VIGRE

REUs (Research Experiences for Undergraduates)

ALPs

Individual REUs

2000-2001 Individual REUs:

1. Michael Baym worked with Prof Michael Bennett on a project in analytic number theory in fall 2000.
2. In spring 2001, Michael Baym worked with Prof. Nigel Boston on another number theory project.
3. Matt Wolak had an REU with Prof. Nigel Boston in cryptography, where he studied breaking the NTRU cryptosystem and signature scheme (see www.ntru.com).
4. Philip Spencer worked with Prof. Julian Palmore on an REU in spring 2001. In this REU, Philip Spencer worked on chaos and fractals, specifically describing fractals by three methods - arithmetic, dynamic, and geometric. He presented his results to the students taking Math 351, History of Mathematics and Physics, a course introduced by Prof. Palmore.
5. Carey Radebaugh pursued an REU under the supervision of Prof. Iwan Duursma. The topic was Rubic’s Tube, specifically the effect of locally defined boundary conditions on global behavior of binary tilings.

2001-2002 Individual REUs:

1. Under the supervision of Nigel Boston (faculty member), two students (Michael Baym and Matthew Wolak) initiated REUs working on listening to smartcards. They looked for a correlation between the radiation emitted by the card and the operations performed by the card.
2. David Deuber completed an REU under the supervision of Andreas Stein (faculty member) in computational number theory.
3. Ricardo Astudillo completed an REU with A. J. Hildebrand (faculty member). He studied properties of sign change sequences, a topic that he began studying in the summer during the NSF VIGRE Summer REU program at UIUC.
4. Graham Evans and John D’Angelo supervised an individual REU with Emily Riehl (Normal, Illinois) on two different problems about polynomials in several variables. Both joint ventures produced papers that are soon being submitted to major mathematics journals. Funding of this REU was provided from REU funds in John D’Angelo’s NSF grant DMS 02-00419, augmented by departmental funds. Emily Riehl is going to be a Harvard freshman in fall 2002.

1. Doug West (faculty) with Noah Prince
   Pagenumber and Decomposition of Graphs
   Fall 2002
2. Christopher French (VIGRE Research Assistant Professor) with Ben Lundell
   Topics in Knot Theory from The Knot Book by Colin Adams
   Fall 2002
3. George Francis (faculty) with Wendy Hubbard
   Evaluation and Adaptation of Certain Geometrical Software Packages Suitable for Current Undergraduate Mathematics Courses at UIUC
   Fall 2002
4. Richard Sowers (faculty) with Melanie Lang
   Instability of Dynamical Systems and Arnold Diffusion
   Fall 2002
5. Julian Palmore (faculty) with Vivek Srikrishnan
   Modeling in Dynamical Systems and the Construction of Attractors
   Spring 2003

