Department of

Mathematics


Seminar Calendar
for events the day of Thursday, November 10, 2005.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, November 10, 2005

11:00 am in 241 Altgeld Hall,Thursday, November 10, 2005

Automorphisms of Manifolds

Bruce Williams (University of Notre Dame)

Abstract: Surgery theory has been successfully used to classify manifolds up to diffeomorphism or homeomorphim (in dimensions larger than 4). However, classical surgery theory is not strong enough to determine the topological groups of self- homeomorphims or self-diffeomorphisms of a manifold. In my talk I'll explain how Michael Weiss and I combine together surgery with higher algebraic K-theory to study this problem.

12:00 pm in 3-110 ESB,Thursday, November 10, 2005

Marginal deformations in AdS/CFT correspondence

Oleg Lunin (U Chicago Physics)

1:00 pm in 241 Altgeld Hall,Thursday, November 10, 2005

Farey fractions and pair-correlation of torsion points on elliptic curves

Maosheng Xiong (UIUC Math)

Abstract: We compute the pair-correlation of Farey fractions and the sum of Farey fractions over subintervals, which implies the existence of the pair-correlation of torsion points and also the sum of torsion points along elliptic curves over $Q$ (more precisely, along the unbounded real part of such elliptic curves). This is joint work with Emre Alkan and Alexandru Zaharescu.

1:00 pm in Altgeld Hall 347,Thursday, November 10, 2005

Groups with no free subsemigroups of rank 2

Derek Robinson (UIUC)

Abstract: A theorem of Rosenblatt states that a finitely generated solvable group which has no free subsemigroups of rank 2 is virtually nilpotent. We will present a streamlined proof of this result and then indicate a wide generalization of it.

2:00 pm in 345 Altgeld Hall,Thursday, November 10, 2005

An Introduction to Green's Conjecture

Jason McCullough (UIUC)

Abstract: This talk will build on Anca's talk covering linear series and canonical curves. Roughly stated, Green's conjecture relates two invariants associated to canonical curves, namely an invariant derived from Betti numbers of the coordinate ring of the curve and the clifford index, which contains a lot of geometric information. I will define these ideas, state and discuss Green's conjecture and try to convey the current status of the problem. This talk should be accessible to those with a little algebraic geometry.

2:00 pm in Altgeld Hall,Thursday, November 10, 2005

No seminar this week

Abstract: Due to prelims, the seminar for this week has been cancelled.

2:00 pm in 243 Altgeld Hall,Thursday, November 10, 2005

Quasisymmetric maps of Sierpinski carpets

Sergiy Merenkov (University of Michigan)

Abstract: I will discuss recent results on rigidity for quasisymmetric maps of Sierpinski carpets, a joint work with Mario Bonk. Quasisymmetric maps are global analogues of quasiconformal maps in the setting of arbitrary metric spaces. We prove, in particular, that every quasisymmetric self-map of the Sierpinski carpet fractal is an isometry, i.e. a rotation or a reflection.

These rigidity questions originate from the study of the boundary at infinity of Gromov hyperbolic groups. One consequense of the above result is that the Sierpinski carpet fractal is not quasisymmetric to the boundary at infinity of such a group.

The main tool that was used, and that I will describe in my talk, is a new invariant for quasisymmetric maps of Sierpinski carpets, a modulus of a curve family with respect to a carpet.

3:00 pm in 241 Altgeld Hall,Thursday, November 10, 2005

A (partial) Lagrangian Piunikhin-Salamon-Schwarz morphism

Peter Albers   [email] (NYU)

Abstract: One of the major tools in symplectic topology is Floer homology, which can be assigned either to a Hamiltonian function on a symplectic manifold or a Lagrangian submanifold. Hamiltonian Floer homology is known to be isomorphic to the singular homology of the symplectic manifold. A particular isomorphism was constructed by Piunikhin, Salamon and Schwarz in 1994. Under some topological assumption Lagrangian Floer homology can be shown to be isomorphic to the singular homology of the Lagrangian submanifold, but in general this is not true; it might even vanish identically. In 1996 Oh constructed a spectral sequence relating Lagrangian Floer homology and singular homology. We show to what extent the approach of Piunikhin, Salamon and Schwarz can be adapted to Lagrangian Floer homology. Furthermore, this leads to a comparison morphism between Lagrangian and Hamiltonian Floer homology resembling the natural homomorphism in singular homology, which is induced by the inclusion. This leads to some new insights into the topological structure of Lagrangian submanifolds.

4:00 pmThursday, November 10, 2005

CANCELLED DUE TO ILLNESS