Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, February 3, 2015.

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Tuesday, February 3, 2015

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

The Integration Pairing and Extended Topological Field Theories

Nerses Aramian   [email] (UIUC)

Abstract: Given a complex line bundle with a connection on a manifold there is a straightforward way of producing 1-dimensional topological field theory over the manifold. One can generalize this procedure by replacing complex line bundles with n-gerbes bound by $\mathbb{C}^\times$, and replacing connections with appropriate connective structures. The resulting topological field theories are n-dimensional and extended. In this talk, we will describe how exactly one can extract these topological field theories using the higher categorical machinery of Jacob Lurie.

1:00 pm in 243 Altgeld Hall,Tuesday, February 3, 2015

Pseudo-Anosov mapping classes not arising from Penner's construction

Hyunshik Shin (UIC Math)

Abstract: We show that Galois conjugates of stretch factors of pseudo-Anosov mapping classes arising from Penner’s construction lie off the unit circle. As a consequence, we show that for all but a few exceptional surfaces, there are examples of pseudo-Anosov mapping classes so that no power of them arises from Penner’s construction. This resolves a conjecture of Penner. View talk at http://youtu.be/lL94FzESags

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

Fractional time Stochastic partial differential equations

Panki Kim (Seoul National University)

Abstract: In this talk, we introduce a class of stochastic partial differential equations (SPDEs) with fractional time-derivatives, and study the L_2-theory of the equations. This class of SPDEs can be used to describe random effects on transport of particles in medium with thermal memory or particles subject to sticking and trapping. This is a joint work with Zhen-Qing Chen and Kyeonghun Kim.

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

Toward Żak's conjecture on graph packing

Andrew McConvey (UIUC Math)

Abstract: Two graphs G and G', each of order n, pack if there is a bijection from V(G) onto V(G') such that for each edge xy in G, f(x)f(y) is not an edge in G'. A well known result of Sauer and Spencer shows that if G and G' together contain at most 3n/2 - 1 edges, then G and G' pack. Bollobás and Eldridge proved that if max{∆(G), ∆(G')} < n-1, then 2n-2 edges is sufficient for G and G' to pack. Recently, Żak considered whether further restricting the bound on max{∆(G), ∆(G')} would increase the number of edges needed to ensure packing. Specifically, he conjectured that if max{∆(G), ∆(G')} < n-1 and |E(G)| + |E(G')| + max{∆(G), ∆(G')} ≤ 3n-7, then G and G' pack and showed that the conjecture is true asymptotically. In this talk we will show that, up to an additive constant, Żak's conjecture is true. In order to prove this result, we prove a stronger result using list packing. This is joint work with Ervin Győri, Alexandr Kostochka, and Derrek Yager.

4:00 pm in 243 Altgeld Hall,Tuesday, February 3, 2015

Cohen's Factorization Theorem

Matthew Wiersma (University of Waterloo)

Abstract: I will talk about a theorem on factorization in Banach algebras due to Paul Cohen, and discuss how this result can be applied to solve easily stated questions about convolution products and Fourier transforms.