Department of

# Mathematics

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

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2013          October 2013          November 2013
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1  2  3  4  5  6  7          1  2  3  4  5                   1  2
8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
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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.