UIUC Dept. of Mathematics Seminar Calendar

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Wednesday, September 28, 2011

Women's Seminar
3:00 pm in 447 Altgeld Hall, Wednesday, September 28, 2011

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Jane Butterfield (UIUC Math)
Games in Graphs: Avoiding Triangles
Abstract: There are several versions of a monochromatic triangle-avoiding game played in a graph. We will talk about three:

1. The two-player off-line game: Builder presents a graph, and Painter has to color each edge with one of $r$ available colors.

2. The two-player on-line game: Builder presents edges one-at-a-time while Painter colors each with one of $r$ available colors.

3. The one-player on-line random game, in which edges appear one-at-a-time at random while Painter colors each with one of $r$ available colors.

In each, Painter loses if she creates a triangle whose edges are all the same color. It turns out that the two-player game is closely related to the one-player random game. We will use a theorem due to Belfrage, Mutze, and Spohel to prove the first non-trivial upper bound for the on-line random game when $r$ is greater than two. This talk will be accessible to a general audience, and will end with a (deceptively?) simple open question.

Mathematics Colloquium: Coble Memorial Lectures
4:00 pm in 245 Altgeld Hall, Wednesday, September 28, 2011

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Ngo Bao Chau (University of Chicago)
Geometry of the Hitchin fibration
Abstract: Nigel Hitchin observed that the cotangent bundle of the moduli space of principal bundles on a Riemann surface has a structure of an algebraic completely integrable system. A deep relation between the geometry of the Hitchen fibration and the geometry of the trace formula has been discovered. This has been helpful in the proof of the fundamental lemma in the Langlands program.

The Coble Memorial Lectures will be held September 27-29, 2011. Before each lecture, coffee and cookies will be served in the Common Room (321 Altgeld Hall) at 3:30 p.m.