Variational Problems and Applications 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, Senior Seminar Assistant, Summer High School Program Assistant 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, Math Circle Mentor and Lecturer Eric Cytrynbaum, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer Tommaso de Fernex, Professor of Mathematics, University of Michigan
VIGRE Activities: Lecturer at the Mini-course on Arc Spaces and Motivic Integration Martin Deraux, Associate Instructor
VIGRE Activities: Lecturer at Mini-Course on Complex Hyperbolic Geometry Allen Dickson, VIGRE Graduate Fellow
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, Diversity Committee Chair, Lecturer at the Mini-course on Nonconvex Variational Problems and Applications Georg Dolzmann, Professor of Mathematics, University of Maryland
VIGRE Activities: Lecturer at the Mini-course on Nonconvex Variational Problems and Applications 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
VIGRE Activities: Math Circle Mentor and Lecturer, Assistant to the Summer REU Program on The Mathematics of Games of Chance Amanda Ellis, 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, Organizer of the Summer REU Program on the Mathematics of Games of Chance 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 Julia Gordon, Professor of Mathematics, University of Toronto
VIGRE Activities: Lecturer at the Mini-course on Arc Spaces and Motivic Integration 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 Christopher Hacon, Professor of Mathematics
VIGRE Activities: Assistant Professor Mentor, Co-Organizer of the Mini-course on Arc Spaces and Motivic Integration Robert Hannum, Professor of Statistics and Operations Technology, University of Denver
VIGRE Activities: Guest Lecturer at the Summer REU Program on "The Mathematics of Games of Chance" 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 Susan Hendry, Mathematics Department Accountant
VIGRE Activities: VIGRE Grant Accountant 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 Casey Johnson, VIGRE Graduate Fellow
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, Distinguished 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 MunJu Kim, Assistant Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer Sarah Kitchen, VIGRE Graduate Fellow
VIGRE Activities: Math Circle Mentor and Lecturer, Calculus Challenge Mentor, ACCESS Program Mentor Teresa Knudson, 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 Young-Seon Lee, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer David Levin, Assistant Professor of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Co-Organizer of Summer REU Program on the Mathematics of Games of Chance 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, Boot Camp Mentor Frank Lynch, VIGRE Graduate Fellow
VIGRE Activities: Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer, Math Circle Mentor, Summer REU Mentor Pejman Mahboubi, VIGRE Graduate Fellow
VIGRE Activities: GRE Preparation Course Mentor, Calculus Challenge Mentor
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, Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer Aaron McDonald, Graduate Student
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, Distinguished Professor and Chair of Mathematics
VIGRE Activities: Graduate Colloquium Lecturer, Undergraduate Colloquium Lecturer, Math Circle Lecturer, Lecturer at the Mini-course on Nonconvex Variational Problems and Applications Claudia Miller, Professor of Mathematics, Syracuse
University
VIGRE Activites: Lecturer at the Mini-Course on Classical Problems in Commutative Algebra Jeremy Morris, Undergraduate Student
VIGRE Activities: Undergraduate Colloquium Lecturer William Nesse, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer Michael Neubert, Associate Scientist at Woods Hole
Oceanographic Institution
VIGRE Activities: Lecturer at the Mini-Course on the Mathematics Behind Biological Invasions Elijah Newren, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer 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 Willis Petersen, VIGRE Graduate Fellow
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 Jason Preszler, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer 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
VIGRE Activities: Math Circle Mentor and Lecturer, Summer High School Program Assistant 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, Lecturer at the Mini-course on Nonconvex Variational Problems and Applications 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 Kazuma Shimomoto, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer 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 Amber Smith, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer Sandra Spiroff, VIGRE Assistant Professor
VIGRE Activities: Lecturer at the Mini-Course on Classical Problems in Commutative Algebra, Undergraduate Colloquium Lecturer, Graduate Colloquium Lecturer, Math Circle Mentor and Lecturer, Boot Camp Mentor, Commutative Algebra Seminar Organizer 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 Nessy Tania, Graduate Student
VIGRE Activities: Graduate Colloquium 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 Joro Todorov, Graduate Student
