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Math Colloquium
Adam Marcus
Yale University
Title: Combinatorial Results using Nonlinear Orders

Abstract: The concept of order is an important one in mathematics, but many of the results in combinatorics deal with inherently linear orders. That is, they have the usual a < b and b < c implies a < c type of transitivity. Many problems, however, do not mold so easily into this framework. I will discuss two such problems and the techniques used to deal with them. In the first part of the talk, I will discuss multi-dimensional orders and show how they were used to solve the Stanley--Wilf and Alon--Friedgut conjectures on permutation and word avoidance. In the second part, I will discuss cylic orders and show how they can can be used to improve the bound on the complexity of planar pseudo-circle arrangements, a problem that has a number of geometric consequences. The results are in collaboration with Gabor Tardos.

Date: Thursday, February 26, 2009
Time: 4:30 pm
Location: Wean Hall 8427