1. Tyler Smith and Patrick Szuta (together with Jonas Grigaliunas) had individual REUs through coordinated interaction with Robert Ghrist in summer 2003. They worked on a variety of problems in configuration complex geometry, computational Cech homology and self-assembly experiments.
2. Konstantin Drapkin has an individual REU with John D’Angelo in summer 2003. He worked on generalizations joint work of D’Angelo, Kos, and Riehl that emerged froma previous REU that Emily Riehl had with John D’Angelo.
3. Ben Lundell had an individual REU with Chris French in summer 2003. They worked on knot invariants.
4. Edward Kung pursued an individual REU with Donald Yau during summer 2003. This led to an interesting short publication on finding a matrix of a given sign pattern and line sum.
5. Ben Emrick conducted individual REUs with Matt Ando in summer 2003 and fall 2003. They worked on a range of problems in topology generally, and homotopy theory in particular.
6. Noah Prince had an individual REU was in fall 2003 with Alexandr Kostochka on graph minors.
7. Ben Lundell had an individual REU with Randy McCarthy in fall 2003. He studied the fundamental group and veering spaces, using various texts.
8. Ben Lundell had an individual REU with Steve Ullom in spring 2004. His project was rational points on elliptic curves and Mordell's theorem. Now he is looking at group laws on singular quadrics.
9. Serge Posudevsky had an individual REU in spring 2004 with Serge Ivanov. He focused his research on topics in the texts by Algli Papantonopoulou, “Algebra: Pure and Applied” and M. I. Kargopolov, “Fundamentals of the Theory of Groups.”
10. Noah Prince and Lucas Wiman had REUs with Douglas West in spring 2004. They studied the Union-Closed Conjecture, often attributed to Peter Frankl from around 1979.
11. Tyler Smith held an individual REU with Randy McCarthy in spring 2004. He worked on a variety of topics in topology and category theory.
12. Joseph Laracy had an individual REU with Julian Palmore in spring 2004. He designed a cryptographic coprocessor (a VHDL implementation of RSA), and in the process learned a great deal of mathematics in a wide scope of topics.
13. Patrick Szuta is pursuing an individual REU with Andres Stein in summer 2004. He is working on the factoring of integers with elliptic curves and applications.
14. Andrew Webster has an individual REU with John D’Angelo in summer 2004. He is working on number-theoretic properties of certain invariant polynomials discovered by John D'Angelo in his work on CR geometry.
15. Blair Flicker is participating as in the group REU being conducted by Peter Brinkmann and George Francis in summer 2004. But his task will also be individualized according to earlier plans to study geometric visualization.
16. Ben Lundell will be working on an individual REU in summer 2004 with Iwan Duursma, and a first year graduate student Jason McCullough. The plan is to study problems in coding theory and algebraic geometry.

Summer Group REUs

The initial plan was to have summer REUs, in groups of about 18 students each time, during the summers of 2001 and 2002 since the funding for the UIUC VIGRE program came too late to advertise and run a program in the summer of 2000. The demand for the summer program for 2001 was so great, with 26 participants from all around the country, and all of the summer REUs were so successful this first time, that an expansion of the program to accommodate between 20 and 30 students is being planned for subsequent years.

Summer 2001 Group REUs:

1. Prof. George Francis organized a group summer REU around computational mathematics and computer visualization that had 9 students. Dr. Karen Shuman, one of our NSF VIGRE postdoctoral faculty members, assisted him. See the appendix for further information about this program. This group’s participants were
   • Benjamin Bernard (UIUC)
   • Benjamin Farmer (UIUC)
   • Mark Flider (UIUC)
   • Douglas Nachand (UIUC)
   • Alison Ortony (UIUC)
   • Lorna Salaman (U. of Puerto Rico)
   • Benjamin Shanbaum (UIUC)
   • Robert Shuttleworth (Youngstown State)
   • Matthew Woodruff (UIUC).

2. Prof. Bob Muncaster conducted a group REU focused on game theory, Markov chains, and basic evolutionary theory that had 10 participants. This group REU built from the continued involvement of Prof. Muncaster with faculty members in the Department of Political Science. This group’s participants were
   • Tina Carpenter (U. of Idaho)
   • Ethan Coon (U. of Rochester)
   • William Cuckler (UIUC)
   • Pritam Dalal (UCBerkeley)
   • Natasha Fast (UIUC)
   • Tom Ferrone (UIUC)
   • Asher Kach (UIUC)
   • Matthew Lee (Harvard)
   • Stephanie Olson (UIUC)
   • David Smyth (UIUC).

3. Profs. A. J. Hildebrand and Alexandru Zaharescu supervised a group REU in number theory with 7 students. The program consisted of short courses and lectures, weekly seminars, group meetings, and individually supervised research, and concluded with two sessions of student presentations. The two short courses were on Farey Fractions and Applications and on Finite Automata in Number Theory. This group’s participants were
   • Rich Astudillo (UIUC)
   • Evan Borenstein (U. of Virginia)
   • Michael Comerford (Princeton)
   • David Dueber (UIUC)
   • Alan Haynes (UT Austin)
   • David Weaver (UNC-Chapel Hill)
   • Jiashen You (U. of Hawaii).

For additional information about the summer 2001 REUs, see the webpage at www.math.uiuc.edu/VIGRE/reu/reu_01.html

Summer 2002 Group REUs

Four summer REU programs were held in summer 2002, with a total of 22 student participants. A new REU program in topology and fractal geometry was held in addition to the programs that ran in summer 2001.

