Seminar Calendar
for Study Seminar in Analysis events the next 12 months of Saturday, August 1, 2009.

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Questions regarding events or the calendar should be directed to Tori Corkery. 
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Tuesday, September 29, 2009

Study Seminar in Analysis and Geometry
3:00 pm   in 441 Altgeld Hall,  Tuesday, September 29, 2009
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Submitted by jmmackay.
Ilya Kapovich (Department of Mathematics, University of Illinois)
On the Cannon-Thurston map
Abstract: A theorem of Cannon and Thurston states that for any closed hyperbolic 3-manifold $M$ fibering over a circle with fiber $S$ there is an associated continuous $\pi_1(S)$-equivariant map from the ideal boundary of the universal cover of the fiber to the ideal boundary of the universal cover of $M$. This yields a space-filling curve given by a continuous finite-to-one surjective map from the circle (the ideal boundary of the hyperbolic plane) to the 2-sphere (the ideal boundary of the hyperbolic 3-space). We will discuss Mitra's proof of the existence of the Cannon-Thurston map in the original setting as well as in the more general context of short exact sequences of word-hyperbolic groups.

Tuesday, October 13, 2009

Study Seminar in Analysis and Geometry
3:00 pm   in 441 Altgeld Hall,  Tuesday, October 13, 2009
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Submitted by jmmackay.
Anton Lukyanenko (Department of Mathematics, University of Illinois)
Tangent approximations to sub-Riemannian manifolds
Abstract: A sub-Riemannian manifold models constrained motion through a choice of a "horizontal distribution" on the tangent bundle. The standard definitions of tangent space and the differential of a smooth map break down in this setting. Following papers by Bellaiche and Ponge, I will discuss the way these notions are replaced by talking about non-abelian vector spaces (Carnot groups) and induced maps between them.

Tuesday, October 27, 2009

Study Seminar in Analysis and Geometry
3:00 pm   in 441 Altgeld Hall,  Tuesday, October 27, 2009
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Submitted by jmmackay.
Patrick Reynolds (Department of Mathematics, University of Illinois)
Rips' Theorem
Abstract: Rips theory is, roughly speaking, a collection of tools allowing one to deduce certain structure in a group $G$ acting nicely on an $\mathbb{R}$-tree. We will introduce the techniques of Rips Theory and present a "detailed sketch" of a proof of Rips' Theorem, that a finitely generated group acting freely on an $\mathbb{R}$-tree is a free product of closed surface groups and free abelian groups. We will present all definitions, assuming only a small amount of knowledge of basic covering theory, and will give examples when possible. If time permits we will mention some applications.