Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, September 5, 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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1  2  3    1  2  3  4  5  6  7          1  2  3  4  5
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Thursday, September 5, 2013

11:00 am in 347 Altgeld Hall,Thursday, September 5, 2013

#### Navarov's estimate of Mahler's volume product

###### Alex Tumanov (UIUC)

Abstract: Continuation of Tuesday's talk; use of the Hormander estimates.

12:30 pm in 243 Altgeld Hall (Note room and building change),Thursday, September 5, 2013

#### Cluster algebra compatible with Cremmer-Gervais Poisson-Lie bracket on $SL_n$

###### M. Shapiro (MSU Lansing)

Abstract: Endowing a Lie group with a Poisson structure that respects group multiplication (Poisson-Lie structure) is instrumental in a study of classical and quantum mechanical systems with symmetries. In turn, a Poisson structure on a variety can be compatible with a cluster structure - a useful combinatorial tool that organizes generators of the ring of regular functions into a collection of overlapping clusters connected via rational transformations. We conjectured that this is the case for an important class of Poisson-Lie groups. We verified this conjecture for a group of invertible matrices equipped with a non-standard (Cremmer-Gervais) Poisson-Lie structure. This talk is based on joint work with M.Gekhtman and A.Vainshtein.

1:00 pm in Altgeld Hall 347,Thursday, September 5, 2013

#### Systoles and Dehn surgery for hyperbolic 3-manifolds

###### Grant Lakeland (UIUC Math)

Abstract: Given a closed hyperbolic 3-manifold $M$ of volume $V$, and a link $L \subset M$ such that the complement $M \setminus L$ is hyperbolic, we establish a bound for the systole length of $M \setminus L$ in terms of $V$. This extends a result of Adams and Reid, who showed that in the case that $M$ is not hyperbolic, there is a universal bound of $7.35534...$ . As part of the proof, we establish a bound for the systole length of a non-compact finite volume hyperbolic manifold which grows asymptotically like $\frac{4}{3} \log{V}$. This is joint work with Chris Leininger.

2:00 pm in 245 Altgeld Hall,Thursday, September 5, 2013

#### Cohomology of the moduli space of curves

###### Rahul Pandharipande (ETH Zürich)

Abstract: The moduli space of curves carries tautological cohomology classes. I will discuss the study of relations amongst these classes starting with ideas of Mumford in the 1980s. The subject advanced in the 1990s with conjectures of Faber and Faber-Zagier. I will explain the current state of affairs based on Pixton's conjectures related to cohomological field theories. The talk represents joint work with A. Pixton and D. Zvonkine.

2:00 pm in 149 Henry Administration Building,Thursday, September 5, 2013

#### Siegel's trace problem and character values of finite groups

###### Amita Malik (UIUC Math)

Abstract: We will try to understand what Siegel's trace problem is about and see some related interesting results. We will see some applications of it to character values of finite groups. If time permits, we will discuss some algorithms to compute the length of a cyclotomic integer and the set of cyclotomic integers with Siegel norm bounded by a given positive real number.

3:00 pm in 243 Altgeld Hall,Thursday, September 5, 2013

#### Organizational Meeting

4:00 pm in 245 Altgeld Hall,Thursday, September 5, 2013

#### Hypergraph generalizations of the extremal graph theorems on paths and cycles

###### Ervin Gyori (Renyi Institute of Mathematics, Budapest, Hungary/University of Memphis, Memphis, TN)

Abstract: Several theorems were proved in the last fifteen years about the size of hypergraphs not containing cycles of given length. The first part of the talk is a review of these results. Then we discuss various hypergraph generalizations of Erdos-Gallai extremal theorem on paths in graphs. In this talk, a systematic discussion of hypergraph versions of this theorem will be presented. Many theorems are proved, but some conjectures are still open.