Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, January 20, 2015.

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Tuesday, January 20, 2015

11:00 am in 243 Altgeld Hall,Tuesday, January 20, 2015

Chromatic unstable homotopy theory

Guozhen Wang (MIT)

Abstract: I will describe how we can understand the unstable homotpy groups of spheres from the chromatic point of view, using techniques such as the Bousfield-Kuhn fuctor and Goodwillie calculus. As an example I will show how to compute the K(2)-local part of the homotopy groups of the three sphere.

1:00 pm in Altgeld Hall 243,Tuesday, January 20, 2015

Thin Monodromy Groups

Elena Fuchs (UIUC Math)

Abstract: In recent years, it has become interesting from a number-theoretic point of view to be able to determine whether a finitely generated subgroup of $GL_n(\mathbb Z)$ is a so-called thin group. In general, little is known as to how to approach this question. In this talk we discuss this question in the case of hypergeometric monodromy groups, which were studied in detail by Beukers and Heckman in 1989. We will convey what is known, explain some of the difficulties in answering the thinness question, and show how one can successfully answer it in many cases where the group in question acts on hyperbolic space. This work is joint with Meiri and Sarnak. View talk at http://youtu.be/BJg-UlUr0w8

3:00 pm in Altgeld Hall 241,Tuesday, January 20, 2015

Sparse bipartite large-girth graphs that are not $k$-choosable (and related topics)

Benjamin Reiniger   [email] (UIUC Math)

Abstract: An $r$-augmented tree is a rooted tree plus $r$ edges added from each leaf to ancestors. For $d,g,r\in\mathbb{N}$, we construct a bipartite $r$-augmented complete $d$-ary tree having girth at least $g$. The height of such trees must grow extremely rapidly in terms of the girth. Using the resulting graphs, we construct sparse non-$k$-choosable bipartite graphs, showing that maximum average degree at most $2(k-1)$ is a sharp sufficient condition for $k$-choosability in bipartite graphs, even when requiring large girth. We also give a new simple construction of non-$k$-colorable graphs and hypergraphs with any girth $g$. This is joint work with Alon, Kostochka, West, and Zhu.