Department of

Mathematics


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

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, October 7, 2008

11:00 am in 241 Altgeld Hall,Tuesday, October 7, 2008

Supersymmetric Euclidean field theories and generalized cohomology

Stephan Stolz (Notre Dame)

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.

1:00 pm in 241 Altgeld Hall,Tuesday, October 7, 2008

Length thresholds for graphic lists with fixed maximum and minimum entries

Kyle Jao (UIUC Math)

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.

1:00 pm in 241 Altgeld Hall,Tuesday, October 7, 2008

Modular forms with coefficients supported on finitely many square classes (mod l)

Jeremy Rouse (Department of Mathematics, University of Illinois)

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.

1:00 pm in 345 Altgeld Hall,Tuesday, October 7, 2008

Near-actions and their point realizations

Aleksandra Kwiatkowska (Department of Mathematics, University of Illinois)

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.

2:00 pm in 273 Altgeld Hall,Tuesday, October 7, 2008

An ancient elliptic locus, II

John E. Wetzel (Department of Mathematics, University of Illinois)

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.

3:00 pm in 347 Altgeld Hall,Tuesday, October 7, 2008

Veech groups of infinite translation surfaces

Gabriela Schmithuesen (Karlsruhe)

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.

3:00 pm in 130 Lincoln Hall,Tuesday, October 7, 2008

Unitary representations of compact quantum groups

Florin Boca (Department of Mathematics, University of Illinois)

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.

3:00 pm in 447 Altgeld Hall,Tuesday, October 7, 2008

U-minimal valued fields are algebraically closed

Isaac Goldbring (Department of Mathematics, University of Illinois)

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.

3:00 pm in 447 Altgeld Hall,Tuesday, October 7, 2008

U-minimal valued fields are algebraically closed

Isaac Goldbring (Department of Mathematics, University of Illinois)

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.

3:00 pm in 243 Altgeld Hall,Tuesday, October 7, 2008

Hilbert scheme of points on a smooth stack

Li Li (Department of Mathematics, University of Illinois)

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.