Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, September 26, 2013.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, September 26, 2013

11:00 am in 241 Altgeld Hall,Thursday, September 26, 2013

#### Arithmetic properties of overpartitions

###### James Sellers (Penn State)

Abstract: Over the past several years, numerous authors have studied properties of the combinatorial objects known as overpartitions (which are natural generalizations of integer partitions). Once these new objects are defined, we will prove a number of Ramanujan-like congruences for the function which enumerates the overpartitions of weight n. We will also mention a number of restricted overpartition functions and prove arithmetic properties satisfied by these functions as well. The proof techniques will be elementary in nature, relying primarily on generating function manipulations, and the talk will be self-contained.

12:30 pm in 464 Loomis Laboratory of Physics,Thursday, September 26, 2013

#### Supersymmetric Quantum Mechanics, Hodge theory, and the Witten Index

###### Sheldon Katz (Illinois Math)

Abstract: In this expository talk, I will discuss the structure of supersymmetric quantum mechanics and show how the space of supersymmetric ground states computes the Witten index once there is more than the minimal amount of supersymmetry. In mathematics, this circle of ideas translates to the Hodge theorem for Riemannian manifolds, while with still more supersymmetry, it becomes the Hodge theorem for Kahler manifolds.

1:00 pm in Altgeld Hall 347,Thursday, September 26, 2013

#### Hyperbolicity of the Cyclic Splitting Graph

###### Brian Mann (University of Utah)

Abstract: There have been several hyperbolic curve complex analogues defined on which the outer automorphism group of a finite rank free group acts. We define a new graph, the Cyclic Splitting Graph, on which the outer automorphism group acts by isometries, and show that it is hyperbolic. If time allows, we shall also talk about some differences between this complex and the other analogues.

2:00 pm in 149 Henry Administration Building,Thursday, September 26, 2013

#### An Introduction to t-Core Partitions

###### James Sellers (Penn State Math)

Abstract: For a fixed positive integer t, we say that a partition of the integer n is a t-core if none of the hook lengths of the corresponding Ferrers diagram of the partition is divisible by t. Such t-core partitions are of immense interest in representation theory for numerous reasons. Moreover, the functions which enumerate the t-core partitions of n (for fixed t) have been studied in their own right, and the arithmetic and combinatorial properties of these functions have proven to be intriguing. It is from this latter point of view that we will discuss the recent history of t-core partitions, focusing primarily on Ramanujan-like congruences which their enumerating functions satisfy. This discussion will include a set of unexpected parity results satisfied by a specific family of t-core partition functions which are closely related to a family of partitions defined by George Andrews and Peter Paule in 2007. We will close with a discussion of some recent work with Mike Hirschhorn which focused on some specific results for 3-cores which were previously proven by Berndt and Baruah. Additional future problems will also be suggested at the end of the talk.

2:00 pm in 243 Altgeld Hall,Thursday, September 26, 2013

###### Roland Vergnioux (University of Normandy, France)

Abstract: The Baum-Connes conjecture has been extended to (torsion-free) discrete quantum groups by Meyer and Nest using the language of triangulated categories. I will present the statement of the conjecture, some positive results for free quantum groups obtained in collaboration with Christian Voigt, as well as applications to K-amenability and the computation of K-theory groups.

3:00 pm in 345 Altgeld Hall,Thursday, September 26, 2013

#### Job hunting seminar for visitors and postdocs

Abstract: TODAY there will be a job hunting seminar for visitors and postdocs. This is in the slot right before the department faculty meeting. If you can't make the seminar, notes are available at http://www.math.uiuc.edu/~schenck/postdoc.pdf

3:00 pm in 243 Altgeld Hall,Thursday, September 26, 2013

#### Local cohomology modules over polynomial rings of prime characteristic - Part III

###### Yi Zhang (UIUC)

Abstract: Let $R=k[x_1,\cdots, x_n]$ be a polynomial ring over a field $k$ of characteristic $p>0.$ If $I$ is an ideal of $R,$ we denote $H^i_I(R)$ the $i$-th local cohomology module of $R$ with support in $I.$ We discuss an adjointness theorem of Frobenius map. Then we use this property to study the dimension of the associated primes of $H^i_I(R),$ the grading on $H^i_{\mathfrak{m}}(H^j_I(R))$ in case $I$ is homogeneous and $\mathfrak{m}=(x_1,\cdots,x_n),$ and an algorithm to determine the vanishing of $H^i_{\mathfrak{m}}(H^j_I(R))$.

4:00 pm in 245 Altgeld Hall,Thursday, September 26, 2013

#### Fall Department Faculty Meeting

Abstract: The Fall Department Faculty Meeting will be held at 4 p.m. in 245 Altgeld Hall, followed by a reception in 243 Altgeld Hall.