The Department of Mathematics announces Summer 2008 Research Experiences for Undergraduates (REUs). Funding for these REUs comes from the National Science Foundation (NSF) Workforce in the Mathematical Sciences Program. Participating students will receive a stipend of $3,200. Participants will be responsible for the cost of travel, food and housing. Descriptions of the programs and application guidelines are below. There are funds for travel to conferences where participants present papers. There are also some funds for books and supplies.

REU on Geometric Group Theory

Geometric group theory lies at the crossroads of geometry, topology, and group theory, yet many of its questions can be attacked by undergraduates. In the first two weeks of the REU, we will explore what it means for a group to have a geometry. We'll start with a hands-on introduction to non-Euclidean geometries, tilings, how to draw graph pictures of groups, and how groups can act on spaces. We will also look at an assortment of groups arising from topology and geometry, such as braid groups, reflection groups, and fundamental groups of surfaces. We will discuss algorithmic questions, such as how to tell when two strings of group generators actually determine the same element in the group.

In the remaining five weeks, students will work on research projects, either individually or in groups of 2-3.

The REU will include an introduction to some of the tools of the trade, including library and online resources, Latex (a program to typeset mathematics), and how to get research published.

Illinois has a strong geometric group theory community. There will be guest lectures by local faculty, as well as the opportunity to visit working seminars.

REU on Geometric Visualization in Virtual Environments

Visualization of mathematical phenomena and their transmutations is a maturing field of geometical computer graphics. Though opportunities to learn and practice this discipline are now plentiful, few universities have as long a tradition and as broad a base of application as Illinois. See http://new.math.uiuc.edu for the role of mathematics in this enterprise.

Students in this program, http://new.math.uiuc.edu/im2006, work with current researchers in diverse areas of mathematics, science and technology, who use a common programming platform, Syzygy. This distributed graphics system powers cluster based virtual environments such as the CAVE, CUBE and CANVAS at UIUC, the DiVE at Duke, and the PORTAL at the Technical University of Berlin.

Students in all majors and at all levels of expertise are encouraged to apply. All will learn to express themselves effectively in TeX and presentation graphics. There will be opportunities to publish or present papers at conferences. Specific questions addressed to gfrancis@uiuc.edu will be answered promptly.

How to Apply

To apply to the program, please send:

• A completed application form (you may print out the application form in pdf format or request one at the mail or e-mail address below).
• Statement of interest (1-2 typed pages).
• A list of math courses completed or currently being taken, with grades for those completed.
• Two letters of recommendation from professors who will comment on your mathematical potential, motivation and work habits.
• Send all application materials to:
  Joseph Miles
  Undergraduate Programs Director
  Department of Mathematics
  University of Illinois at Urbana-Champaign
  313 Altgeld Hall
  1409 W. Green St.
  Urbana, IL 61801

Questions about this application should be directed to Joseph Miles, dirug@math.uiuc.edu

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