Seminar Calendar
for events the day of Thursday, October 15, 2009.

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Questions regarding events or the calendar should be directed to Tori Corkery. 
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Thursday, October 15, 2009

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, October 15, 2009
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Submitted by kapovitc.
Johanna Mangahas (University of Michigan)
"Short-word" pseudo-Anosovs
Abstract: The problem of finding "short-word" pseudo-Anosovs relates to proving effective versions of the Tits alternative for the mapping class group. I'll describe both problems, their relation, and their solutions.

Number Theory Seminar
1:00 pm   in 241 Altgeld Hall,  Thursday, October 15, 2009
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Submitted by jarouse.
Talk rescheduled for next week (10/22)

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, October 15, 2009
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Submitted by aimo.
Alexander Tumanov (Department of Mathematics, University of Illinois)
Global Beltrami equation on the torus
Abstract: Beltrami equation is a generalized Cauchy-Riemann equation for conformal maps. For the Riemann sphere, the global solution follows from the local one and the general uniformization theorem. Ahlfors and Vekua in 1955 independently gave direct solutions to the global problem on the sphere. We give an analogue for the torus. The solution is explicit and may be useful in applications such as Calderon's inverse conductivity problem.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, October 15, 2009
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Submitted by beder.
Alexandra Seceleanu (Department of Mathematics, University of Illinois)
Weak Lefschetz Property and Powers of Linear Forms
Abstract: Classically, the weak Lefschetz theorems compare the topology of complex projective varieties and of their hyperplane sections. In an algebraic setting, an Artinian graded algebra has the Weak Lefschetz Property (WLP) if multiplication by a general linear form, from any graded component to the next, has maximal rank. I will explain how recent work of Brenner and Kaid expresses the weak Lefschetz property in terms of the cohomology of a certain syzygy bundle. I will prove, using this technique, that an Artinian quotient of K[x; y; z] by an ideal I generated by powers of linear forms has the Weak Lefschetz Property. Our proof works without the semistability hypothesis of Brenner and Kaid, which typically does not hold. The latter part is joint work with H. Schenck.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, October 15, 2009
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Submitted by clein.
David Nicholls (University of Illinois at Chicago)
Boundary Perturbation Methods for Electromagnetic Scattering
Abstract: The scattering of electromagnetic waves by irregular obstacles arises in a wide array of applications including remote sensing, nondestructive testing, and imaging. In this talk we will discuss a class of highly accurate numerical methods for the simulation of rough-surface scattering based upon the classical approach of Lord Rayleigh from the early 1900's. While these methods feature rapid execution times and exponentially fast convergence, subtle cancellations in the underlying recursions render them unreliable for very challenging problems (e.g., non-smooth surfaces). We will show how a simple change of variables produces not only a robust and highly accurate numerical procedure applicable to the most difficult configurations, but also delivers a proof of the algorithm's convergence. Furthermore, we will illustrate how these ideas can be adapted to the multi-scale problem of high-frequency scattering where the wavelength of the electromagnetic radiation is many orders of magnitude smaller than the features of the scattering obstacle.