VIGRE Activities: Graduate Colloquium Lecturer 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, Lecturer at the Mini-course on Nonconvex Variational Problems and Applications 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
VIGRE Activities: Algebraic Geometry Seminar Organizer, Assistant for the Mini-course on Arc Spaces and Motivic Integration Willem Veys, Professor of Mathematics, University of Leuven
VIGRE Activities: Lecturer at the Mini-course on Arc Spaces and Motivic Integration David A. Vogan, Professor of Mathematics, MIT
VIGRE Activities: Undergraduate Colloquium Lecturer 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, REU Mentor, Graduate Colloquium Lecturer, Math Circle Lecturer Dali Zhang, Graduate Student
VIGRE Activities: 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, Boot Camp Organizer Back to Table of Contents ## Programs for High-School StudentsMATH CIRCLE 2004-2005By Peter Trapa The purpose of these notes is to document the activities of the Math Circle during the 2004-2005 academic year. The 2004-2005 Utah Math Circle met for two-hours weekly during the academic year. Average attendance hovered at about 18 students. Sessions were structured in the same way as they were in previous years, and so I won't recall further details here. In the three years I have coordinated the programs, this year was, in my opinion, the best. Part of the reason for the success was a stellar supporting cast of VIGRE students and postdocs. Crofts was an excellent assistant. Our postdocs Bell, Margalit, Spiroff, and Wright each led very nice sessions. This year was the first year we also had graduate students (other than the official assistant) lead sessions. Earnshaw, Kitchen, and Richins each did a fine job. The practice of having graduate students lead sessions should, in my opinion, become a permanent feature of the program. This year, as in past years, Sarah Strong and Kathleen Moore offered superb administrative support. The current webpage (maintained by Kathleen) is an excellent source of information for potential participants. Participant evaluations were almost uniformly positive. The most substantive comment was the the contests (of which there were five this year) were often perceived as too difficult. We might consider toning them down a little for next year. The Math Circle has now been running for four years. As is often the case, the first few years are the most difficult (and most critical). We've gotten over that hump. The program now has substantial momentum. I hope to build upon that again next year. Topics, in chronological order, were as follows: - Primality Tests and Cryptography (Peter Trapa, 2 weeks)
- Counting, Permutations, and Probability (Robert Bell, 2 weeks)
- Pigeon Hole Principle (Peter Trapa, 2 weeks)
- Nonlinear Root Finding (Grady Wright, 2 weeks)
- Fibonacci (Sandra Spiroff, 2 weeks)
- Preparation for the State Math Contest (Peter Trapa, 3 weeks)
- Sequences and the Difference Operator (Berton Earnshaw, 1 week)
- Introduction to Difference Equations (Berton Earnshaw, 1 week)
- Counting Infinite Sets (Peter Trapa, 1 week)
- Representations of Numbers (Scott Crofts, 1 week)
- Boolean Functions and Boolean Algebra (Scott Crofts, 1 week)
- Introduction to Permutation Groups (Sarah Kitchen, 1 week)
- Permutation Groups and Polynomials (Russell Richins, 1 week)
- Five weeks were devoted to contests
SUMMER HIGH SCHOOL PROGRAMBy Jim Carlson Jim Carlson returned from Cambridge, Massachusetts in June to direct the Summer Mathematics Program for High School Students, now in its sixth year. Three graduate students, Maria Scott, Matthew Clay, and Russell Richins, and one undergraduate assistant, Tim Simmons, an alumnus of the program, assisted him. Sixteen students participated, twelve from the Wasatch Front area and four from out of state (Arizona, Florida, Pennsylvania, and Texas). The VIGRE program provided the majority of the financial support for the program. The program ran for three weeks, four days a week, 8:30 a.m. to 4:00 p.m. In the morning sessions, students worked on number theory, learning about Diophantine Equations, modular arithmetic, properties of the primes, continued fractions, etc. After lunch, students attended a colloquium given by various faculty members whose topics ranged widely indeed: Ken Golden, "Sea Ice"; Klaus Schmitt, "Fractals"; Fred Adler, "Cicadas"; Peter Alfeld, "Hotel Infinity"; Stewart Ethier, "How Slot Machines Work"; Jim Carlson, "The Mathematics of Google"; Fletcher Gross, "How Did Archimedes Do It?"; David Dobson, "Smelborp Esrevni" (Inverse Problems); Davar Khoshnevisan, "The Marriage Problem". Graduate assistants Russ Richins and Matt Clay each gave one of the afternoon talks as well. We appreciate all of the colloquium speakers. The students enjoyed the talks, learned a lot, and were inspired (which is what this program is all about). The day ended with a 90-minute computer lab in which the students learned to program in Python and do experimental number theory with it. The program ended with a mathematical game show in the tradition of "Jeopardy," covering topics discussed during