Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, October 22, 2013.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, October 22, 2013

11:00 am in 243 Altgeld Hall,Tuesday, October 22, 2013

A resolution of the spectrum $E^{h\mathbb{S}_2^1}$ at the prime 2

Irina Bobkova (Northwestern)

Abstract: The homotopy of the $p$-local sphere spectrum $S$ is determined by a family of localizations $L_{K(n)}S$ with respect to Morava K-theories $K(n)$. We will discuss some computations when $p, n=2$. Considerable information here can be derived from the action of the Morava stabilizer group on the Lubin-Tate theory. Goerss, Henn, Mahowald and Rezk have constructed a resolution of the $K(2)$-local sphere at the prime 3 which allows to simplify computations of $\pi_*L_{K(2)}S$. We will discuss a generalization of their work to the prime 2 and construct a resolution of the spectrum $E^{h\mathbb{S}_2^1}$, which is closely related to the K(2)-local sphere at the prime 2.

11:30 am in SEO 636 at UIC,Tuesday, October 22, 2013

Midwest Model Theory Day at UIC

Abstract: The MidWest Model Theory Day takes places at UIC on Tuesday October 22. The speakers are Vincent Guingona, Bradd Hart and Salma Kuhlmann. For details, see http://www.math.wisc.edu/~andrews/MWMTD7.html

1:00 pm in 243 Altgeld Hall,Tuesday, October 22, 2013

Right-angled Artin groups and finite subgraphs of the curve graph of a surface

Thomas Koberda (Yale)

Abstract: I will discuss the relationship between right-angled Artin subgroups of mapping class groups and finite subgraphs of the curve graph. Among other results, we will show that for each sufficiently complicated surface $S$, there is a right-angled Artin subgroup $A(\Gamma)$ of the mapping class group of $S$ such that the graph $\Gamma$ does not occur as a subgraph of the curve graph of $S$, thus answering a question of Matt Clay. This represents joint work with Sang-hyun Kim.

2:00 pm in Altgeld Hall 347,Tuesday, October 22, 2013

Curvature-Dimension Inequalities on Contact Manifolds and Gradient Estimates for Associated Markov Processes

Jing Wang (Purdue Math)

Abstract: In this joint work with F. Baudoin, we study the subelliptic diff usion operators that are canonically associated to sub-Riemannian structures. In particular we study the sub-Laplacian L on a contact Riemannian manifold M which appears as the generator of a Markov process on M. By developing the so-called generalized curvature-dimension inequality for L we prove that under suitable geometric conditions, spectral gap estimates can be obtained as well as the convergence to the equilibrium of the associated Markov semigroup. The curvature-dimension inequality plays a role of translating geometric information of the underlying manifold into analytic language.

2:00 pm in 345 Altgeld Hall ,Tuesday, October 22, 2013

Generalizations of the pentagram map and AGD flows

Gloria Mari-Beffa (University of Wisconsin Madison)

Abstract: In this talk I will give a description of generalizations of the pentagram map using intersections of planes of different dimensions, and will describe the combinations needed to generate discretizations of Adler-Gel'fand-Dikii flows. I will also describe the complete integration of a particular choice of map discretizing the lowest order AGD flow and the complications that arise in the (unknown) integration of discretizations of higher order ones.

3:00 pm in 241 Altgeld Hall,Tuesday, October 22, 2013

Algebraic methods in hypergraph colorability

Luboš Thoma   [email] (University of Rhode Island)

Abstract: A uniform hypergraph is properly $k$-colorable if each vertex can be colored by one of k colors such that no edge is monochromatic. I will report on commutative algebra tools for hypergraph colorability and present a complete algebraic characterization of colorability of uniform hypergraphs. Joint work with Michael Krul.

4:00 pm in 243 Altgeld Hall,Tuesday, October 22, 2013

Propaganda for Higgs Bundles

Brian Collier (UIUC Math)

Abstract: The goal of the talk is introduce the Hitchin System associated to the moduli space of Higgs bundles and the spectral data associated to it. The talk will introduce/review some facts about the moduli spaces of holomorphic vector bundles and Einstein metrics and illustrate how Higgs bundles generalize this picture.