|There are two types of REUs sponsored by the VIGRE grant,
individual year REUs and summer REUs.
Each student participating in an individual REU has a faculty supervisor.
The supervisor and student agree together on a research activity, which
involves independent research, possibly in conjunction with study of the
existing literature. The undergraduate student is paid a stipend of $2,000
for an individual REU. REUs proved to be an excellent opportunity for students
to gain insight into the nature of mathematical research, while also learning
much more about an area of mathematics that interests them.
2000-2001 Individual REUs:
- Michael Baym worked with Prof Michael Bennett on a project in analytic
number theory in fall 2000.
- In spring 2001, Michael Baym worked with Prof. Nigel Boston on another
number theory project.
- Matt Wolak had an REU with Prof. Nigel Boston in cryptography, where
he studied breaking the NTRU cryptosystem and signature scheme (see
- 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.
- Carey Radebaugh pursued an REU under the supervision of Prof. Iwan
Duursma. The topic was Rubicís Tube, specifically the effect of locally
defined boundary conditions on global behavior of binary tilings.
2001-2002 Individual REUs:
2002-2003 Individual REUs:
- 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.
- David Deuber completed an REU under the supervision of Andreas Stein
(faculty member) in computational number theory.
- 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
- Graham Evans and John DíAngelo 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 DíAngeloís NSF grant DMS 02-00419, augmented
by departmental funds. Emily Riehl is going to be a Harvard freshman
in fall 2002.
2003-2004 Individual REUs:
- Doug West (faculty) with Noah Prince
Pagenumber and Decomposition of Graphs
- Christopher French (VIGRE Research Assistant Professor) with Ben Lundell
Topics in Knot Theory from The Knot Book by Colin Adams
- George Francis (faculty) with Wendy Hubbard
Evaluation and Adaptation of Certain Geometrical Software Packages Suitable
for Current Undergraduate Mathematics Courses at UIUC
- Richard Sowers (faculty) with Melanie Lang
Instability of Dynamical Systems and Arnold Diffusion
- Julian Palmore (faculty) with Vivek Srikrishnan
Modeling in Dynamical Systems and the Construction of Attractors
These research experiences are for undergraduate students. The summer REUs
are planned as group activities with one or more faculty supervisors, and
perhaps graduate students as assistants. These programs typically run for
8 weeks during the summer sessions at UIUC. NSF funds the undergraduate
student with a stipend of $2,700 during a summer REU. The Department of
Mathematics increased the 2001 stipend to $3,200 using its own funds. The
students paid for their own travel, housing, and board out of this stipend.
- 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.
- Konstantin Drapkin has an individual REU with John DíAngelo in summer 2003. He worked on generalizations joint work of DíAngelo, Kos, and Riehl that emerged froma previous REU that Emily Riehl had with John DíAngelo.
- Ben Lundell had an individual REU with Chris French in summer 2003. They worked on knot invariants.
- 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.
- 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.
- Noah Prince had an individual REU was in fall 2003 with Alexandr Kostochka on graph minors.
- Ben Lundell had an individual REU with Randy McCarthy in fall 2003. He studied the fundamental group and veering spaces, using various texts.
- 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.
- Serge Posudevsky had an individual REU in spring 2004 with Serge Ivanov. He focused his research on topics in the texts by Algli Papantonopoulou, ďAlgebra: Pure and AppliedĒ and M. I. Kargopolov, ďFundamentals of the Theory of Groups.Ē
- 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.
- Tyler Smith held an individual REU with Randy McCarthy in spring 2004. He worked on a variety of topics in topology and category theory.
- 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.
- 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.
- Andrew Webster has an individual REU with John DíAngelo 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.
- 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.
- 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.
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
Summer 2001 Group REUs:
- 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
groupís 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).
- 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 groupís
- 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).
- 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 groupís 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
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.
- 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 groupís participants
- Prudence Heck (Rutgers)
- Bryce Johnson (Washington U.)
- Christopher Jones (Youngstown)
- Michael Mulligan (UIUC)
- Patrick Watts (Augustana)
- 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)
- Professor Bob Muncaster conducted a group REU focused on game theory,
Markov chains, and basic evolutionary theory that has 5 participants.
This groupís participants were:
- Whitney Bush (Bradley)
- Kristie Engemann (UIUC)
- Ana Pavasovic (College Intl)
- Ken Scheiwe (UIUC)
- Tim Teravainen (New College Florida)
- Professor A. J. Hildebrand supervised a group REU in number theory
with 6 students. The program was like the previous summerís program
with modification to fit the new group of students. This groupís participants
- 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
Two group programs were organized for summer 2003, with a total of 13 student participants.
- Bob Muncaster conducted a group REU focused again on game theory, Markov chains, and basic evolutionary theory that has 6 participants. This groupís 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)
- Kim Whittlesey conducted a group REU focused on geometric group theory. This REU group consisted of 7 people This groupís 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
Three group programs were held in summer 2004, with a total of 16 student participants. The three group themes in the program are geometrical computing,
geometric group theory, and mathematical modeling.
- 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 groupís participants were:
- William Baker (UIUC)
- Benjamin Kauk (UIUC)
- Gregory Stanton (UIUC)
- Emily Gunawan (Wells)
- Brett Witt (UIUC)
- Kim Whittlesey conducted a group REU focused on geometric group theory. This REU group consisted of 6 people.
This groupís participants were:
- Seth Case (UIUC)
- Adam Levine (Harvard)
- Aja Johnson (Elon)
- Xin Jia Johnson (UCLA)
- Tyler Smith (UIUC)
- Christopher Spicer (Mt. Mercy)
- Bob Muncaster conducted a group REU focused on mathematical modeling of social and political issues.
This REU group consisted of 5 people. This groupís 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.