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for events the day of Tuesday, November 3, 2015.

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Tuesday, November 3, 2015

11:00 am in 243 Altgeld Hall,Tuesday, November 3, 2015

Framed Correspondences and the Milnor-Witt K-theory

Alexander Neshitov (Ottawa)

Abstract: The theory of framed motives developed by Garkusha and Panin based on ideas by Voevodsky, gives a tool to construct fibrant replacements of spectra in A^1-homotopy category. In the talk we will discuss how this construction gives an explicit identification of the motivic homotopy groups of the base field with its Milnor-Witt K-theory. In fact, this identification can be done similar to the theorem of Suslin-Voevodsky which identifies motivic cohomology of the base field with Milnor K-theory.

12:00 pm in Altgeld Hall 345,Tuesday, November 3, 2015

Ergodic Theory and Rigidity of Nilpotent Groups

Michael Cantrell (University of Illinois at Chicago)

Abstract: Random aspects of the coarse geometry of finitely generated groups both occur naturally and have applications to the deterministic case. First, we describe the asymptotic behavior of certain random metrics on nilpotent groups, which generalizes a theorem of Pansu and implies an asymptotic shape theorem for first passage percolation. Seen from another perspective, this is a subadditive ergodic theorem for nilpotent groups. Second, we describe a measurable cocycle analog of Pansu's Rademacher-type differentiation theorem for Carnot spaces, answering a question of Austin. From this we deduce Pansu's quasi-isometric rigidity theorem.

1:00 pm in 241 Altgeld Hall,Tuesday, November 3, 2015

Bergman theory on generalized Hartogs triangles

Luke Edholm (The Ohio State University)

Abstract: We introduce a class of non-smooth, pseudoconvex domains which generalize the Hartogs triangle. After obtaining the explicit formula for the Bergman kernel of each domain, these formulas are used to understand the mapping properties of the Bergman projection. We discover a restricted range of $p$ for which the Bergman projection is a bounded operator on $L^p$ and show that this range is sharp. We conclude by observing surprising and intriguing behavior of the bounded $L^p$ mapping range with respect to limit domains. This work is joint with Jeff McNeal.

1:00 pm in 345 Altgeld Hall,Tuesday, November 3, 2015

Algebraic Topology Meets Descriptive Set Theory

Alexander Izzo   [email] (Bowling Green State Univ. Math)

Abstract: Let $k$ and $n$ be positive integers with $k < n$, and let $f:\mathbb{R}^n \to \mathbb{R}^k$ be a continuous map. Can $f$ be one-to-one on the complement of a set of Lebesgue measure zero? Can $f$ be one-to-one on the complement of a set of first category? The motivation for these questions will be discussed, and one of them will be answered. The other question remains open.

2:00 pm in 347 Altgeld Hall,Tuesday, November 3, 2015

Parabolic Harnack inequality on fractal-like Dirichlet spaces

Janna Lierl   [email] (UIUC Math)

Abstract: I will present some recent results on extending the parabolic Moser iteration method to the setting of fractal-type local Dirichlet spaces satisfying appropriate geometric conditions. I will also discuss the case of non-symmetric perturbations of the Dirichlet form. This method yields a parabolic Harnack inequality. Consequently, upper and lower bounds for the associated heat propagator can be obtained.

3:00 pm in 241 Altgeld Hall,Tuesday, November 3, 2015

Families of sets with a forbidden intersection size

Zoltán Füredi   [email] (Renyi Institute of Mathematics, Budapest)

Abstract: We start with a proof of an old result (joint with P Frankl). Observe that the family $\mathcal{F}(n,t)$ (in case of n+t is odd) consisting of all subsets of $[n]$ of sizes at least $(n+t+1)/2$ or at most $(t-1)$ contains no two members meeting in exactly $t$ elements. For $n > n_0(t)$ this is the largest hypergraph with this intersection property.

3:00 pm in 243 Altgeld Hall,Tuesday, November 3, 2015

Linear coordinates for stability conditions on surfaces and applications

Cristian Martinez (UC Santa Barbara)

Abstract: From the definition of Gieseker stability for sheaves we derive linear coordinates for Bridgeland stability conditions on surfaces. Bridgeland stability conditions have the advantage that, unlike Gieseker stability, they come equipped with a well-behaved wall-crossing. In this talk I will show how classical results on variation of polarization for the Gieseker moduli spaces can be obtained by studying the Bridgeland wall-crossing. Same techniques allow us to express classical birational geometry of surfaces as variation of stability conditions. This is joint work with Aaron Bertram.

4:00 pm in 149 Henry building,Tuesday, November 3, 2015

Quasiconformal Mappings

Colleen Ackerman (UIUC)

Abstract: Visually, a mapping from $\mathbb{C}\to \mathbb{C}$ is quasiconformal if it takes infinitesimal circles to infinitesimal ellipses of uniformly bounded eccentricity. Quasiconformal mappings have applications in many fields including PDE's, complex dynamics and Teichm\"{u}ller theory. Their usefulness may in part be due to their many definitions of different flavors. I will briefly describe some common past definitions of quasiconformal mappings, and then go through a proof by pictures of a new characterization. This talk will be easily accessible to all graduate students.