Department of

Mathematics


Seminar Calendar
for events the day of Friday, April 7, 2006.

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                        30                                         

Friday, April 7, 2006

12:00 pm in 343 Altgeld Hall,Friday, April 7, 2006

Rogers-Ramanujan Identities

Mourad Ismail (University of Central Florida)

Abstract: We present some generalizations of the Rogers-Ramanujan identities through connection relations for special orthogonal polynomials. The technique used is to evaluate integrals in two different ways, one gives the series side and the other gives the infinite product side. The Jacobi triple triple product identity is a key tool.

1:00 pm in 141 Altgeld Hall,Friday, April 7, 2006

A simpler axiomatization of the Spencer-Shelah almost sure theories

Michael C. Laskowski (University of Maryland)

Abstract: Shelah and Spencer proved that when alpha is irrational in (0,1) there is an almost sure theory T of random graphs of size n, when the edge probability is n^{-alpha}. Somewhat later, Baldwin observed that the same theory T can be visualized as the theory of a generic object of a generalized Fraisse construction. We give an AE axiomatization of T and examine other countable models of T. Somewhat surprisingly, even though it can be uniquely characterized as being a Fraisse limit, the generic does not appear to be any particularly `special' model of T. Although most of the talk will focus on this specific example, we will discuss applicability of these methods to other Fraisse constructions.