Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, April 6, 2006.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, April 6, 2006

1:00 pm in 241 Altgeld Hall,Thursday, April 6, 2006

#### TBA

1:00 pm in 347 Altgeld Hall,Thursday, April 6, 2006

#### Random Quotients of the Modular Group are Rigid and Essentially Incompressible

###### Paul Schupp (UIUC-Math)

Abstract: We consider finitely presented quotients of the modular group, that is groups with a presentation $G = \angle a,b ; a^2, b^3, r_1, ...,r_m \rangle$. We show that such quotients generically satisfy a very strong Mostow-type rigidity. Given such a group $G$ its associated geometric structure is its Cayley graph $\Gamma (G, \&ob; a,b \&cb;$ on the generators $a,$. Generically, two such quotients are algebraically isomorphic if and only if their associated Cayley graphs are isometric by a graph-isomorphism fixing the identity element.

2:00 pm in 243 Altgeld Hall,Thursday, April 6, 2006

#### Distance preserving maps on operator algebras

###### Jinchuan Hou (Shanxi Teachers University, China (visiting UIUC))

Abstract: I'd like to talk about some characterizations of general surjective maps that preserve the distance on C*-algebras and nest algebras.

2:00 pm in 241 Altgeld Hall,Thursday, April 6, 2006

#### Iwasawa modules and p-adic L-series

###### Jonathan Webster (UIUC Math)

Abstract: (RAP Elliptic Curves and Iwasawa Theory, Part 9) This week: The relation between characteristic polynomials of Iwasawa modules and L-series.

2:00 pm in 443 Altgeld Hall,Thursday, April 6, 2006

#### What is Elliptic Cohomology?

###### Hsian-Yang Chen (UIUC Math)

Abstract: Elliptic chomology arises from the complex cobordism theory, whose coefficient ring classifies the formal group laws. Also, every elliptic curve inherits naturally a formal group law. In this talk, I will explain these terminologies, construct elliptic cohomology by connecting these objects, and discuss some variants.

4:00 pm in 245 Altgeld Hall,Thursday, April 6, 2006

#### Orthogonal Polynomials, Discriminants, and Electrostatic Equilibrium Problems

###### Mourad E.H. Ismail (University of Central Florida)

Abstract: Stieltjes and Hilbert derived closed form expressions for discriminants of Jacobi polynomials. Stieltjes studied the electrostatics equilibrium problem of n-unit charged particles restricted to (–1,1) under the external field of charges (á +1)/2 and (â +1)/2 at ±1. The potential is a logarithmic potential. Stieltjes showed that the equilibrium position of the particle is at the zeros of the Jacobi polynomial Pn(á,â) (x). We discuss the recent developments on this problem, its extension to general orthogonal polynomials and the role discriminants play in the solution of the problem. This includes deriving first order raising and lowering operators and second order differential equations for general orthogonal polynomials. Host: Bruce Berndt