Seminar Calendar
for events the day of Tuesday, August 24, 2010.

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Tuesday, August 24, 2010

Topology Seminar
11:00 am   in Altgeld Hall,  Tuesday, August 24, 2010
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Submitted by mando.
No Meeting

Number Theory
1:00 pm   in 241 Altgeld Hall,  Tuesday, August 24, 2010
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Submitted by berndt.
Paul Pollack (UIUC)
Euler's function and sums of squares
Abstract: Let phi denote Euler's function. How often is phi(n) a perfect square? The answer: Surprisingly often. (I'll be more precise in the talk.) We will discuss the general question of how often phi(n) is a sum of squares, with particular attention paid to 3 squares. There will be many historical/mathematical digressions.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, August 24, 2010
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Submitted by west.
Alexandr V. Kostochka (UIUC Math)
List coloring of simple hypergraphs
Abstract: The list chromatic number of a hypergraph G is the least integer s such that for every assignment of s colors to each vertex of G, there is a vertex coloring such that the color of each vertex is from its list and there are no monochromatic edges. Before 2000, Alon proved that every graph with "high" average degree cannot have small list chromatic number. We prove the same for simple r-uniform hypergraphs under a different notion of "high".

We use the result to prove that for any finite set of points X in the plane and any integer s, one can assign a list of s distinct colors to each point of the plane, so that any coloring of the plane that colors each point by a color from its list contains a monochromatic isometric copy of X. This work is joint with Noga Alon.