Department of

Mathematics


Seminar Calendar
for events the day of Thursday, February 16, 2006.

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Thursday, February 16, 2006

12:00 pm in 464 Loomis,Thursday, February 16, 2006

The A-model as a Thom Form (cont.)

Josh Guffin (UIUC Physics)

Abstract: I will show that the A-model path integral is a representative of the Thom form of a certain infinite dimensional vector bundle on MAP(\Sigma,X). I will also prove that the path integral localizes to holomorphic maps.

1:00 pm in Altgeld Hall,Thursday, February 16, 2006

Conformal structures on boundaries of hyperbolic groups

Igor Mineyev (UIUC Math)

Abstract: I will define the notions of conformal and symmetric maps between metric spaces, and present a construction of a metric on the boundary of a hyperbolic complex X that makes the Isom(X)-action on the ideal boundary bi-Lipschitz, Moebius, symmetric, and conformal. All this in particular applies to hyperbolic groups. I will describe the notion of hyperbolic dimension for a hyperbolic group that seems to be related (at least philosophically) to the Pansu's conformal dimension.

1:00 pm in 241 Altgeld Hall,Thursday, February 16, 2006

A New Class of Modular Equations

Bill Hart (UIUC Math )

Abstract: Modular equations can be thought of as algebraic relationships between modular functions. The standard example is for the Klein j-function. i.e. there is a polynomial for each n \in \N, P_n(X,Y) \in \Z[X,Y] such that P_n(j(\tau),j(n\tau)) = 0 is an identity for all \tau in the complex upper half plane. Other modular equations have been developed by Ramanujan, Russel, Jacobi, Weber and many others. I will present a new kind of modular equation which bears some resemblance to a class of modular equations developed by Weber. I will give numerous explicitly computed examples of these new equations, speak briefly about the proof and some applications to computation of class invariants.

2:00 pm in 241 Altgeld Hall,Thursday, February 16, 2006

Elliptic Curves I

Radoslav Kirov (UIUC Math)

Abstract: (RAP Elliptic Curves and Iwasawa Theory, Part 3) This week and next week will be a review of results on Elliptic Curves. We discuss arithmetic properties over an algebraically closed field and over local fields.

2:00 pm in 443 Altgeld Hall,Thursday, February 16, 2006

Exotic 7-spheres (cont'd)

David Lipsky (UIUC Math)

2:00 pm in 243 Altgeld Hall,Thursday, February 16, 2006

Dirichlet problems for quasilinear elliptic differential equations with lower order terms

Takayori Ono (Fukuyama University)

Abstract: We consider quasi-linear second order elliptic differential equations with lower order terms and weighted structure conditions on euclidean domain. We discuss Dirichlet problems for the equations. Moreover, we give convergence of Dirichlet solutions under perturbation of the lower order term (joint work with F-Y. Maeda).