UIUC Dept. of Mathematics Seminar Calendar

     January 2012          February 2012            March 2012     
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
  1  2  3  4  5  6  7             1  2  3  4                1  2  3
  8  9 10 11 12 13 14    5  6  7  8  9 10 11    4  5  6  7  8  9 10
 15 16 17 18 19 20 21   12 13 14 15 16 17 18   11 12 13 14 15 16 17
 22 23 24 25 26 27 28   19 20 21 22 23 24 25   18 19 20 21 22 23 24
 29 30 31               26 27 28 29            25 26 27 28 29 30 31

Tuesday, February 7, 2012

Topology Seminar
11:00 am in 243 Altgeld Hall, Tuesday, February 7, 2012

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Submitted by franklan.

Nathaniel Stapleton (MIT)
Transchromatic twisted character maps
Abstract: The ring of coefficients of the codomain of the transchromatic generalized character maps is constructed to be the universal extension of the K(t)-localization of Morava E_n over which the p-divisible group associated to E_n splits as a sum of a height t connected p-divisible group and a height n-t constant p-divisible group. We will describe a refinement of this story to the universal extension of E_n over which the p-divisible group is a non-trivial extension of a height t connected p-divisible group by a height t constant p-divisible group. This refinement is able to recover the transchromatic generalized character maps and also recovers the classical generalized character theory of Hopkins, Kuhn, and Ravenel when t=0.

Probability Seminar
2:00 pm in Altgeld Hall 347, Tuesday, February 7, 2012

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Submitted by kkirkpat.

Jonathan Weare [email] (U Chicago Math)
A modified diffusion Monte Carlo and other ensemble sampling methods
Abstract: This talk will survey my efforts with coworkers to develop and analyze Monte Carlo sampling algorithms for complex (usually high dimensional) probability distributions. These sampling problems are typically difficult because they have multiple high probability regions separated by low probability regions and/or they are badly scaled in the sense that there are strong unknown relationships between variables. I'll begin the talk by discussing a simple modification of the standard diffusion Monte Carlo algorithm that results in a more efficient and much more flexible tool for use, for example, in rare event simulation. If time permits I'll discuss a few other ensemble based sampling tools designed to directly address energy barriers and scaling issues.

Geometry Seminar
2:00 pm in 243 Altgeld Hall, Tuesday, February 7, 2012

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Submitted by sba.

Dick Bishop (UIUC)
Comparison geometry, total curvature, pursuit-evasion
Abstract: (Joint work with S. Alexander and R. Ghrist.) After a review of comparison geometry, total curvature, and pursuit-evasion in CAT(0) spaces, the properties of pursuit flow, particularly its invariant conics (see Figure), for an evader tracking a line in the plane will be examined. A comparison for a pursuer of an evader tracking a geodesic in a CAT(0) space is given. More generally, any evader curve of finite total curvature in a CAT(0) can be developed to a curve in the plane with the same total curvature on all corresponding segments and there is a comparable pursuit flow in the plane.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, February 7, 2012

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Submitted by west.

Robert Jamison (UIUC Math and Clemson University)
Sum-Tolerance Graphs with Eutactic Rank
Abstract: This talk will focus on certain classes of rank-tolerance graphs that generalize the co-threshold-tolerance (co-TT) graphs introduced by Monma, Reed, and Trotter. In a rank-tolerance representation of a graph, each vertex is assigned two parameters: a rank, which represents the size of that vertex, and a tolerance, which represents an allowed extent of conflict with other vertices. Two vertices are adjacent if and only if their joint rank exceeds (or equals) their joint tolerance.

This study is motivated by the class SP of sum-product graphs, introduced by Golumbic and RJ, where the tolerance coupling function is the sum of the two tolerances and and the rank coupling function is the product of the two ranks. Many properties of sum-product graphs remain valid when product is replaced by a general eutactic function --- one that satisfies a certain convexity condition. The class of eutactic functions is quite broad. For example, it includes all symmetric polynomials (in two variables) with positive coefficients.

We show that SP strictly contains co-TT as well as all complete bipartite graphs $K_{2,n}$, and we survey a number of other results. My advisor Victor Klee vowed as graduate student that he would avoid formulae involving binomial coefficients. I vowed that I would never get involved with multidimensional calculus. In the talk I will explain (briefly) why we were both wrong.

Women's Seminar
4:00 pm in 241 Altgeld Hall, Tuesday, February 7, 2012

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Submitted by funk3.

Sogol Jahanbekam (UIUC Math)
Application of Combinatorial Nullstellensatz to graph factor and the 1,2-Conjecutre; Dynamic coloring of grids; Antiramsey Theory
Abstract: I will first talk about applications of Combinatorial Nullstellensatz to graph factors, the 1,2-Conjecture, and the 1,2,3-Conjecture. I'll give some sufficient conditions for a graph to have a specified factor and sufficient conditions with respect to minimum degree and chromatic number such that the 1,2-Conjecture or the 1,2,3-conjecture hold for the graph.

Next subject will be about r-dynamic coloring of grids, and finally I will introduce a future aim in Antiramsey Theory.