the program. The game show was followed by a viewing of the Nova documentary, "The Proof," the story of Andrew Wiles' proof of Fermat's Last Theorem. All in all this was a very successful year for the Summer Mathematics Program for High School Students. We had a more qualified applicant base than in previous years, refinements to the program made over the past several years helped this year's program run smoothly, and most importantly the students learned a lot while having a good time and gained a greater appreciation for mathematics. Back to Table of Contents ## Programs for Undergraduate StudentsACADEMIC YEAR REU PROGRAMBy 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 12 individual research projects, including those supported by VIGRE and NSF REU Supplements. The topics have included neural networks, fluid permeability of random pipe networks, asymptotic properties of time series, inverse problems, hyperbolic geometry, spiral composite materials, CAT(0) groups, Fourier analysis and wavelets. The participants ranged from freshmen to seniors, and three of these projects were conducted by women undergraduates. Many of our students have given lectures on their projects in a range of venues, including local seminars and national undergraduate conferences. Over the past three years, six of our REU students have journeyed to the Arctic for field experiments on sea ice, with additional trips to the Geophysical Institute at University of Alaska Fairbanks for collaborative laboratory and theoretical work. In the past year, one paper arising from an REU project has been accepted for publication in Mechanics of Materials, and three more have been submitted - to Econometric Theory, Games and Economic Behavior, and Biophysical Journal. Another paper will be submitted to Annals of Glaciology in October 2005, and at least seven other publications from already completed REU projects, involving undergraduates as co-authors or authors, are expected. This list includes three papers from the six week Summer 2005 REU on Mathematics of Games of Chance, run by Stewart Ethier. Out of six REU publications either accepted or submitted in 2005, four involve women undergraduates. Since the inception of the REU program in 2001, about 72 students have participated. Of these, we know of 47 students who have graduated, and some are still in the program. Among the students who have graduated, 30 have entered graduate or professional schools, most of them in mathematics or closely related areas. At least another 3 who have graduated are working in industry in mathematically related areas such as software engineering, genetic analysis, and financial services. 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 five years from 2000 to 2004, the values of M have been 160, 158, 206, 223, and 247. In 2005 the number of declared majors is 313, so that M will be greater than 313. Thus, since the beginning of VIGRE in September 2001, the number of math majors at the University of Utah has effectively doubled. Back to Table of Contents SUMMER REU GROUP PROGRAMBy Stewart Ethier The Summer 2005 REU Program on "Mathematics of Games of Chance" was held at the University of Utah during the six-week period June 6 to July 15, 2005. The first goal of the program was for the students to become familiar with an interesting and historically important application of probability, namely the mathematics of gambling. (We used "games of chance" in the title at the request of the chairman to avoid negative publicity.) We attempted to accomplish this by presenting lectures from Stewart Ethier's unfinished book manuscript titled \textit{Probabilistic Aspects of Gambling}. On June 6 the book was about 75 percent finished (about 450 pages), and we provided a bound copy for each participant at department expense. The second goal of the program, and certainly the more important one, was for each student to complete a research project on a topic related to gambling or games of chance. The lectures were given by Stewart, with David Levin and graduate students Berton Earnshaw and Lars Louder assisting in the program. A total of ten students participated. Five students were from the University of Utah and the remaining five were from out of state (UC Berkeley, MIT, Cornell, Rutgers, and Duquesne). One participant was denied funding because he had just graduated and was technically no longer an undergraduate. The planned format of the program was to meet for two hours each morning for lectures, with one hour in the afternoon devoted to a computer lab run by David and another hour devoted to a problem session run by Berton and Lars. The topics of the lectures were as follows. Week 1: overview, house advantage, gambler's ruin, betting systems. Week 2: game theory, bold play, Kelly system, card theory. Week 3: slot machines, roulette, keno, craps. Week 4: house-banked poker, video poker, faro, baccarat. Week 5: trente et quarante, blackjack, poker. Week 6: student presentations. While some of these topics may not sound very deep, it should be noted that the mathematical level of the program was at least as high as that of our 5040 course (stochastic processes and simulation). The