Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, September 4, 2018.

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Tuesday, September 4, 2018

1:00 pm in 345 Altgeld Hall,Tuesday, September 4, 2018

Distality in Pairs

Travis Nell (UIUC)

Abstract: The notion of distality attempts to isolate the notion of a purely unstable behavior in an NIP theory. I will examine certain cases of expansions of o-minimal structures by a unary predicate. Each of these examples will be non-distal. In the case that the predicate is a proper, dense elementary substructure, I will characterize the distal types. In the case of the expansion of an ordered divisible abelian group and the predicate is a dense independent set, I will talk about how to find a distal expansion of this structure.

2:00 pm in 243 Altgeld Hall,Tuesday, September 4, 2018

Cut-edges and regular factors in regular graphs of odd degree

Dara Zirlin (Illinois Math)

Abstract: Previously, Hanson, Loten, and Toft proved that every $(2r+1)$-regular graph with at most $2r$ cut-edges has a 2-factor. We generalize their result by proving for $k \leq (2r+1)/3$ that every $(2r+1)$-regular graph with at most $2r-3(k-1)$ cut-edges has a $2k$-factor. We show that the restriction on $k$ and the restriction on the number of cut-edges are sharp and characterize the graphs that have exactly $2r-3(k-1)+1$ cut-edges but no $2k$-factor. This is joint work with Alexandr Kostochka, André Raspaud, Bjarne Toft, and Douglas West.

2:00 pm in 347 Altgeld Hall,Tuesday, September 4, 2018

Proper holomorphic maps and compressed sensing

John D'Angelo (Illinois Math)

Abstract: For source dimension $n$ at least $2$, it remains an open problem to prove sharp degree estimates for a rational proper holomorphic map from the $n$-ball to the $N$-ball in terms of $n,N$. Twenty five years ago the speaker conjectured specific sharp bounds which have been proved in the case of monomial maps. In the talk I will reformulate these results in the language of compressed sensing and hope to show how the techniques of proof in the monomial case might provide some useful methods in applied linear algebra. Some of the key ideas are due to Simon Kos, a physicist, and to Jiri Lebl. In particular I will discuss a related paper by Lebl-Lichblau.

3:00 pm in 243 Altgeld Hall,Tuesday, September 4, 2018

Tamely ramified geometric Langlands correspondence in positive characteristic

Shiyu Shen (UIUC Math)

Abstract: I will describe a generic version of tamely ramified geometric Langlands correspondence (GLC) in positive characteristic for $GL_n$, generalizing the work of Bezrukavnikov-Braverman on the unramified case. Let $X$ be a smooth projective curve over an algebraically closed field $k$ of characteristic $p>n$. I will give a spectral description of the parabolic Hitchin fiber over an open subset of the Hitchin base, and describe a correspondence between flat connections with regular singularities on $X$ and twisted Higgs bundles on the Frobenius twist $X^{(1)}$. Then I will explain how to use a twisted version of Fourier-Mukai transform to establish the GLC.