Seminar Calendar
for events the day of Tuesday, October 26, 2010.

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Tuesday, October 26, 2010

Logic Seminar
1:00 pm   in UIC SEO 636,  Tuesday, October 26, 2010
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Submitted by phierony.
NO SEMINAR
Abstract: There will be no seminar, but there will be a MidWest Model Theory Day at UIC. See http://www.math.wisc.edu/~andrews/MWMTD.html for details.

Number Theory
1:00 pm   in 241 Altgeld Hall,  Tuesday, October 26, 2010
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Submitted by berndt.
Members of the Audience (Illinois (probably))
Mini-Lectures and Gems in Number Theory
Abstract: Members from the audience will provide mini-lectures up to 10 minutes each on their favorite theorems, proofs, or open problems.

Geometry Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, October 26, 2010
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Submitted by sba.
Chanyoung Jun (UIUC Math)
Pursuit curves and time-dependent gradient curves
Abstract: First, we introduce an applied problem, namely, pursuit-evasion games. These problems are generated from robotics, control theory and computer simulations. We define CAT(0) and CAT(K) spaces, and explain why they are suitable playing fields, and vastly generalize the usual playing fields in the pursuit-evasion literature. Recently, time-independent gradient flow has been studied extensively in CAT(0) spaces. Pursuit curves are downward gradient curves for the distance from a moving evader, that is, for a time-dependent gradient flow. We consider not only pursuit curves, but also more general time-dependent gradient flow. We describe our existence and uniqueness theorems for solution curves, as well as our convergence estimates and regularity theorem.

Graduate Geometry and Topology Seminar
2:00 pm   in 345 Altgeld Hall,  Tuesday, October 26, 2010
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Submitted by lukyane2.
Rosona Eldred (UIUC Math)
Spectra, Linear Functors, and (Co)homology: going `under the hood' in Algebraic Topology.
Abstract: If you've ever studied any algebraic topology then you've already been working with spectra, perhaps unknowingly! In this talk, I'll explain what spectra are, how they show up in topology, and how they lead naturally to the notion of linearity of a functor. This is a general talk; little to no background assumed.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, October 26, 2010
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Submitted by nevins.
David Jordan (MIT)
Quantization of Multiplicative Quiver Varieties
Abstract: Quiver varieties, as introduced by Lusztig and Nakajima, are related to such diverse topics as Hilbert schemes, representations of Hecke algebras and semi-simple Lie algebras, canonical bases, and character varieties of Riemann surfaces. Recently, Crawley-Boevey and Shaw solved the Deligne-Simpson problem by introducing so-called multiplicative quiver varieties and studying their algebro-geometric properties. In this talk, we construct certain algebras Aλd, which quantize the symplectic structure on multiplicative quiver varieties. Our construction involves Hamiltonian reduction by quantum group actions. As applications, we give a new description of the representation category of the spherical double affine Hecke algebra of type An-1 with formal parameters.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, October 26, 2010
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Submitted by west.
John Lenz (UIUC Math)
Ramsey-Turán numbers of graphs
Abstract: Erdős and Sós initiated the study of Ramsey-Turán numbers of graphs. For a graph H, let RT(n,H,f(n)) be the maximum number of edges in an n-vertex, H-free graph with independence number at most f(n). From the viewpoint of Turán theory, we are asking what happens when we restrict the size of the independent sets. From the viewpoint of Ramsey theory, we are asking what happens when we allow the size of the forbidden blue graph to depend on n.

In this talk, I will give an overview of the history of the theory of Ramsey-Turán numbers. Additionally, I will talk about recent progress on open problems of Erdős, Hajnal, Simonovits, Sós, and Szemerédi. This is joint work with József Balogh.