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University of Michigan
Department of Mathematics
Fall 2006 Topology Seminar
Thursdays 3-4, 4096 East Hall
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For more information, contact Emina Alibegovic.
If you want to check the list of seminars held in previous terms, click on
the appropriate link below.
Winter 2006,
Fall 2005,
Winter 2005, Fall 2004, Winter 2004, Fall 2003, Winter 2003, Fall 2002, the year 2000-1.
Schedule of Talks
Abstracts
September 21
Abstract: I will discuss a topic which originally
belongs to physics, but recently got some attention
in algebraic topology (for reasons I may briefly outline).
In particular, it is believed that to each Calabi-Yau
3-fold there is assigned a conformal field theory
known as its \sigma-model: these theories are prime
candidates for string vacua in physics. Yet, the
theories were never constructed rigorously mathematically.
In this talk, I will discuss some evidence *against*
the conjectured picture, i.e. evidence that the \sigma-models
may not generically exist as conformal field theories
in the mathematical axiomatic sense, after all. (joint work with Hao Xing)
October 19
I will discuss some relations between the geometry of closed
hyperbolic 3-manifolds and the minimal number of elements needed to
generate their fundamental groups. As an application I will sketch
recent advances towards conjectures of McMullen and Waldhausen.
October 26
Abstract: The chromatic viewpoint of stable homotopy theory uses
the geometry of formal groups -- which arise from complex oriented
cohomology theories -- to organize computations and constructions.
An important construction we would like to make is to realize
families of complex oriented homology theories as diagrams of
spectra; the inverse limit of such diagrams can hold a great deal
of information. Part of the basic input to this realization problem
is the cotangent complex of the moduli stack of smooth 1-
dimensional formal groups. In this talk, I'll
go into more detail on the realization problem, then tell what
I know about the cotangent complex.
November 9
Abstract: Tukia's theorem on quasiconformal maps of the n sphere can be used to show
quasi-isometric rigidity of cocompact lattices in hyperbolic space.
I will discuss a Tukia-like theorem for boundaries of certain solvable
groups. Eskin-Fisher-Whyte recently proved quasi-isometric rigidity for a
wide class of polycyclic groups. One of the ingredients in their proof is
this version of Tukia's theorem. This talk will focus on describing the
geometry of these solvable groups, their boundaries and then
briefly explaining the proof idea of the theorem.
November 16
Abstract: The volume of a hyperbolic manifold with torus boundary always goes down under Dehn filling.
The question is, how far does it go down? I will describe a new estimate that explicitly bounds the change
in volume as a function of the slope length on a maximal cusp. As an application, this estimate gives
diagrammatic bounds for the volumes of many hyperbolic knots. This is joint work with Effie Kalfagianni and Jessica Purcell.
November 30
Abstract:
Let $G$ be a locally compact group. A discrete subgroup $\Gamma$ of $G$
is called a lattice if $\Gamma \backslash G$ has finite volume. We study
lattices in $G$ the automorphism group of a locally finite polyhedral
complex $X$, such as a hyperbolic building. Questions considered include
existence and covolumes of lattices, and (in joint work with Seonhee Lim)
the asymptotics of the number of overlattices of a fixed lattice $\Gamma$.
December 7
Abstract:
I will define what I mean by a VF group,
I will explain why one might expect them to contain
few conjugacy classes of finite subgroups, and I
will describe a construction of VF groups having
many conjugacy classes of finite subgroups. This
construction answers questions of H. Bass, K. S.
Brown and J.-P. Serre. Part of this is joint work
with Brita Nucinkis.
December 14
Abstract:Grafting is a geometric operation in which a measured lamination on a hyperbolic surface is thickened,
changing the conformal structure of the surface. We show that when restriced to a fixed hyperbolic surface, grafting
defines a homeomorphism from the space of measured laminations to Teichmuller space. This allows us to define "polar
coordinates" on Teichmuller space centered at any point. This is joint work with Mike Wolf of Rice University.
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