Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, March 16, 2017.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2017            March 2017             April 2017
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4             1  2  3  4                      1
5  6  7  8  9 10 11    5  6  7  8  9 10 11    2  3  4  5  6  7  8
12 13 14 15 16 17 18   12 13 14 15 16 17 18    9 10 11 12 13 14 15
19 20 21 22 23 24 25   19 20 21 22 23 24 25   16 17 18 19 20 21 22
26 27 28               26 27 28 29 30 31      23 24 25 26 27 28 29
30


Thursday, March 16, 2017

11:00 am in 241 Altgeld Hall,Thursday, March 16, 2017

#### A gumbo with hints of partitions, modular forms, special integer sequences and supercongruences

###### Armin Straub (University of South Alabama)

Abstract: Euler's partition theorem famously asserts that the number of ways to partition an integer into distinct parts is the same as the number of ways to partition it into odd parts. In the first part of this talk, we describe a new analog of this theorem for partitions of fixed perimeter. More generally, we discuss enumeration results for simultaneous core partitions, which originates with an elegant result due to Anderson that the number of $(s,t)$-core partitions is finite and is given by generalized Catalan numbers. The second part is concerned with congruences between truncated hypergeometric series and modular forms. Specifically, we discuss a supercongruence modulo $p^3$ between the $p$th Fourier coefficient of a weight 6 modular form and a truncated $_6F_5$-hypergeometric series. The story is intimately tied with Apéry's proof of the irrationality of $\zeta(3)$. This is recent joint work with Robert Osburn and Wadim Zudilin.

12:30 pm in 464 Loomis Laboratory,Thursday, March 16, 2017

#### Quivers, Monopoles and q-geometric Langlands

###### Vasily Pestun (IHES)

Abstract: I will present the relationship between N=2 4d quiver gauge theories and integrable system of periodic monopoles and its quantization, and some conjectures concerning q-deformation of the geometric Langlands correspondence.

1:00 pm in 347 Altgeld Hall,Thursday, March 16, 2017

#### Biological Fluid Mechanics in Reproduction and Development

###### Dave Smith (School of Mathematics, University of Birmingham)

1:00 pm in 243 Altgeld Hall,Thursday, March 16, 2017

#### On Grothendieck's proof of the Fundamental Theorem of Stability Theory

###### Sergei Starchenko (Notre Dame)

Abstract: In the paper "Model theoretic stability and definability of types, after A. Grothendieck" (2014) Itai Ben Yaacov observed that the Fundamental Theorem of Stability Theory (also known as the Definability of Types Theorem) follows from Grothendieck's paper "Critères de compacité dans les espaces fonctionnels généraux" (1952) on what can be called "double limits property". In this talk we discuss this connection and provide an elementary proof of a version of Grothendieck's theorem equivalent to the Fundamental Theorem of Stability Theory.

2:00 pm in 243 Altgeld Hall,Thursday, March 16, 2017

#### Regularity and transversality for Sobolev hypersurfaces

###### Valentino Magnani (University of Pisa)

Abstract: We show how the regularity of a Sobolev hypersurface implies a measure theoretic transversality with respect to a nonintegrable smooth distribution of possibly lower dimensional subspaces. We consider the model case where the distribution generates a stratified Lie group. These results have been obtained in collaboration with Aleksandra Zapadinskaya.

3:00 pm in 347 Altgeld Hall,Thursday, March 16, 2017

#### Levi subgroup actions on Schubert varieties in the Grassmannian

###### Reuven Hodges (Northeastern University)

Abstract: Let L be the Levi part of the stabilizer in GL_N(C) (for left multiplication) of a Schubert variety X(w) in the Grassmannian. For the induced action of L on C[X(w)], the homogeneous coordinate ring of X(w) (for the Plucker embedding), I will give a combinatorial description of the decomposition of C[X(w)] into irreducible L-modules. Using this combinatorial description, I give a classification of all Schubert varieties X(w) in the Grassmannian for which C[X(w)] has a decomposition into irreducible L-modules that is multiplicity free. This classification is then used to show that certain classes of Schubert varieties are spherical L-varieties. Also, I will describe interesting related results on the singular locus of X(w) and multiplicities at points in X(w).

4:00 pm in 245 Altgeld Hall,Thursday, March 16, 2017

#### The Topological Closure of Algebraic and Semi-Algebraic Flows on Complex and Real Tori

###### Sergei Starchenko (Notre Dame)

Abstract: Let $A$ be a complex abelian variety and $\pi\colon \mathbb{C}^n\to A$ be the covering map. In this talk we consider the topological closure $\pi(X)$ of an algebraic subvariety $X$ of $\mathbb{C}^n$ and describe it in terms of finitely many algebraic families of cosets of real subtori. We also obtain a similar description when $A$ is a real torus and $X$ is a semi-algebraic subset of $\mathbb{R}^n$. This is joint work with Y. Peterzil.