lectures on poker (four hours) were presented by a guest speaker, Robert Hannum of the University of Denver. We had to find another source to fund his expenses and honorarium, because we learned after he was invited that there was no money in the REU budget for outside speakers. The students especially enjoyed these lectures. Attendance at the regular lectures was excellent for the first two weeks, and then started to drop off, settling at about 50 percent. Many of the students had difficulty arriving by 9 in the morning. The computer labs covered MatLab and LaTeX but were discontinued near the end of the second week due to lack of student interest (it is likely that most students already had some familiarity with these topics). The plan for the problem sessions was to have students work about four problems each day, but the students voted to discontinue the problem sessions before the end of the first week because no one was doing the problems and they preferred to use the time to play frisbee, according to Berton. On the first day we handed out a list of 16 potential research projects, and by the third day each student had chosen a project from the list. (One more project was added to the list for a student who couldn't find a project on the original list that interested him.) We scheduled half-hour meetings with the students once a week in the afternoons to make sure they were making good progress. These meetings were very helpful and probably should have been started during the second week rather than the third week. (Originally, we thought it would take them longer to decide on a project.) With only six weeks, some students ran out of time. Each student gave a presentation during the final week, describing what he or she had accomplished. Some gave PowerPoint presentations, while others used the blackboard or an overhead projector. During the program several social/recreational activities were arranged. We hiked Grandeur Peak in Millcreek Canyon followed by dinner at a restaurant, and we had a picnic at Mirror Lake, despite up to three feet of snow in mid June. We also had a barbecue at Stewart's house in Wanship. A planned weekend trip to Arches National Park did not materialize. Of course there was no money in the budget for any of these activities. At the end of the program none of the students had finalized his or her project, but one did within two weeks. We wrote to the the other nine, explaining why it was important to turn in their final reports. (One reason was to ensure they they get credit for their results, and another was to establish that they have research experience, which may be useful if they apply to graduate school.) This produced six responses, with the three others ignoring the message. In future I would suggest withholding the final stipend payment until a final report is received. There should be some accountability on the part of the students.
The quality of the research done by the students varied considerably, though it must be acknowledged that some of the projects were more accessible than others. At least three of the students obtained publishable results, while most of the others obtained results that were either not deep enough or not conclusive enough for publication. One student, a sophomore who turned out to be too immature for the program, accomplished nothing. Another student had a death in the family and had to quit the program early. Neither of these two students responded to our request for a final report. Was the program a success? Overall, yes. Certainly, the students were given an excellent opportunity to see if they were well suited to doing mathematical research. Not all of them took full advantage of this opportunity, but several did and their results speak for themselves. For example, one student has already submitted his paper to a professional game theory journal. Thus, the main goal of the program, from the perspective of the NSF, was clearly met. On the other hand, the level of interest in the subject by the students, as reflected by their cancellation of the problem sessions, their poor attendance at the lectures, and their apparent unwillingness to read the manuscript, was a disappointment. From the perspective of the principal organizer, the program was a partial success. Five of the students have provided abstracts of their research with two others promising to send them later, and these can be found at http://www.math.utah.edu/vigre/reu/summer05/ Back to Table of Contents UNDERGRADUATE COLLOQUIUMBy Gordan Savin The Undergraduate Colloquium is presently organized by Angie Gardiner and Gordan Savin (after Jim Carlson and Nat Smale). It meets weekly. 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 5 and 14 students formally enrolled in the Fall 2004 and Spring 2005 semesters, respectively. The general attendance was about 20 during the Fall term, but it was considerably greater during the Spring term in large part due to increased enrollment. The speakers were our regular faculty, instructors, visitors and an undergraduate student reporting on REU. We had a total of 27 lectures. The following is a selection of talks: - Peter Alfeld: What can you do with a slide rule?
