UIUC Dept. of Mathematics Seminar Calendar

    September 2009          October 2009          November 2009    
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Tuesday, October 6, 2009

Topology seminar
11:00 am in 241 Altgeld Hall, Tuesday, October 6, 2009

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Submitted by bertg.

Megan Guichard Shulman (University of Chicago)
RO(Z/p)-graded cohomology of some classifying spaces
Abstract: When dealing with G-spaces for a finite group G, there are many reasons to think that RO(G)-graded Bredon cohomology is the ``correct'' equivariant cohomology theory to consider. Unfortunately, it is also very difficult to compute with. Gaunce Lewis calculated the RO(Z/p)-graded cohomology of complex projective spaces in the 1980s, and William Kronholm calculated the RO(Z/2)-graded cohomology of some real projective spaces in his 2008 thesis, but to date no other calculations have been done. In this talk, I will describe an equivariant spectral sequence which can be used in conjunction with the equivariant Serre spectral sequence and the equivariant cohomology of complex projective spaces to identify the RO(Z/p)-graded cohomology of the equivariant classifying space B_{Z/p} O(2).

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, October 6, 2009

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Submitted by west.

Kevin Milans (UIUC Math)
Acyclic sets in k-majority tournaments
Abstract: Given a set S of permutations of a ground set X, the majority digraph of S is the directed graph on X where there is an edge from u to v when a majority of the permutations in S rank u above v. For odd k, a k-majority tournament is a tournament that arises as the majority digraph of a set of k permutations. Alon, Brightwell, Kierstead, Kostochka, and Winkler proved that for some constant c, every k-majority tournament contains a dominating set of size at most cklogk.

We study the maximum size of an acyclic set of vertices in k-majority tournaments. Every n-vertex 3-majority tournament contains an acyclic set of size n^1/2; we present a family of 3-majority tournaments that have no acyclic sets of size larger than 2n^1/2. We show that every n-vertex 5-majority tournament contains an acyclic set of size n^1/4. For general k, every k-majority tournament contains an acyclic set of n^f(k), where f(k) = 3^-(k-1)/2. This is joint work with Dan Schreiber and Douglas B. West.

Mathematics in Science and Society (MSS)
4:00 pm in 245 Altgeld Hall, Tuesday, October 6, 2009

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Submitted by rdeville.

Eric Vanden-Eijnden (Courant Institute)
Modeling and simulation of reactive events
Abstract: The dynamics of biomolecular systems is typically characterized by a wide range of time scales, complicating their study via computer simulations. Of particular difficulty are situations which involve rare reactive events such as conformation changes of macromolecules, nucleation events during first-order phase transitions, or chemical reactions. The occurrence of these rare events is related to the presence of dynamical bottlenecks of energetic and/or entropic origin which effectively partition the configuration space of the system into metastable basins. The system spends most of its time fluctuating within these long-lived metastable states and only rarely makes transitions between them. The rare events then determine the long-time evolution of the system which is often of most interest to us but is typically beyond the reach of brute-force simulations. In this talk, I will discuss basic statistical mechanics questions related to the description of rare reactive events, explain why such a statistical description is not only useful but also necessary, and present numerical methods that permit us to identify the pathway, free energy and rate of these events.