Seminar Calendar
for events the day of Thursday, October 6, 2011.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, October 6, 2011

BCDE Math/Physics Seminar
12:00 pm   in 464 Loomis Laboratory,  Thursday, October 6, 2011
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Submitted by katz.
 Jeffrey Teo (UIUC Physics)Topological insulators and superconductors: physical realization of Bott's periodicityAbstract: The topological and analytic index of a momentum parametrized family of band Hamiltonians will be discussed. Their equality will be illustrated physically by the "bulk-boundary correspondence" that relates the topology of band Hamiltonians and their gapless defect spectrum. Bott's 2-fold, 8-fold and (1,1)-periodicities for K, KO and (twisted) KR theory will be revisited using defect band Hamiltonian formalism.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, October 6, 2011
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Submitted by kapovich.
 Nathan Dunfield (UIUC Math)Twisted Alexander polynomials, hyperbolic geometry, and knot genusAbstract: A hyperbolic knot has an associated Alexander polynomial that is twisted by the holonomy representation of the hyperbolic structure. I will discuss properties of this invariant and give evidence that it is extremely good at detecting knot genus and fibering. This is joint work with Stefan Friedl and Nicholas Jackson.

2:00 pm   in 241 Altgeld Hall,  Thursday, October 6, 2011
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Submitted by lukyane2.
 Austin Rochford (UIUC Math)Abstract Harmonic Analysis, Operator Algebras, and Geometric Group TheoryAbstract: We motivate the construction of the Fourier algebra of a general group by considering the classical theory of harmonic analysis on abelian groups. We will characterize amenability of a group in terms of an analytic property of their Fourier algebras. We will proceed to show that the Fourier algebras of groups which act nicely on certain geometric spaces possess slightly weaker analytic properties than those of amenable groups.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, October 6, 2011
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Submitted by aimo.
 David Kerr (Texas A&M University)Sofic entropyAbstract: A couple of years ago Lewis Bowen introduced a notion of entropy for probability-measure-preserving actions of countable sofic groups which admit a generating partition with finite Shannon entropy. This greatly extends the classical entropy for amenable acting groups as originally defined for single transformations by Kolmogorov, who similarly required the existence of a generating partition. In Kolmogorov's case, Sinai saw how to remove the generator assumption by taking a supremum over all partitions, yielding what is now the standard definition of entropy in the amenable case. This does not work in the sofic setting, and to circumvent this problem Hanfeng Li and I developed an operator-algebraic approach which provides a much more flexible notion of generator. In this talk I will show how sofic entropy can in fact be defined using partitions in a generator-free way, in the spirit of Sinai. This definition also facilitates the computation of entropy for Bernoulli actions, which I will outline.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, October 6, 2011
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Submitted by beder.
 Javid Validashti (UIUC Math)Uniform Equivalence of Symbolic and Adic Topologies (part 3)Abstract: This is part 3 of a series. We show that the symbolic topology defined by a prime ideal is uniformly linearly equivalent to the adic topology for a large class of isolated singularities. This talk is based on a joint work with Craig Huneke and Dan Katz.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, October 6, 2011
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Submitted by kapovich.
 Yuliy Baryshnikov (Department of Mathematics and Department of Electrical and Computer Engineering, University of Illinois)On Stokes SetsAbstract: In asymptotic expansions of integrals, Stokes' sets correspond to the values of parameters where the structure of the asymptotic expansion changes. They are hard to notice (the terms appearing or vanishing are exponentially small), but are responsible for many peculiarities of the asymptotic analysis, and have in essence a topological origin. In this talk I will address the combinatorial structure of the Stokes' sets for polynomial phases (in the simplest example of the Airy function, the Stokes' set is the union of three rays in the plane of the parameter). It turns out that the combinatorial structure of the Stokes sets is governed by certain polyhedra interpolating between cubes and Stasheff polyhedra. In conclusion I will discuss some enumerative questions around these polyhedra - a recent work with UIUC grad students L. Hickok, N. Orlow and S. Son.