Department of Mathematics Colloquium


Abstract 

Given a permutation (thought of as a sequence
of integers), one can construct a graph (in the sense of vertices and
edges) called the Bruhat graph. I will give a characterization of
permutations whose Bruhat graphs can be drawn without edges crossing in
terms of the elementary notion of pattern avoidance. The
motivation for this theorem comes from theoretical questions about
pattern avoidance further motivated by questions in representation
theory. Though the motivation involves deep mathematics, the new
theorems will be accessible to most middle schoolers and were proven by
Chris Conklin, an undergraduate student who worked with me in the
summer of 2010. Undergraduate students are encouraged to attend. 