1. Professor Slawomir Solecki led an REU group in topology, both point-set topology and fractal geometry. The topic area offers many very interesting topics worthy of study. Also, there are a number of open problems that are accessible to undergraduate students in these areas, especially in issues connected with the dimension of fractals. This group’s participants were:
   • Prudence Heck (Rutgers)
   • Bryce Johnson (Washington U.)
   • Christopher Jones (Youngstown)
   • Michael Mulligan (UIUC)
   • Patrick Watts (Augustana)

2. Professor George Francis again organized a group summer REU around computational mathematics and computer visualization. Six students participated:
   • Amit Chatwani (Princeton)
   • Ben Farmer (UIUC)
   • Michael Henry (Augustana)
   • Abdul Hamide (Xavier)
   • Wendy Hubbard (UIUC)
   • Yana Malysheva (UIUC)

3. Professor Bob Muncaster conducted a group REU focused on game theory, Markov chains, and basic evolutionary theory that has 5 participants. This group’s participants were:
   • Whitney Bush (Bradley)
   • Kristie Engemann (UIUC)
   • Ana Pavasovic (College Intl)
   • Ken Scheiwe (UIUC)
   • Tim Teravainen (New College Florida)

4. Professor A. J. Hildebrand supervised a group REU in number theory with 6 students. The program was like the previous summer’s program with modification to fit the new group of students. This group’s participants were:
   • Sharon Chuba (Penn State)
   • David Dueber (UIUC)
   • Aleck Johnsen (UIUC)
   • Paul Pollack (Univ. of Georgia)
   • Jeremy Rouse (College Intl)
   • Erin Wolf (UIUC)

For additional information about the Summer 2002 REU activities, see the webpage www.math.uiuc.edu/VIGRE/reu/reu_02.html.

Summer 2003 Group REUs

1. Bob Muncaster conducted a group REU focused again on game theory, Markov chains, and basic evolutionary theory that has 6 participants. This group’s participants were:
   • Andrew Badr (UIUC)
   • Aubrey da Cunha (Iowa State)
   • Robert Fitzgerald (Arizona State)
   • Kapil Kamdar (UIUC)
   • Anatoly Kats (Carnegie Mellon)
   • James Urick (Rochester Institute)

2. Kim Whittlesey conducted a group REU focused on geometric group theory. This REU group consisted of 7 people This group’s participants were:
   • Jesse Beder (U of Chicago)
   • Vishal Doshi (UIUC)
   • Kalina Gospodinova (Whittier College)
   • Jacobus Machalow (UIUC)
   • Eric Radke (Case Western Reserve)
   • Andrew Webster (UIUC)
   • Ian Wyckoff (U of Arizona)

For additional information about the Summer 2003 REU activities, see the webpage www.math.uiuc.edu/VIGRE/reu/reu_03.html.

Summer 2004 Group REUs

1. George Francis and Peter Brinkmann are conducting the group REU on geometrical computing illiMath2004. This is an improved and updated version of the previous REUs run by George Francis in the summers 2001, 2003 This REU group consisted of 6 people This group’s participants were:
   • William Baker (UIUC)
   • Benjamin Kauk (UIUC)
   • Gregory Stanton (UIUC)
   • Emily Gunawan (Wells)
   • Brett Witt (UIUC)
2. Kim Whittlesey conducted a group REU focused on geometric group theory. This REU group consisted of 6 people. This group’s participants were:
   • Seth Case (UIUC)
   • Adam Levine (Harvard)
   • Aja Johnson (Elon)
   • Xin Jia Johnson (UCLA)
   • Tyler Smith (UIUC)
   • Christopher Spicer (Mt. Mercy)
3. Bob Muncaster conducted a group REU focused on mathematical modeling of social and political issues. This REU group consisted of 5 people. This group’s participants were:
   • James Freitag (UIUC)
   • Mathew Louis-Rosenberg (Swarthmore)
   • Alina Marinova (Bard)
   • Janeta Marinova (Bard)
   • Jennifer Mo (Northwestern)

For additional information about this summer's activity, see our webpage www.math.uiuc.edu/VIGRE/reu/reu_04.html.