Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, February 15, 2005.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2005          February 2005            March 2005
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1          1  2  3  4  5          1  2  3  4  5
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Tuesday, February 15, 2005

11:00 am in Altgeld Hall 241,Tuesday, February 15, 2005

#### Witt vectors and K-theory of endomorphisms

###### Morten Brun (Osnabruck)

1:00 pm in 345 Altgeld Hall,Tuesday, February 15, 2005

#### Polynomially bounded o-minimal structures with $C^\infty$ uniformization.

###### Daniel Miller (University of Toronto)

Abstract: An o-minimal expansion of the real field is said to have "$C^\infty$ uniformization" if every definable compact set is the image of a definable compact $C^\infty$ manifold under a definable $C^\infty$ mapping. It follows from a model completeness and o-minimality proof of Rolin, Speissegger and Wilkie [RSW] that an o-minimal expansion of the real field is polynomially bounded and has $C^\infty$-uniformization if and only if it is interdefinable with an expansion of the real field by a collection of restricted functions closed under differentiation and contained in a certain kind of quasianalytic class, and in this language the structure is model complete. I plan to discuss a more careful version of the RSW construction which keeps track of parameters in a way similar in spirit to what Wilkie and Macintrye did to study the real exponential field. The talk will consist of some completed work and also of some work in progress. Falling in the latter category is an attempt to use the RSW construction to read off an explicit universal-existential axiomatization of the theories of these structures.

1:00 pm in 241 Altgeld Hall,Tuesday, February 15, 2005

#### Congruences for the coefficients of weakly holomorphic modular forms, I

###### Stephanie Treneer (UIUC)

Abstract: Recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. We show that this type of phenomena is completely general, by finding similar congruences for the coefficients of any weakly holomorphic modular form. In particular, we give congruences for a wide class of partitions functions and for traces of CM values of arbitrary modular functions on certain congruence subgroups of prime level. Tuesday's talk will consist of an introduction to the problem, a statement of the main theorems, and a discussion of the two applications. Thursday we will prove the main theorems.

2:00 pm in 345 Altgeld Hall,Tuesday, February 15, 2005

#### Asymptotics of Orthogonal Polynomials, the Riemann-Hilbert Problem and Universality in Matrix Models

###### Alexander Its (IUPUI Math)

Abstract: Recent developments in the theory of random matrices and orthogonal polynomials have revealed striking connections of the subject to integrable nonlinear differential equations of both the KP and the Painlev\'e types. These connections, in particular, make it possible to use nontraditional analytical schemes of the theory of integrable systems, such as the Riemann-Hilbert asymptotic method, for proving Dyson's universality conjecture concerning the scaling limit of correlations between eigenvalues for a wide class of exponential weights. In the talk, the essence of the Riemann-Hilbert approach to matrix models will be presented together with a review of the most recent developments in the area.

2:00 pm in Altgeld Hall,Tuesday, February 15, 2005

#### Progress Report on the Z-worm in the 30 Degree Pie Slice

###### Prof. Patrick R. Coulton (EIU Departrment of Mathematics and Computer Science)

Abstract: I will show that all unit z-worms with large middle section (nearly 1) fit in the 30 degree pie slice with radius 1. This appears to be one of the toughest cases, but unfortunately, the proof is analytic. Handouts of the computation will be provided. In particular, I will show that as the length of the middle section tends to 1, the second derivatives of the independent variables for the distance function (from the vertex) are tending to negative infinity. I will outline what needs to be done to finish the proof that all worms are covered. This part will be primarily geometric.

2:00 pm in 241 Altgeld Hall,Tuesday, February 15, 2005

#### Henn's calculation of the cohomology of S_2 at p=3, II

###### Charles Rezk (UIUC Math)

Abstract: I continue the discussion of Henn's calculation of the cohomology of the Morava stabilizer group of height 2 at the prime 3.

3:00 pm in 347 Altgeld Hall,Tuesday, February 15, 2005

#### Harald Bohr meets Stefan Banach

###### Prof. Andreas Defant (University Oldenburg (Germany))

3:00 pm in 241 Altgeld Hall,Tuesday, February 15, 2005

#### On 2-factor unique graphs

###### Ron Gould (Emory University)

Abstract: A graph G is 2-factor unique if it has a 2-factor X and every 2-factor of G is isomorphic to X. We consider questions about 2-factor unique graphs, tracing some old results as well as some very new results. A number of open questions will be presented. In particular, we will consider the case when the 2-factor is a hamiltonian cycle; such graphs are 2-factor hamiltonian. The maximum number of edges in such graphs will be determined exactly in both the bipartite and general cases. Further, extremal graphs will be shown, and we will determine when these graphs are unique.

4:00 pm in 341 Altgeld Hall,Tuesday, February 15, 2005