Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, February 4, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, February 4, 2014

1:00 pm in 347 Altgeld Hall,Tuesday, February 4, 2014

Enhancement of biological reaction by chemotaxis

Yao Yao (U of Wisconsin-Madison)

Abstract: In this talk, we consider a system of equations arising from reproduction processes in biology, where two densities evolve under diffusion, absorbing reaction and chemotaxis. We prove that chemotaxis plays a crucial role to ensure the efficiency of reaction: Namely, the reaction between the two densities is very slow in the pure diffusion case, while adding a chemotaxis term greatly enhances reaction. While proving our main results we also obtain a weighted Poincare's inequality for the Fokker-Planck equation, which might be of independent interest. This is a joint work with A. Kiselev, F. Nazarov and L. Ryzhik.

3:00 pm in 241 Altgeld Hall,Tuesday, February 4, 2014

Maximizing the number of nonnegative subsets

Hao Huang   [email] (Institute for Advanced Study & DIMACS)

Abstract: Given a set of n real numbers, if the sum of elements of every subset of size larger than $k$ is negative, what is the maximum number of subsets of nonnegative sum? In this talk we show that the answer is ${n-1 \choose k-1} +...+ {n-1 \choose 0}+1$, settling a problem of Tsukerman. We provide two proofs, the fi rst establishes and applies a weighted version of Hall's Theorem and the second is based on an extension of the non-uniform Erdos-Ko-Rado Theorem. Joint work with Noga Alon and Harout Aydinian.

4:00 pm in 245 Altgeld Hall,Tuesday, February 4, 2014

Homotopy and arithmetic: a duality playground

Vesna Stojanoska (MIT)

Abstract: Homotopy theory can be thought of as the study of geometric objects and continuous deformations between them, and then iterating the idea as the deformations themselves form geometric objects. One result of this iteration is that it replaces morphism sets with topological spaces, thus remembering a lot more information. There are many examples to show that the approach of replacing sets with spaces in a meaningful way can lead to remarkable developments. In this talk, I will explain some of my recent work in the case of implementing homotopy theory in arithmetic in a way which produces new results and relationships between some classical notions of duality in both fields.