Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, April 20, 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 20, 2006

1:00 pm in 347 Altgeld Hall,Thursday, April 20, 2006

#### On rigidity and the isomorphism problem for four strand tree braid groups

###### Lucas Sabalka (UIUC-Math)

Abstract: Given a tree braid group $B_nT$ on $n = 4$ strands, we are able to reconstruct the tree $T$. Thus tree braid groups $B_4T$ and trees $T$ (up to homeomorphism) are in bijective correspondence. That such a bijection exists is not true for higher dimensional spaces, and is an artifact of the 1-dimensionality of trees. We use this bijection to solve a version of the isomorphism problem for tree braid groups with $n = 4$ strands. We also make some comments on the possibility of generalizing this solution to tree braid groups with more strands.

1:00 pm in 241 Altgeld Hall,Thursday, April 20, 2006

#### Siegel Modular Forms and Their Satake Parameters

###### Nathan Ryan (UCLA)

Abstract: The first half of this talk will be an introduction to the basic theory of Siegel modular forms and their Hecke theory. These forms can be thought of as being higher dimensional generalizations of elliptic forms. In the second half of the talk, I will discuss computations I have done on the Satake parameters of a given form. The Satake $p$-parameters of a genus n Hecke eigenform are, roughly speaking, an (n+1)-tuple of nonzero complex numbers that encode all the eigenvalues for operators in the pth part of the Hecke algebra. If time allows, I will mention some computational results about the degrees of the parameters when the parameters are algebraic integers.

2:00 pm in 241 Altgeld Hall,Thursday, April 20, 2006

#### Properties of Kolyvagin's systems of units

###### Iwan Duursma (UIUC Math)

Abstract: (RAP Elliptic Curves and Iwasawa Theory, Part 11) This week: Properties of Kolyvagin's systems of units, the last ingredient for the proof of the One-Variable Main Conjecture.

2:00 pm in 243 Altgeld Hall,Thursday, April 20, 2006

#### Completely $p$-summing maps on the operator Hilbert space $OH$ for $1 < p < 2$

###### Khye Loong Yew (Academy of Mathematics and System Sciences in Chinese Academy of Sciences)

Abstract: We illustrate how the completely $p$-summing norm ($1 < p <2$) of the identity map on the $n$-dimensional operator Hilbert space $OH_n$ is bounded by a logarithmic factor. This is in sharp contrast to the Banach space situation. As applications, we estimate the completely $(2,p)$-mixing constant of $OH_n$ and show completely $p$-summing maps on $OH$ is the same as completely $1$-summing for $1 < p < 2$. All necessary background and definitions will be provided.

3:00 pm in 345 Altgeld Hall,Thursday, April 20, 2006

#### Generalized Poisson Distributions

###### Prof. M. Rao (University of Florida)

Abstract: This talk is postponed to a later date, the speaker could not make it here due to the closure of Atlanta airport on Wed, 04/19.

4:00 pm in 245 Altgeld Hall,Thursday, April 20, 2006

#### Intermittency and the parabolic Anderson model

###### Michael Cranston (University of California at Irvine)

Abstract: The Anderson model was introduced as a model for the behavior of electrons in crystals with impurities. In its parabolic form, it has proven to be a model for many interesting physical phenomena such as stellar magnetic fields, polymer dynamics and population growth models to name just a few. It exhibits a clumping phenomena called intermittency, which is in some sense the opposite of uniformity. It is the existence of widely spaced high peaks in a field (random function.) We will introduce the Anderson model, some of its applications and discuss the phenomenon of intermitency all at a nontechnical level. Host: R. Sowers