Organizers: Bruce Hughes and Mark Sapir
Wednesdays, in SC 1310 (unless otherwise noted)
Speaker: Stacy Hoehn,
Title: The Moduli Space of Compact Topological Fiber Bundle Structures on a Fibration
Abstract: Several classical geometric invariants have parametrized versions that can be used to answer questions about families of spaces. For example, there is a parametrized version of Wall's finiteness obstruction which can be used to determine when a compact fiber bundle structure can be placed on a fibration whose fibers are finitely dominated. We will explain how ideas related to this parametrized finiteness obstruction can also be used to compute the moduli space of all such bundle structures on a fibration.
(Joint seminar with the Subfactor Seminar, in SC 1432)
Michael V. Ershov,
Title: Kazhdan quotients of Golod-Shafarevich groups
Abstract: Informally speaking, a finitely generated group G is said to be Golod-Shafarevich (with respect to a prime p) if it has a presentation
with a small set of relators, where relators are counted with different weights depending on how deep they lie in the Zassenhaus p-filtration. Golod-Shafarevich groups are known to behave like (non-abelian) free groups in many ways: for instance, every
Golod-Shafarevich group G has an infinite torsion quotient, and the pro-p completion of G contains a non-abelian free pro-p group.
In this talk I will extend the list of known largeness properties of Golod-Shafarevich groups by showing that they always have an infinite quotient with Kazhdan's property (T). An important consequence of this result is a positive answer to a well-known question on non-amenability of Golod-Shafarevich groups.
Title: Introduction to Quasimorphisms
Abstract: I'll introduce the concept of quasimorphism and discuss its applications in geometric group theory.
Title: Degenerate Maxima of Hamiltonian Loops
Abstract: We will discuss topological results of manifolds
admitting Hamiltonian circle actions as well as those admitting
certain Hamiltonian loops. We will also discuss the Hofer
geometry associated to certain symplectic 4-manifolds.
Title: Actions of Product Groups on Manifolds
Abstract: This is a joint work with Nicolas Monod. We analyze volume-preserving actions of products of Kazhdan groups on Riemannian manifolds.
Under a natural irreducibility assumption we obtain lower bounds on the dimension of the manifold in terms of the number of factors in the acting group, and strong restrictions for actions of non-linear groups.
We prove our results by means of a new cocycle superrigidity theorem of independent interest, in analogy to Zimmer's programme.
University of Muenster (
Title: Obstruction to fibering a manifold
Abstract: Given a map f : M --> B between closed topological manifolds, is it homotopic to the projection map of a fiber bundle whose fibers are closed manifolds? If the target space is the circle, and the dimension of M is greater than five, classical results by Farrell show that there are obstructions in algebraic K-theory that vanish if and only if f fibers. The goal of this talk is to show how obstructions to fibering can be defined for arbitrary target spaces B and to indicate why these obstructions reduce to the classical ones in the case B=S^1. This is joint work with F.T. Farrell and Wolfgang Lueck.
Title: Einstein metrics and exotic smooth structures on 4-manifolds
Title: JSJ Decompositions of Coxeter Groups over FA subgroups
Abstract: A group G has property FA if G fixes a point of every tree on which G acts without inversions. A Coxeter group W, with finitely many Coxeter generators S, has property FA if and only if the product of any two elements of S has finite order in W. A visual subgroup of a Coxeter system (W,S) is a subgroup of W generated by a subset of S. A graph of groups decomposition of a Coxeter system (W,S) is said to be visual if every vertex and edge group is visual. We prove that every Coxeter system of finite rank has a visual JSJ graph of groups decomposition with edge groups having property FA. As an application, we reduce the twist conjecture to Coxeter systems that are indecomposable with respect to amalgamated products over visual subgroups with property FA.
Title: Non-linear matrix groups
Abstract: Joint with Martin Kassabov. We prove that the group EL_n(R) is not linear for many rings R (including the free ring) and n>2.
Title: Chern-Weil theory, representation theory, and topological K-theory
Abstract: In a number of computations, it has been observed that below the (rational) cohomological dimension of a group G, there is a discrepancy between the representation theory of G, which is captured by the spaces Hom(G, U(n)), and the topological K-theory of the classifying space of G. This discrepancy is closely analogous to Beilinson-Quillen-Lichtenbaum conjectures relating algebraic K-theory and Galois cohomology. Focusing on the case in which G is the fundamental group of an aspherical, closed manifold, I'll describe joint work with Tom Baird, which explains this phenomenon. The main ingredients are Chern-Weil theory and the homotopical relationship between flat connections, representations, and K-theory. I'll discuss how these results fit with particular examples, including products of surfaces and certain crystallographic groups.
Speaker: Romain Tessera, CNRS
Title: A finitely-generated amenable group with very poor compression into Lebesgue spaces
Abstract: We shall discuss the paper by Tim Austin with the above title.