TITLE:  Toric posets in Coxeter groups, toggle groups, non-crossing partitions, and homomesy.

ABSTRACT:  A toric poset is a cyclic analogue of an ordinary poset that arises as a chamber of a toric graphic hyperplane arrangement. In this talk, I will show how toric posets turn classic concepts and problems on reducibility in Coxeter groups into new problems on cyclic reducibility and conjugacy. After that, I will give a brief introduction to dynamic algebraic combinatorics and the toggle group introduced by Striker and Williams, and show how toric equivalence arises in a number of groups actions involving toggles and the homomesy phenomenon of Propp and Roby.

Title: Various Aspects of Eulerian Numbers

Abstract: In this talk we will survey various properties of Eulerian numbers, including connections to number theory, enumerative combinatorics, geometric combinatorics, toric algebra, and other topics as time permits.