Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, April 13, 2006.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, April 13, 2006

1:00 pm in 347 Altgeld Hall,Thursday, April 13, 2006

#### No meeting this week

1:00 pm in 241 Altgeld Hall,Thursday, April 13, 2006

#### Covering systems and periodic arithmetical functions

###### Zhi-Wei Sun (Nanjing University)

Abstract: If the ring $\Z$ of integers is the union of finitely many residue classes $a_1(\mo\ n_1),\ldots,a_k(\mo\ n_k)$, then the system $A=\{a_s(\mo\ n_s)\}_{s=1}^k$ is called a cover of $\Z$ or a covering system. There are many problems and results on this topic initiated by Paul Erd\"os. In this talk we introduce progress on the main open problems in this field, as well as the algebraic theory of periodic arithmetical maps motivated by the speaker's research on covering systems. The talk is related to number theory, combinatorics, algebraic structures and special functions.

1:00 pm in Altgeld Hall,Thursday, April 13, 2006

#### To Be Announced

2:00 pm in 443 Altgeld Hall,Thursday, April 13, 2006

#### Folded symplectic structures

###### Christopher Lee   [email] (UIUC Math)

Abstract: I will introduce the notion of a folded symplectic form on an even dimensional smooth manifold. Essentially, a folded symplectic form is a closed two form whose top power is satisfies a certain transversality condition, making its zero locus a smooth hypersurface of the manifold. We then consider the two-form to be symplectic "away from the hypersurface". Following a formalization of these notions, we will consider examples.

2:00 pm in 57 Everitt Lab,Thursday, April 13, 2006

#### Lieb-Thirring Inequalities

###### Dirk Hundertmark (UIUC Math)

Abstract: We continue to study Lieb-Thirring inequalities, and their connection to the Stability of Matter.

2:00 pm in 241 Altgeld Hall,Thursday, April 13, 2006

#### Tools from Iwasawa Theory

###### Steve Ullom (UIUC Math)

Abstract: (RAP Elliptic Curves and Iwasawa Theory, Part 10) This week: Tools from Iwasawa Theory needed for the one-variable Main Conjecture.

3:00 pm in 243 Altgeld Hall,Thursday, April 13, 2006

#### Hilbert polynomials over regular local rings via intersection theory on the blow-up

###### Claudia Miller   [email] (Syracuse University)

Abstract: Hilbert polynomials have classically been shown to be dtermined by intersections with hyperplanes. We give another approach over regular local rings via Intersection Theory on the blow-up scheme.

4:00 pm in 314 Altgeld Hall,Thursday, April 13, 2006

#### Some Ring - Theoretic problems inspired by Combinatorial Group Theory

###### Efim Zelmanov (University of California at San Diego )

Abstract: I will list open problems concerning infinite dimensional algebras and explain how each problem arises in Combinatorial Group Theory or is inspired by it.

Efim Zelmanov will present the Coble Memorial Lectures April 11-13 at 4 p.m. each day in 314 Altgeld Hall. Tea, coffee and cookies will be served at 3:15 p.m. before the lecture. A reception will be held Tuesday, April 11, at 5 p.m. in 321 Altgeld (Common Room).