Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, October 10, 2013.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2013          October 2013          November 2013
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  5  6  7          1  2  3  4  5                   1  2
8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
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22 23 24 25 26 27 28   20 21 22 23 24 25 26   17 18 19 20 21 22 23
29 30                  27 28 29 30 31         24 25 26 27 28 29 30



Thursday, October 10, 2013

11:00 am in 241 Altgeld Hall,Thursday, October 10, 2013

#### Colored Partition Identities Arising from Modular Equations

###### Bruce Berndt (UIUC Math)

Abstract: Beginning with work of Farkas and Kra, a large number of partition identities have been established from theta function identities and modular equations in the past dozen years. In this lecture we examine a particular type of modular equation, namely, formulas for multipliers, and derive several interesting identities for colored partitions. We also examine 30 conjectured partition identities by Sandon and Zanello. We show that modular equations can be employed to prove many of these conjectures. This is joint work with Rui Zhou, who was a visiting graduate student from Dalian University during the past year. A review of the speaker's first lecture on this topic will be given.

1:00 pm in 347 Altgeld Hall,Thursday, October 10, 2013

#### Homological shadows of attracting laminations

###### Asaf Hadari (Yale)

Abstract: Given a free group $F_n$, a fully irreducible automorphism $f \in \mbox{Aut}(F_n)$, and a generic element $x \in F_n$, the elements $f^k(x)$ converge in the appropriate sense to an object called an attracting lamination of $f$. We introduce a homological version of this convergence, which possesses a great deal of geometric structure. We will discuss connections of this object to 3-manifolds that fiber over the circle

2:00 pm in 149 Henry Administration Building,Thursday, October 10, 2013

#### Methods for recurrences

###### Jennifer Lansing (UIUC Math)

Abstract: We discuss some examples of proving and dealing with recurrences of sequences. Some common methods are direct proofs, induction, and generating functions. We also discuss the less common tool of matrices and Markov chains.

2:00 pm in 243 Altgeld Hall,Thursday, October 10, 2013

#### The Novikov Conjecture on singular spaces

###### Pierre Albin (UIUC Math)

Abstract: The Novikov conjecture on the homotopy invariance of the higher signatures of a manifold is an important open problem in topology. An analytic approach due to Mischenko and Kasparov solves the problem for closed manifolds with appropriate fundamental groups. I will discuss joint work with Eric Leichtnam, Paolo Piazza, and Rafe Mazzeo on carrying out this approach on singular spaces.

3:00 pm in 243 Altgeld Hall,Thursday, October 10, 2013

#### Mathieu Subspaces of Associative Algebras

###### Wenhua Zhao (Illinois State University)

Abstract: In this talk we will discuss a new notion of associative algebras, namely, Mathieu subspaces, which generalizes the notion of ideals. More precisely, we will discuss some recent developments on the notion; the relations of the notion with the Jacobian conjecture; and also some open problems on the notion. Some results in the talk are joint work with Arno Van Den Essen and David Wright.

4:00 pm in 245 Altgeld Hall,Thursday, October 10, 2013

#### A Survey of Applications of Floer Homology to Three Manifold Topology

###### Tom Mrowka (MIT)

Abstract: Floer homology has proved to be an important and powerful tool for answering questions about three manifold topology. This talk will give a brief introduction to various kinds of Floer homology and then give historic overview of applications of applications to questions in low dimensional topology.