Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, November 29, 2005.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     October 2005          November 2005          December 2005
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1          1  2  3  4  5                1  2  3
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Tuesday, November 29, 2005

11:00 am in 241 Altgeld Hall,Tuesday, November 29, 2005

#### Higher Grothendieck-Witt groups and A^1-homotopy theory

###### Marco Schichting (Louisiana State)

Abstract: I will explain two results motivated by A^1-homotopy theory. 1) An analogue of Matsumoto's theorem for quadratic forms, and (if time permits) 2) cdh-descent for Karoubi's stabilized Witt groups.

1:00 pm in 241 Altgeld Hall,Tuesday, November 29, 2005

#### Ten minute talks

Abstract: Ten minute talks contributed by members of the seminar.

1:00 pm in 345 Altgeld Hall,Tuesday, November 29, 2005

#### First Return Recovery of Functions on Ultrametric Spaces

###### Jonathan Duncan (Indiana University)

Abstract: In 1995 U.B. Darji and M.J. Evans introduced the concept of a first return recoverable function. They showed that on compact separable metric spaces, first return recoverable functions are exactly the Baire class one functions. Several years later, D. Lecomte exhibited an ultrametric space on which there exists a Baire class one function which is not first return recoverable. My work focuses on identifying the properties required of an ultrametric space in order to ensure the existence of a non-first return recoverable Baire class one function. This talk will review the definitions and results mentioned above as well as the results of my research thus far.

1:00 pm in 347 Altgeld Hall,Tuesday, November 29, 2005

#### L_2 bounds for the radius of the attractor of the Kuramoto-Sivashinsky equation

###### Thomas Gambill (UIUC Math)

Abstract: We consider the Kuramoto-Sivashinsky (KS) equation in one dimension with periodic boundary conditions. By applying a Lyapunov function argument similar to the one first introduced by Nicolaenko, Scheurer, and Temam, and later improved by Collet, Eckmann, Epstein and Stubbe, and Goodman, we prove that the set &ob; u(x,t) : ||u(x,t) - phi(x) ||2  <  C L1.5 &cb; is invariant and exponentially attracting in forward time. We further show that for a large class of functions phi(x) the exponent 1.5 cannot be improved.

2:00 pm in 243 Altgeld Hall,Tuesday, November 29, 2005

#### No meeting this week

2:00 pm in 152 Henry,Tuesday, November 29, 2005

#### No Meeting This Week

2:00 pm in 241 Altgeld Hall,Tuesday, November 29, 2005

#### A description of sofic groups in terms of nonstandard analysis, II

###### Evgeny Gordon (Eastern Illinois University)

Abstract: Sofic groups were first defined by M. Gromov as a common generalization of amenable groups and residually finite groups. B. Weiss proved that the old problem of Gottschalk on surjunctive groups has a positive solution for sofic groups. The problem of existence of non-sofic groups remains open. In this talk we discuss this topic in terms of nonstandard analysis, which allows us to simplify some definitions and proofs.

3:00 pm in 241 Altgeld Hall,Tuesday, November 29, 2005

#### On set edge-choosability of graphs

###### Weiting Cao (UIUC Math)

Abstract: A graph is (r,s)-colorable if we can assign each vertex an s-subset of [r] such that adjacent vertices receive disjoint sets. It is (r,s)-choosable if such a coloring can be chosen whenever each vertex has a list of r available colors (instead of always the same set [r]). A graph is (r,s)-edge-choosable if its line graph is (r,s)-choosable.

For a simple graph G and a fixed integer s, we seek the minumum r such that G is (r,s)-edge-choosable. We prove that the Petersen graph is (7,2)-edge-choosable and that every 3-edge-colorable graph is (7,2)-edge-choosable. It remains open whether all graphs with maximum degree 3 are (7,2)-edge-choosable. (This is joint work with Daniel Cranston.)

3:00 pm in 243 Altgeld Hall,Tuesday, November 29, 2005

#### Today's seminar cancelled

###### (UIUC Math)

4:00 pm in 2369 Beckman Institute,Tuesday, November 29, 2005

#### Hilbert Series of Subspace Arrangements (d'apres Harm Derksen)

###### Robert Fossum   [email] (UIUC Math)

Abstract: Subspace Arrangements arise when segmenting data, such as images. Derksen has established a closed formula for the Hilbert Function of the vanishing ideal of a subspace arrangement that is useful in the analysis of the arrangements. In particular in segmenting images. The first few lectures in this series will go over Derksen's proof. Later applications will be made.