For more information, contact Valentina Joukhovitski.

If you want to check the list of seminars held in previous terms, click on the appropriate link below.

Winter 2007, Fall 2006, Winter 2006, Fall 2005, Winter 2005, Fall 2004, Winter 2004,  Fall 2003,  Winter 2003,  Fall 2002, the year 2000-1.

Schedule of Talks

Abstracts

Higher twistings for K-theory.

Abstract: In this talk I will discuss the so-called higher twistings for twisted K-theory.

It is known that for a compact space X, twistings of K-theory over X are classified by [X,BGL1(K)]. Here GL1K~ Z/2x K(Z,2)x BSU^{o ­}is the space of units of K with H-space structure induced by the tensor product of vector bundles. The twistings corresponding to the factor [X,BBSU^o]  are called higher twistings. In the talk I will give a definition for the most general twistings of K-theory. This has been worked out rigorously on the literature only for the lower twistings and only sketched for the general situation.

The idea of the construction is to consider a category consisting of Fredholm operators for different Hilbert space to get a semigroup.

I will also discuss the equivariant setting limited to the case over a point. I will show that if G is a compact Lie group, then there are no higher twistings for completed twisted G-equivariant K-theory over a point. I contrast; one can see that this is not the case for topological groups in general.

Chen-Ruan cohomology of the cotangent orbifold and orbifold string topology.

Abstract: In this talk I will how to define a ring structure on the orbifold cohomology that arises at considering the constant loops of the orbifold string topology ring. This ring structure on the orbifold cohomology turns out to be isomorphic to the Chen-Ruan ring structure of the cotangent orbifold. This work is a joint work with A. Gonzalez, E. Lupercio, C. Segovia and M. Xicotencatl.

A chain model of the free loop space and string topology.

Abstract: In this talk we will study the Frobenius structure on the chain complex of a smooth manifold, and then construct a chain (and also the equivariant chain) model of its free loop space. From such a chain complex we show that there is a Batalin-Vilkovisky algebra on its homology, which models the string topology of Chas-Sullivan. Some of the other structures on the loop space and their applications will also be discussed.

Orbifold cup products and ring structures on Hochschild cohomologies.

Abstract: In this talk we'll discuss calculations of Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. We will also discuss relations of these calculations to Chen-Ruan orbifold cohomology.

Heegaard Floer homology and fibred three-manifolds.

Abstract: Heegaard Floer homology is a theory introduced by Ozsváth and Szabó as an analogue to Seiberg-Witten theory. For knots in 3-manifolds, this theory is refined to a filtered version, called knot Floer homology. Ozsváth and Szabó conjectured that knot Floer homology detects fibred knots in the three-sphere. In this talk, we will discuss a proof of this conjecture, based on the works of Paolo Ghiggini and of the speaker. In fact, one can show that Heegaard Floer homology detects whether a 3-manifold is fibred, namely, whether it is a surface bundle over the circle. Some applications will also be discussed.

From foliations to actions.

Abstract: Joint with R.C. Penner we introduced what could be called a combinatorial models of open/closed conformal field theory. It is based on partially measured foliations on surfaces with boundaries and marked points on the boundaries. From this geometry we derived actions of certain moduli spaces of surfaces on Hochschild cochains of a Frobenius algebra which extend our proofs of Deligne's conjecture and its cyclic generalization. This has applications in string topology. First, we will review the operadic structures on the geometric level and chain level. Then, we will construct the action using so-called operadic correlation functions and graph Feynman rules. We end with an outlook on further research and a connection to $D$-branes.

This page last updated on December 28, 200720 .