- David Vogan (MIT): Diagonalizing Group Actions.
- Jeremy Morris (REU): How Big is the University of Utah?
- Fletcher Gross: Rubik's Cube.
- Andrejs Treibergs: Symmetrization and the Isoperimetric Inequality.
- Klaus Schmitt: How can one generate a "brocciflower" using simple mathematics?
- Fred Adler: Why are there so many Common Colds?
- Aaron Bertram: Waring's Problem for Integers and Polynomials.
- Davar Khoshnevisan: Counting After Cantor.
Back to Table of Contents ACCESS PROGRAMBy 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 over 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 2005. He was assisted by VIGRE graduate student Sarah Kitchen. In addition, math IGERT student Meagan McNulty was the teaching assistant for the entire eight week course. 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. Sarah 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 led by Sarah and Nick 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 anaolgy 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. Jon also mentioned recent genetic work on whale lice which his group has undertaken to reconstruct the family tree for right whales, and the fact that a former ACCESS student played a key role. 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. Meagan gave a 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. This is close to her own research interests in mathematical biology, namely the lung and cystic fibrosis. 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 1800's. 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, some with former ACCESS students. For more information on the ACCESS program, go to http://www.science.utah.edu/access.html. For more details about this year's mathematics component, go to http://www.math.utah.edu/~korevaar/ACCESS2005. Back to Table of Contents Presentation SeminarBy Nick Korevaar We have been running a version of the presentation seminar since the 2002-2003 academic year, as a way for REU students to - hear about some interesting math from some of their peer Math majors, and maybe make some new friends.
- experience the process of preparing for and making a mathematical exposition.
- take a step towards making presentations elsewhere.
The seminar was held on Wednesday afternoons of spring semester, roughly bi-weekly, starting at 4:00 pm and continuing for about an hour. Having learned from previous years that it is a good idea to help the presenters prepare, we met with each speaker at least once before their presentation for a run-through. We also encouraged students to speak with their REU mentor about presentation ideas and strategies. Mentors were also encouraged to attend their students' presentations. We tried to keep presentations informal and to encourage questions; we were usually successful. Following are the titles of presentations with the names of the presenter and mentor. - Jeremy Morris(2/9): "How big is the University of Utah"
Faculty Mentor: Peter Trapa - Nancy Newren (2/23): "Tri-trophic systems: predator, prey,
and pasasitoid"
Faculty Mentor: Janet Andersen - Kellen Petersen (3/9): "Composite materials"
Faculty Mentor: Graeme Milton - Jeremy Pecharich(4/6): "Actions and Voyages through CAT(0) Space"
Faculty Mentor: Robert Bell - Adam Gully (4/13): "Electromagmetic Responses of Sea Ice"
Faculty Mentor: Ken Golden - Will Newton (4/20): "Stability results for the caterpillar-
grass-wasp tritrophic system"
Faculty Mentor: Janet Andersen
Back to Table of Contents Problem Solving ContestBy Dan Margalit This past year, I was the faculty advisor for the undergraduate problem solving contest. The basic goal of the contest is to engage students' interest in mathematics by posing interesting problems and offering prizes for correct solutions. My basic function was to meet with Mark Thomas, the undergraduate coordinator, and discuss problems for possible use in the contest. Mark was in charge of posting the problems, checking the submitted solutions, and posting the solutions. Angie Gardiner provided invaluable assistance, in the form of sending emails to undergraduates, posting winners on the bulletin board, and handling the prizes. Problems were posted approximately once per month. Solutions were submitted to the front desk in the main office. At the end of the year, the overall winner, Aaron Wood, and Mark Thomas attended MathFest in Albuquerque, NM (at the expense of the department) to participate in the national competition. Last year, Mike Hoffman (the undergraduate coordinator) took second place in the national competition at MathFest. I have not been able to contact Aaron or Mark since the contest. There were 7 contests throughout the year, posted approximately once per month. The following is a table listing the number of responses, the number of correct solutions, and the winner for each problem. The winning solution is the first correct solution.
