Seminar Calendar
for events the day of Thursday, February 23, 2012.

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Thursday, February 23, 2012

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, February 23, 2012
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Submitted by kapovich.
Nathan Dunfield (UIUC Math)
Integer homology 3-spheres with large injectivity radius
Abstract: Conjecturally, the amount of torsion in the first homology group of a hyperbolic 3-manifold must grow rapidly in any exhaustive tower of covers (see Bergeron-Venkatesh and F. Calegari-Venkatesh). In contrast, the first betti number can stay constant (and zero) in such covers. Here "exhaustive" means that the injectivity radius of the covers goes to infinity. In this talk, I will explain how to construct hyperbolic 3-manifolds with trivial first homology where the injectivity radius is big almost everywhere by using ideas from Kleinian groups. I will then relate this to the recent work of Abert, Bergeron, Biringer, et. al. In particular, these examples show a differing approximation behavior for L^2 torsion as compared to L^2 betti numbers. This is joint work with Jeff Brock.

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, February 23, 2012
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Submitted by lukyane2.
Brian Collier (UIUC Math)
Motivating Hamiltonian Floer Theory
Abstract: The focus of this talk will be to motivate the main ideas in Hamiltonian Floer theory. To start, we will review the notion of a Hamiltonian vector field and other important things in symplectic geometry. We will then talk about Morse Theory in a manner that will generalize most naturally to the infinite dimensional situation. Finally I will introduce Hamiltonian Floer Theory as the analog of the Morse theory of a certain action functional.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, February 23, 2012
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Submitted by kapovich.
Amie Wilkinson (University of Chicago)
Absolute continuity, exponents, and rigidity
Abstract: The geodesics in a compact surface of negative curvature display stability properties originating in the chaotic, hyperbolic nature of the geodesic flow on the associated unit tangent bundle. Considered as a foliation of this bundle, this collection of geodesics persists in a strong way when one perturbs of the Riemannian metric, or the geodesic flow generated by this metric, or even the time-one map of this flow: for any perturbed system there is a corresponding "shadow foliation" with one-dimensional smooth leaves that is homeomorphic to the original geodesic foliation. A counterpart to this foliation stability is a curious rigidity phenomenon that arises when one studies the disintegration of volume along the leaves of this perturbed shadow foliation. I will describe this phenomenon and its underlying causes. This is recent work with Artur Avila and Marcelo Viana.