Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, November 3, 2005.

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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, November 3, 2005

11:00 am in 241 Altgeld Hall,Thursday, November 3, 2005

#### Finiteness theorems for curves, 5.

###### Prof. D. Grayson (UIUC Math)

Abstract: In a series of lectures, we'll present a gentle introduction to finiteness theorems for algebraic and arithmetic curves, aiming at cohomology and K-theory via stable vector bundles and the corresponding concept for lattices in the geometry of numbers. This talk will take up the case of rings of integers in a number field.

12:00 pm in 464 Loomis,Thursday, November 3, 2005

#### On singular effective superpotentials in supersymmetric gauge theories

###### Mohammad Edalati (U. Cincinnati, Physics)

1:00 pm in 347 Altgeld Hall,Thursday, November 3, 2005

#### Intersecting subgroups in free products of groups, II

###### Sergei Ivanov (UIUC Math)

Abstract: Some results and problems related to the rank and the Kurosh rank of the intersection of subgroups in free products of groups will be discussed.

1:00 pm in Altgeld Hall,Thursday, November 3, 2005

#### Hilbert Series of

1:00 pm in Altgeld Hall,Thursday, November 3, 2005

#### Hilbert Series of "

2:00 pm in 345 Altgeld Hall,Thursday, November 3, 2005

#### More On Canonical Curves in Low Genus

###### Anca Mustata (UIUC)

Abstract: We'll continue our discussion of canonical curves in low genus, and, if there is time, discuss how to find quadrics in the ideal of a canonical curve.

2:00 pm in Altgeld Hall,Thursday, November 3, 2005

#### Computing roots of certain polynomials

###### Marc Masdeu Sabate (UIUC Math)

Abstract: In 1831, the French Academy rejected a proof given by Galois of the statement "A degree-p irreducible polynomial over the rationals is solvable by radicals if and only if all its roots can be expressed as rational functions over Q of any two of them". This theorem is actually true, and the result is still attributed to Galois. However, it is highly non-constructive, so finding the actual relations among such roots is still an open problem. I will explain how Spearman and Williams found a solution for the first non-trivial example (the dihedral group of 10 elements), and how it can be extended to all dihedral groups of 2p elements for p prime. The next unsolved case is the Frobenius group of 20 elements, so everyone is invited to propose their own algorithm for this case.

2:00 pm in 243 Altgeld Hall,Thursday, November 3, 2005

#### The Distal Points of a Cascade

###### Robert Kaufman (UIUC Math)

Abstract: A cascade is a system (X, f), where X is a compact metric space and f a homeomorphism of X onto X. A pair (x,y) of points is called proximal if the infimum of d(f^nx,f^ny) is 0; otherwise the pair is distal. A point is distal if it is proximal only to itself. The distal concept is central in dynamics. How bad (or good) can the set of distal points be? We provide an answer via flows in the plane (these flows flow; they don't jump).

3:00 pm in 345 Altgeld Hall,Thursday, November 3, 2005

#### Probability estimates for random walks with barriers

###### Kevin Ford (UIUC Math)

Abstract: Abstract: We consider a recurrent random walk S_0, S_1, ..., where S_j = X_1 + ... + X_j and the X_j are i.i.d. random variables with mean 0 and variance 1. We prove very precise estimates for the probability that S_j < y (j=0,1,...,n-1) given that S_n = x, under very general conditions on the distribution of X_i. We will discuss an application of these bounds to the theory of order ststistics, giving a sharpening and generalization of an estimate of Smirnov from 1939.

4:00 pm in 245 Altgeld Hall,Thursday, November 3, 2005

#### Mathematical Models of Viscoelastic Fluids: Wormlike Micelles

###### Pamela Cook (University of Delaware)

Abstract: Modeling challenges in describing flows of viscoelastic (polymer) solutions will be described as well as the physical measurements that support the modeling process and that indicate the need for model predictions. Special attention will be given to flows of "living polymers", that is wormlike micelles. Both kinetic theory and network theory will be introduced, with some inclusion of and description of reptation theory. The challenges of solving the resulting nonlinear partial differential equation system in an inhomogeneous flow will be described. Host: Rinat Kedem

7:30 pm in Foellinger Auditorium,Thursday, November 3, 2005

#### An Evening with Barry Greenstein: UIUC alumnus, mathematician, author of "Ace on the River,"and world-renowned poker player.

Abstract: Barry Greenstein was an undergraduate computer science major and a mathematics graduate student at the University of Illinois in the 1970s and 1980s. He is one of the world's very best professional poker players, and the author of the acclaimed book "Ace on the River." Sometimes known as "the Robin Hood of poker," Greenstein has donated millions of dollars of his tournament winnings to charity over the past several years.
Free and open to the public. General admission--no tickets required.
http://www.math.uiuc.edu/BG