Aaron Wood was declared the winner since he was the winner for two problems, as was Neil McBride, and Aaron handed in the most (6) correct solutions overall. Two students (Wood and McBride) participated in all 7 problems. Darren Bartholemew did 6, Ryan Shepherd did 5, and everybody else did 3 or fewer. I am told that one teacher in the deparment offered extra credit for sutdents who participated in Problem #2, hence the large number of participants. One measure of the success of the contest is that we had 26 different students do at least one of the problems. Also, I think that Mark Thomas's critical thinking and organizational skills particularly benefitted from the experience. He came up with a couple of the problems himself, and in other cases altered problems he found elsewhere. Some points of possible improvement for next year: - Should we have more frequent problems?
- Can we encourage other teachers to offer extra credit?
- Should the problems be easier? harder? Should they have easy parts and then harder parts?
- Is there a better system than rewarding the first solution as the winner?
- Should we better define the undergraduate coordinator's job?
Back to Table of Contents ## Programs for Graduate StudentsGraduate ColloquiumBy Josh Thompson The Fall 2004 GSAC Colloquium began with a series of talks given by Postdoctoral and Visiting Professors. Topics ranged from "Braid Groups" to "A Mechanistic Model for Seed Dispersal". The next two month's talks were given by several graduate students and Assistant Professors here at the University of Utah. In keeping with the goals of this colloquium, the speakers gave introductory lectures on their current research interests or related field. Questions came from those outside of the speaker's specialty. The last six talks were given by graduate students with topics including "Twin Prime Numbers" and "Cardiac Dynamics". There were fifteen talks given this fall semester. Each talk of Spring 2005 GSAC Colloquium was given by a University of Utah graduate student. Titles of talks given included "A Journeu into Outer Space" and The Role of R _{0} in Epidemiology". Many talks given related strongly to those given in previous weeks and previous GSAC Colloquia. This overlap in content helped to bring continuity to the GSAC Colloquium as a whole. There were ten talks given in the spring semester.
The colloquium was well attended by a broad range of individuals. This range included graduate students (many of whom where in their first two years of study), members of the faculty, and some undergraduates. The 2004-2005 GSAC Colloquium served both as a forum for budding mathematicians to hone their exposition skills, and to provide young graduate students an introduction into modern mathematics and its uses. Back to Table of Contents TA/TF TrainingThe following is a schedule of events for the TA workshop:
Back to Table of Contents Mini-course on "Arc Spaces & Motivic Integration"By Aaron Bertram & Christopher Hacon This spring, through the support of the department's VIGRE grant and local funds, the University of Utah held a mini-course on the "Arc Spaces and Motivic Integration". The aim of the course was to introduce graduate students to the the theory of Motivic Integration. The main speakers were Manuel Blickle (University of Essen), Tommaso de Fernex (University of Michigan), Julia Gordon (University of Toronto) and Wim Veys (University of Leuven). Each speaker gave 5 lectures. The topics covered included a detailed introduction to the theory of geometric motivic integration for smooth complex varieties, applications of motivic integration to the study of invariants in birational geometry (such as a characterization of the log canonical threshold of a pair in terms of dimensions of the jet spaces, Batyrev's stringy invariants, Kontsevich's theorem on the Hodge numbers of birational Calabi-Yau's, "stringy Chern classes") as well as some topics in arithmetic motivic integration (such as Weil's theorem that relates p-adic volume with counting points over a finite field and a cell decomposition theorem for p-adic integrals). Several exercise sessions and informal discussions were organized in the afternoons. The course was well attended. The local students were: Renzo Cavalieri, Erin Chamberlin, Ken Chu, Sarah Kitchen, Fumi Sato, Kazuma Shimomoto. Students also attended from other institutions through the support of the VIGRE grant or their own funding: Lauri Ojala (University of Helsinki), Peter Petrov (University of Georgia), Michael Rose (University of Wisconsin-Madison), Zachary