Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, February 10, 2005.

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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, February 10, 2005

1:00 pm in 241 Altgeld Hall,Thursday, February 10, 2005

#### Diophantine Approximation with mild divisibility constraints

###### Emre Alkan (UIUC)

Abstract: I will present a survey on the history of Diophantine approximation problems using special subsets of integers and also talk about recent work on this jointly with A. Zaharescu and G. Harman

1:00 pm in Altgeld Hall 347,Thursday, February 10, 2005

#### General Graph Braid Groups and the Two Strand Case

###### Lucas Sabalka (UIUC)

Abstract: If $\Gamma$ is any finite graph, then the \emph{unlabelled configuration space of $n$ points on $\Gamma$} is the space of $n$-element subsets of $\Gamma$ (without repetition). The \emph{braid group of $\Gamma$ on $n$ strands} is the fundamental group of this space. Let $\Gamma$ be a planar graph. We prove that the two strand braid group on $\Gamma$ has a presentation in which every relator is a commutator "given by" the boundaries of two disjoint regions in $\Gamma$, and any two disjoint regions give rise to a commutator relator.

2:00 pm in 345 Altgeld Hall,Thursday, February 10, 2005

#### Isotopies of Lagrangian spheres

###### Richard Hind (Notre Dame)

Abstract: Lagrangian spheres arise naturally in symplectic manifolds as vanishing cycles of Lefschetz fibrations. We try to classify such spheres up to Hamiltonian diffeomorphism in some simple symplectic 4-manifolds. Sometimes, like in S^2 x S^2, there is a unique Lagrangian sphere, but other manifolds contain nonequivalent Lagrangian spheres which can be homotopic or even smoothly isotopic.

2:00 pm in 241 Altgeld Hall,Thursday, February 10, 2005

#### Henn's calculation of the cohomology of S_2 at p=3

###### Charles Rezk (UIUC Math)

2:00 pm in Altgeld Hall 243,Thursday, February 10, 2005

#### Optimal transportation and the quasiconformal Jacobian problem

###### Leonid Kovalev (Washington University, St. Louis)

Abstract: The quasiconformal Jacobian problem, which originated in a 1990 paper of David and Semmes, asks for an analytic description of the Jacobian determinants of quasiconformal mappings. A part of this difficult problem is to characterize the singular sets of such Jacobians. We prove that every set of Hausdorff dimension less than 1 is a singular set for some quasiconformal mapping. The proof involves some ideas from the theory of optimal transportation, such as the Wasserstein metric. This is joint work with Diego Maldonado.

3:00 pm in 347 Altgeld Hall,Thursday, February 10, 2005

#### Elimination of Imaginaries in Algebraically Closed Valued Fields

###### David Lippel (Notre Dame)

Abstract: This talk will provide an overview of the work done to describe the models of ACVF.

3:00 pm in 243 Altgeld Hall,Thursday, February 10, 2005

#### Tight Closure and Its Applications (II)

###### Jinjia Li   [email] (UIUC Math)

Abstract: We will discuss the colon capturing phenomena of tight closure and use it to prove that direct summand of a regular ring is Cohen-Macauly in characteristic p.

4:00 pm in 245 Altgeld Hall,Thursday, February 10, 2005

#### Representations of Affine Lie algebras

###### Vyjayanthi Chari (University of California at Riverside)

Abstract: In this talk, we first discuss briefly the definition of affine Lie algebras and their quantum analogs, and survey the various kinds of representation theory of these algebras. We then discuss a surprising connection between these representations discovered in joint work with S. Loktev, in particular an isomorphism between the Weyl modules and the Demazure modules. We also show that the results solve a substantial case of some conjectures of Feigin and Loktev on the fusion product of modules. Host: Bill Haboush