Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, December 1, 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, December 1, 2005

12:00 pm in 464 Loomis,Thursday, December 1, 2005

#### D-branes and superpotentials: the A-infinity category structure of the derived category

###### Sheldon Katz   [email] (UIUC Math and Physics)

Abstract: Physics summary: The worldvolume theory of B-branes in Calabi-Yau compatifications has a superpotential which has been computed in recent years by many researchers using various dualities (Seiberg, toric, ...). In this talk it will be shown how to formulate the superpotential in the language of algebraic geometry, then further shown how it can be explicitly computed via Cech cohomology without reference to any dualities. Math summary: The A-infinity category structure of the derived category of coherent sheaves on an algebraic variety can be computed explicitly by representing objects of the derived category by complexes of locally free sheaves and then using Cech cohomology. As an application, if the variety is a Calabi-Yau threefold, superpotentials of B-branes in string theory can be computed explicitly. This talk is based on joint work with Paul Aspinwall, hep-th/0412209.

1:00 pm in Altgeld Hall 341,Thursday, December 1, 2005

#### Bounded cohomology and group homomorphisms

###### Anna Wienhard (IAS Princeton)

Abstract: Bounded cohomology classes give rise to invariants for group homomorphism. These invariants sometimes determine group homomorphsisms up to conjugation and sometimes they single out geometrically interesting classes of homomorphisms. In this talk I will explain how a special bounded cohomology class arises from a geometric construction and how the invariants it defines can be used to study homomorphisms of finitely generated groups into semisimple Lie groups like e.g. SU(1,n), SU(n,m), Sp(2n,R).

1:00 pm in 241 Altgeld Hall,Thursday, December 1, 2005

#### Covering Congruences: An Empirical Quest

###### Don Gibson (UIUC)

Abstract: In a previous talk, we surveyed some of the history and results associated with covering congruences, a favorite topic of Erdos. In this talk, we examine some computational approaches to the problem of constructing covering congruences.

2:00 pm in 243 Altgeld Hall,Thursday, December 1, 2005

#### Lipschitz approximation of the Sobolev functions

###### Xiao Zhong (University of Jyväskylä, Finland)

Abstract: I will discuss a method due to Acerbi, Fusco, and Lewis. The idea is to truncate a Sobolev function along the level set of the maximal function of its gradient to construct a Lipschitz function. I will also discuss the applications of this method in the study of very weak quasiregular mappings and in the study of Hardy's inequality.

3:00 pm in 241 Altgeld Hall,Thursday, December 1, 2005

#### Teichmuller geodesic rays which do not have a limit in PMF

###### Anna Lenzhen (UIC)

Abstract: We construct a Teichmuller geodesic ray which does not have a limit on the Thurston boundary of Teichmuller space.

3:00 pm in 243 Altgeld Hall,Thursday, December 1, 2005

#### Solution to General Baer Splitting Problem, cont.

###### Phillip Griffith   [email] (UIUC Math)

4:00 pm in 245 Altgeld Hall,Thursday, December 1, 2005

#### Noncommutative Fourier transform, Chen's iterated integrals and path integrals

###### Mikhail Kapranov (Yale University)

Abstract: The usual exponential functions exp, x=(x1, ..., xn), depend on the vector a of exponents. Various ways of lifting such a function to noncommutative variables xi (which can be, say, indeterminate matrices) depend on a choice of a path joining 0 and a in the phase space. This lifting can be seen as the generating function of the iterated integrals of Chen. Since there are as many noncommutative exponentials as there are paths, one is led to considering a "noncommutative Fourier transform" which would identify an appropriate space of functions of noncommutative variables and the space of ordinary functions (or measures) on the space of paths. The talk will discuss various aspects of such (conjectural) transform. Host: Matt Ando