Treisman (University of Washington) and Cornelia Yuen (University of Michigan). Various post-docs and regular faculty from the Univ. of Utah also attended the mini-course. The course seemed to be very successful. In a relatively short period of time, the students were introduced to this very interesting and active field of research. The speakers provided lectures that ranged from a gentle introduction to the subject to current research topics. It seemed that all students were able to benefit from at least part of these lectures. The size of the course was relatively small compared to a standard conference and most of the attendees were graduate students. This more informal setting gave the students the opportunity to meet faculty and students at other institutions and to learn about what they are doing. The students were able to discuss the material and exercises from the course directly with the speakers (and of course with each other). The more advanced students were also able to get feedback on their research projects from experts in the field. Students we talked to were very enthusiastic about the mini-course, and eager to attend future such courses at the University of Utah. We are also quite satisfied with the outcome, and we would like to mention in particular that Kathleen Moore and the rest of the staff did a superb job of helping the course to run smoothly for all participants. Back to Table of Contents Mini-course on "Nonconvex Variational Problems & Applications"By Elena & Andrej Cherkaev This May, thanks to the support of the department's VIGRE grant, the Math Department of the University of Utah held a mini-course on the "Nonconvex Variational Problems and Applications". The course was designed to introduce graduate students to one of the key areas in the calculus of variations/PDE. The cost was shared with the Army Research Office through the research grant of Andrej Cherkaev. There were two main speakers invited. Professor Andrea Braides, Mathematics, University of Rome Tor Vergata, Rome, Italy, presented the ten-hours course "From Discrete Systems to Continuous Variational Problems." Professor Georg Dolzmann, Math, University of Maryland, College Park, MD, presented the ten-hours course "Macroscopic Models for Phase Transforming Materials" These courses were supplemented by the lectures by the faculty of local math department. Tutorials were organized by Marian Bocea; they included introduction to convexity, nonconvex variational problems, and Young measures. The local lecturers presented a broad spectrum of topics. Andrej Cherkaev lectured on introduction to irregular variational problems and on new results on polyconvexity. Klaus Schmitt discussed classical and modern results in variational inequalities. David Dobson discussed optimization of eigenvalues, Clark gradient and nonsmooth optimization. Graeme Milton gave lectures on thermodynamics and nonconvexity of entropy. Elena Cherkaev discussed nonconvex energies and variational approaches in image reconstruction. Andrejs Treibergs gave two lectures on variational problems in geometry. Two guest lecturers (the visiting faculty) were invited. Professor Smyshlyaev, University of Bath, UK, and Professor Grabovsky, Temple University, gave lectures about their current research. The course was fairly well attended. The students were: Daniel Onofrei, Worcester Polytechnic Institute, Cristina Popovici, Carnegie Mellon University, Tadele Mengesha, Temple University, Jungho Lee, Courant Institute, New York University, and Dali Zhang, Lyubima Simeonova, An Le, Nathan Albin, Seubpong Leelavanichkul, Carlos Bonifasi-Lista, Yuan Zhang, University of Utah. The course was a success. The lectures by the top world experts in the field were very informative. The active informal discussions helped the students to be exposed to very active research area. The atmosphere was friendly and local students took care of the visiting ones. Area of the needed improvement. The VIGRE constraints of the
support for USA citizens/residents is discouraging for able foreign
graduate students. Some advisers do not recommend the VIGRE school to
their foreign students. We are thankful to NSF for the support of the
school, but we strongly recommend to
lift the constraint of citizenship which does not make much sense
in the graduate education. Most of the graduate students in math,
both American and foreign, will become a part of USA academic
community. Dividing them for nonacademic reasons is counterproductive.
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