MAAGC 2019 ABSTRACTSDave Anderson (Ohio State University):Title: TBA Karola Meszaros (Cornell and IAS):Title: TBA Vic Reiner (University of Minnesota):Title: On the "coincidental" reflection groupsAbstract: Much combinatorics these days involves finite reflection groups, both real and complex. In this talk, we will focus on results that work out especially nicely for what have been called the "coincidental" reflection groups. These are the groups generated by n reflections acting on n-dimensional space whose exponents form an arithmetic sequence. They include the real reflection groups of types A, B, H_3, dihedral groups, and all of the non-real reflection groups that are symmetries of regular complex polytopes, which are known as Shephard groups. In particular, the coincidental groups have some extra elegant invariant theory, leading to product formulas for the face numbers and h-vectors of their associated cluster complexes, and a q-analogue of the transformation taking the h-vector to f-vector. This is joint work with Anne Shepler and Eric Sommers. Michelle Wachs (Miami):Title: TBA |