VIGRE

ALPs (Across Level Peers)

ALPs

Under supervision of the VIGRE administrative team, two additional types of peer groups have been formed to carry out mentoring and interpersonal, professional support. The first type of group is Across Level Peers (ALPs) which includes undergraduate students, graduate students, and faculty of all types in groups to pursue a variety of agendas allowing for a wide-ranging discussion of career plans, and to give general personal support. The other type of group is Research Among Peers (RAPs) which includes graduate students, postdoctoral associates and other faculty. These groups will focus more on the specific research interests of the members, and be a source for consultation in the forming, presentation, and dissemination of research work. Both ALPs and RAPs are meant to be peer groups, but not necessarily peers in the sense of age or professional development peers. They are peer groups in the sense of being aligned by common interests and objectives.

Across Level Peers (ALPs) conducted to date include:

1. In Fall 2000 Prof. Nigel Boston organized an ALP in basic cryptography, meeting once a week. It involved undergraduate students, beginning graduate students, and faculty members. They started with an analysis of the new cryptosystem NTRU. The participants included undergraduate students Michael Baym, David Duebner, Carey Radebaugh, Matt Wolak. Michael Baym, Carey Radebaugh, and Matt Wolak also were REU participants with support from the UIUC VIGRE program. The faculty participants included: Profs. Blahut (ECE), Duursma (Math), Ralf Koetter (ECE), and Andreas Stein (Math). The graduate student participants included students who gave talks: Bogdan Petrenko (Math), Haris Domazet (Math), Diana White (Math), John Jossey (Math), Jake Wallace (Math), Colin Ferguson (Math), and also other students who participated: Katia Hayati (Math), Negar Kiyavash (ECE), Adam Slagell (CS), Yihsiang Liow (CS), and Han Duong (Math). See www.math.uiuc.edu/~boston/infoprot.html for more information.

2. In Fall 2000 George Francis (faculty member) led an ALP that focused on information technology at the university in undergraduate mathematics courses. Prof. George Francis worked with a group of 8 undergraduate students who had been taking a geometric modeling course. The ALP was built around the abuses of linear algebra non-math courses in engineering and sciences. The student participants were Angela Bennett, Brodie Bertrand, Mark Flider, Aaron Guitierrez, Jessica Jackson, Byron Persino, Ben Shanbaum, and Doug Nachand. Stuart Levy (NCSA), John Sullivan (Math), and Paul Schupp (Math) also were involved in this ALP.

3. Prof. Bruce Berndt has led an ALP in q-Series for the past three years (2001-2003) including meeting during the summer months. About ten people regularly attend the seminar. These include the graduate students of the convener, Bruce Berndt, a few other interested graduate students, and one or two postdocs. Berndt frequently gives lectures on open problems accessible to graduate students. Other semniar participants alsolecture on either his or her own work or from a book on q-series such as the book Basic Hypergeometric Series and Applications by N.J. Fine, or more recently lectures have been given from Basic Hypergeometric Series by G. Gasper and M. Rahman. About two years ago, one of the problems suggested by Berndt arose from a preprint by
Zhi-Guo Liu, a mathematician in Shanghai. After nearly two years of efforts, a paper by two of the seminar participants, Liu, and Berndt was completed. This 18 page paper will soon appear in Quarterly Journal of Mathematics (Oxford). Berndt also suggested a long term project to which several seminar members have contributed. After over two years of work, a 49 page manuscript with eight authors has emerged that will soon be submitted for publication.

4. In Spring 2001, Profs. Harold Diamond and A. J. Hildebrand organized a "Problem Solving Seminar" within the VIGRE ALP framework. Intended as a follow-up to the training sessions for the Putnam Exam, which Diamond and Hildebrand have been offering for many years during the fall semester, the seminar was aimed at a similar audience of students with an interest in, and talent for, mathematical problem solving, but was more intense and demanding than the training sessions. In contrast to the training sessions, the seminar was offered as a regular course for which students could earn credit, including honors credit.

Four students participated in this seminar (David Dueber, Chong Kian Soh, David Smyth, and Dennis Turpin). The students were asked to choose problems from problems sections of journals such as the American Mathematics Monthly, work on these problems under the guidance of faculty, write up their solutions, and, if possible, submit the solutions to the journal. Diamond and Hildebrand each supervised two of the students, who would work on the problems individually, and meet with their advisor on a regular basis to discuss progress - in much the same way as a thesis student meets with his/her advisor.

Periodic group meetings provided the students an opportunity to present their solutions in front of an audience, receive feedback from their peers, and exchange ideas. At the end of the semester, a compilation of all the solutions obtained by the students was prepared and distributed among the participants. Several of these solutions have been submitted to the journal in which the problems appeared.

5. Robert Muncaster and Mark Anderson conducted an ALP on Evolutionary Game Theory in fall 2002. This activity has existed in less organized forms over several years as an ongoing interaction between students and faculty in the Departments of Mathematics and Political Science.

6. A. J. Hildebrand and Alexandru Zaharescu (faculty members) led the Putnam Examination preparation seminars in Fall 2002.

7. Robert Ghrist conducted an ALP in spring 2003 on Engineering Self-assembly. This new activity involves nearly a dozen undergraduate and graduate students from several departments in ongoing discussions and presentations on the important engineering problem of stable, effective self-assembly. For more information, see http://www.math.uiuc.edu/~ghrist/SA.html.

8. Robert Ghrist conducted an ALP in Spring 2004. The topic for this ALP was on those features of robotics problems which are most geometric. This meant reading works in motion planning, localization and mapping, complexity, and visualization. The group was composed of 7 graduate students and 4 undergraduate students.