Seminar Calendar
for events the day of Tuesday, October 7, 2008.

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Tuesday, October 7, 2008

Topology seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, October 7, 2008
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Submitted by mando.
Stephan Stolz (Notre Dame)
Supersymmetric Euclidean field theories and generalized cohomology
Abstract: This is a report of ongoing joint work with Peter Teichner (Berkeley). Elaborating Segal's axiomatic approach to conformal field theories, we define supersymmetric Euclidean field theories over a manifold X. It turns out that the set of concordance classes of such field theories over X of dimension d is in bijective correspondence to the cohomology of X (with complex coefficients) for d=0 and to the K-theory of X for d=1. We speculate that for d=2 we obtain the "Topological Modular Form theory" of Hopkins-Miller. Evidence is provided by our result that the partition function of a supersymmetric Euclidean field theory of dimension 2 is a weakly holomorphic integral modular form.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, October 7, 2008
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Submitted by ssolecki.
Aleksandra Kwiatkowska (Department of Mathematics, University of Illinois)
Near-actions and their point realizations
Abstract: Let (X,m) be the Lebesgue space, and let Aut(X,m) be the group of all measure preserving transformations of X with the natural topology. Given a continuous homomorphism h from a Polish group G to Aut(X,m), it is important to determine if h has a point realization, that is, if it arises from a Borel measure preserving action of G on (X,m). Mackey gave an affirmative answer to this question for G Polish locally compact, and recently Glasner and Weiss, using different methods, gave an affirmative answer for G a closed subgroup of the group of all permutations of natural numbers. In the talk, I will present a common generalization of these two results to a class of groups that includes also, for example, countable products of locally compact groups. This is a joint work with Slawek Solecki.

Number Theory
1:00 pm   in 241 Altgeld Hall,  Tuesday, October 7, 2008
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Submitted by mdrogers.
Jeremy Rouse (Department of Mathematics, University of Illinois)
Modular forms with coefficients supported on finitely many square classes (mod l)
Abstract: We will discuss half-integer weight modular forms whose Fourier coefficients are supported on finitely many square classes modulo a prime $\ell$, and their applications to values of $L$-functions and values of the partition function.

Graph Theory and Combinatorics
1:00 pm   in 241 Altgeld Hall,  Tuesday, October 7, 2008
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Submitted by west.
Kyle Jao (UIUC Math)
Length thresholds for graphic lists with fixed maximum and minimum entries
Abstract: A gap-free list is a list of positive integers where each value between the maximum and minimum occurs in the list. All long gap-free even-summed lists are graphic. Explicitly, any gap-free even-summed list with maximum r, minimum s, and length at least r+(r+s)/(2s) is graphic. In general, any even-summed list with maximum r, minimum s, and length at least (r+s+1)²/(4s) is graphic.

Geometric Potpourri Seminar
2:00 pm   in 273 Altgeld Hall,  Tuesday, October 7, 2008
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Submitted by j-wetzel.
John E. Wetzel (Department of Mathematics, University of Illinois)
An ancient elliptic locus, II
Abstract: We supply the proofs of Frans van Schooten's locus, which we had too little time to present last week, and we establish the precise condition for the locus to collapse to a line segment. Today's talk will not seriously depend on Part 1 presented last Tuesday.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, October 7, 2008
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Submitted by nevins.
Li Li (Department of Mathematics, University of Illinois)
Hilbert scheme of points on a smooth stack
Abstract: Hilbert schemes of points on a smooth surface have many desirable properties, and have been intensively studied for a long time. In this talk, we first review some of these properties, then study the Hilbert schemes of points on a smooth stack of dimension 2, in particular the quotient of affine plane by a finite cyclic group. The betti number, and hence the cellular decomposition, is given in terms of combinatorical data.

Joint Group Theory/Differential Geometry Seminar
3:00 pm   in 347 Altgeld Hall,  Tuesday, October 7, 2008
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Submitted by clein.
Gabriela Schmithuesen (Karlsruhe)
Veech groups of infinite translation surfaces
Abstract: The Veech group of a translation surface is a discrete subgroup of SL(2,R) which encodes a lot of information about the dynamics on the translation surface. Particular explicit examples are provided by origamis or square tiled surfaces for which the Veech group is always a subgroup of SL(2,Z) and can be described in an alternative way using subgroups of the automorphism group of F_2. We study an infinite family of infinite volume origamis. They come from coverings of the torus of infinite degree; these translation surfaces are not of finite type. We show that their Veech groups are not finitely generated. This is joint work with Pascal Hubert.

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, October 7, 2008
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Submitted by pfima.
Florin Boca (Department of Mathematics, University of Illinois)
Unitary representations of compact quantum groups
Abstract: In preparation for the Peter-Weyl theorem I plan to discuss the (right) regular representation of a compact quantum group and some elements of representation theory.

Motivic Integration
3:00 pm   in 447 Altgeld Hall,  Tuesday, October 7, 2008
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Submitted by vlopes2.
Isaac Goldbring (Department of Mathematics, University of Illinois)
U-minimal valued fields are algebraically closed
Abstract: In this talk, I will give the proof that a u-minimal valued field is algebraically closed. The proof follows the method of proof used by van den Dries, Macintyre, and McKenna where they show that an infinite field whose theory in the language of rings admits quantifier elimination is algebraically closed. I will prove the theorem modulo two blackboxes: one of them a purely valuation-theoretic fact about u-minimal fields and the other a general fact about definable sets being dense in a ball having nonempty interior. One or both of these blackboxes will be addressed in Friday's talk.

Motivic Integration
3:00 pm   in 447 Altgeld Hall,  Tuesday, October 7, 2008
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Submitted by vlopes2.
Isaac Goldbring (Department of Mathematics, University of Illinois)
U-minimal valued fields are algebraically closed
Abstract: In this talk, I will give the proof that a u-minimal valued field is algebraically closed. The proof follows the method of proof used by van den Dries, Macintyre, and McKenna where they show that an infinite field whose theory in the language of rings admits quantifier elimination is algebraically closed. I will prove the theorem modulo two blackboxes: one of them a purely valuation-theoretic fact about u-minimal fields and the other a general fact about definable sets being dense in a ball having nonempty interior. One or both of these blackboxes will be addressed in Friday's talk.