Geometry and Topology Seminar

Tuesday August 3, 15:00, room B3.02

Kasra Rafi (Oklahoma)

Coarse differentiation and the rank of Teichmuller space

Thursday October 7, 15:00, room MS.03

No seminar

NA

Abstract: NA

Thursday October 14, 15:00, room MS.03

András Juhász (Cambridge)

The decategorification of sutured Floer homology

Abstract: Sutured manifolds were introduced by David Gabai to study taut foliations on 3-manifolds, and they proved to be powerful tools in 3-dimensional topology. We study a torsion invariant for sutured manifolds, and show that it agrees with the Euler characteristic of sutured Floer homology. The torsion is easily computed and shares many properties of the usual Alexander polynomial. We also compare several norms defined on the homology of a sutured manifold. This is joint work with Stefan Friedl and Jacob Rasmussen.

Thursday October 21, 15:00, room MS.03

Jason Behrstock (CUNY)

Curve complex projections and the mapping class group

Abstract: We will explain a certain natural way to project elements of the mapping class to simple closed curves on subsurfaces. Generalizing a coordinate system on hyperbolic space, we will use these projections to describe a way to characterize elements of the mapping class group in terms of these projections. This point of view is useful in several applications; time permitting we shall discuss how we have used this to prove the Rapid Decay property for the mapping class group. This talk will include joint work with Kleiner, Minksy, and Mosher.

Thursday October 28, 15:00, room MS.03

Sarah Rees (Newcastle)

Artin groups: automatic structures and geodesics

Thursday November 4, 15:00, room MS.03

Albert Marden (Minnesota)

Plumbing

Abstract: Start with one or two Riemann surfaces which have hyperbolic metrics of finite area: finitely punctured surfaces. Classical plumbing is to choose (i) a pair of the punctures p,q, (ii) small neighborhoods of them, and then (iii) cut the neighborhoods out and join their boundaries together, thus creating either a handle, or joining two surfaces together. When this process is done precisely, it depends on an analytic parameter t. For small values of |t|>0, one obtains a holomorphic family S(t) of surfaces (why?). These surfaces are connected and all have the same topological type. Are the opened surfaces conformally distinct from each other? Do the plumbing t-parameters have analytic extensions so as to provide global holomorphic coordinates for Teichmueller space?

The answers will be given in the talk, which will also indicate how the work leads to an analytic compactification of moduli space.

The exposition covers part of ongoing joint work with Cliff Earle. It should be accessible to anyone who has heard of Teichmueller spaces (deformation spaces) of Riemann surfaces, and hyperbolic 3-manifolds (kleinian groups), both of which will be briefly reviewed.

Thursday November 11, 15:00, room MS.03

Clifford Earle (Cornell)

Some rigidity properties of analytic families of Riemann surfaces

Abstract: In our joint work on augmented Teichmueller and moduli spaces, Albert Marden and I construct analytic families of Riemann surfaces over certain quotients of classical Teichmueller spaces. Our analysis of these families led us to some uniqueness theorems for more general families. Some of these will be discussed in this talk, which will begin with an introduction to the theory of analytic families.

Thursday November 18, 15:00, room MS.03

NA (NA)

NA

Abstract: NA

Thursday November 25, 15:00, room MS.03

Marco Schlichting (Warwick)

Motivic homotopy theory and the algebraic analogue of KO

Abstract: Motivic homotopy theory is a framework for doing homotopy theory in the context of algebraic geometry. It allows us to think in geometric terms about objects which (historically) have a rather obscure definition. For instance, Quillen's algebraic K-theory (over any field) is represented in this world by ZxBGl just as complex K-theory is represented by ZxBU in topology (Morel and Voevodsky). In this talk I will explain joint work with Girja Tripathi in which we show that algebraic Hermitian K-theory is represented by orthogonal Grassmannians in motivic homotopy theory just as ordinary orthogonal Grassmannians represent real K-theory in topology.

Thursday December 2, 15:00, room MS.03

Alexandra Pettet (Oxford)

The fundamental group of Hom(Z^k,G)

Abstract: Let G be a compact Lie group, and consider the variety Hom(Z^k,G) of representations of the rank k Abelian free group Z^k into G. We prove that the fundamental group of Hom(Z^k,G) is naturally isomorphic to the direct product of k copies of the fundamental group of G. This is joint work with Jose Manuel Gomez and Juan Souto.

Thursday December 9, 15:00, room MS.03

Mark Pollicott (Warwick)

Counting circles in Apollonian circle packings

Abstract: The classical theory of Apollonian circle packings has been revisited in the past year or two by Oh et al, Bourgain-Fuchs and Sarnak, who have studied the sequence of diameters of the associated circles. In this talk I want to explain some of the results, put them into a broader context and present some related results.