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.

Fall 2007, 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

Koszul Duality for Dioperads

Abstract: The notion of dioperad is intermediate between operad and PROP. I will speak on their theory of Koszul duality and the example of Lie bialgebra dioperad whose Koszul dual is closely related to commutative Frobenius algebras.

Higher Steinberg Relations

Abstract: We will discuss, following a suggestion of S. Bloch, the construction of certain motives associated to the projective line minus the points 0, 1, and infinity. In the end, this will reduce to the question of producing a cellular approximation of a certain dg-module over a dga, and we will see that the construction of this cell module is controlled by Massey products in the motivic cohomology of the ground field. The vanishing of these Massey products would give higher Steinberg relations in motivic cohomology and algebraic K-theory.

No prior knowledge of the theory of motives will be assumed!

Using right-angled Artin groups to interpolate between mapping class groups and linear symplectic groups

Abstract: The right-angled Artin group (RAAG) of a graph is the group whose generators are the vertices of the graph and whose only relations are that adjacent vertices commute. I will use RAAGs to define a family of groups, called \emph{mapping class groups over graphs}, that interpolate between the mapping class group of a genus $g$ surface with a single boundary component and the symplectic group $\mathrm{Sp}(2g,\mathbb{Z})$. I will sketch a proof that these groups are finitely generated. As part of the proof, I will develop some algorithmic techniques from the study of free groups and linear groups that have been adapted to apply to right-angled Artin groups.

Hurwitz spaces and string topology

Abstract: String topology, originating in the work of Chas and Sullivan in the late 90's, concerns itself with the algebraic and topological properties of loop spaces of manifolds. Many interesting connections to representation theory and symplectic geometry have recently been established. Hurwitz spaces are moduli spaces of branched covers of Riemann surfaces. In this talk we will propose a generalization of this notion that serves as a bridge between the two subjects, and allows for the construction of operations in string topology governed by the moduli spaces of Riemann surfaces. Using this construction, we prove a vanishing theorem for the string topology of classifying spaces.

Dynamics of the Teichmuller geodesic and horosphere flows

Abstract: In this talk, we describe basic ergodic properties of the Teichmuller "horosphere" flow on the moduli space of holomorphic quadratic differentials. We also discuss open questions bases on analogies between the Teichmuller geodesic flow and the geodesic flow of a compact negatively curved manifold.

Universal Cannon--Thurston maps and the complex of curves

Abstract: I'll describe joint work with Mj (Mitra) and Schleimer in which we construct a type of universal Cannon--Thurston map associated to the Birman Exact Sequence for mapping class groups and the action on the complex of curves. As a consequence, we show that the Gromov boundary of 1-punctured surface curve complexes are locally path connected and path connected.

Simplicial embeddings of pants complexes are geometric

Abstract: We will show that, for most surfaces, every simplicial embedding of one pants complex into another is induced by an embedding of surfaces. We will discuss some consequences of our work and, time permitting, we will give some details of the proof.

This page last updated on March 21, 200820 .