Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015

Notre Dame Math Graduate Student Seminar, 2015-2016

Min-max methods have been used recently to solve several long-standing problems in differential geometry by Fernando Coda Marques and Andre Neves. I will explain the basic idea of the method and I will give a sketch of some of these applications.

September 14, 2015

Speaker

Alexander Diaz

Title

Peak Sets of Classical Coxeter Groups

Abstract

Given a permutation (or more generally a signed permutation) we can "graph" it and study its "peaks." The combinatorial study of peaks of permutations is a topic that has caught the attention of mathematicians in the past 20 years. For example, it has been shown that the set of sums of permutations with a given peak set is a subalgebra of the group algebra. Extending the notion of peaks to signed permutations, we can generalize some of the results for usual permutations, while some others do not admit a generalization. In this talk I will survey some of the most relevant and beautiful results in this area, including some of my work in collaboration with Jose Pastrana and many others.