Theme Semester in Recent Advances in Combinatorics

Marcelo Aguiar (Texas A&M University)
François Bergeron (Université du Québec à Montréal)
Nantel Bergeron (York University)
Mark Haiman (University of California, Berkeley)
Stephanie van Willigenburg (University of British Columbia)

The goal of this workshop is to take stock of ongoing work, and of the many rich problems that still need to be addressed in two area, naturally linked through the combinatorics behind the study of Macdonald polynomials. On one side, the recent past has seen a marked deepened interest in the study of graded Hopf algebras, in part because of their fundamental interactions with algebraic combinatorics, but also because of their importance for Theoretical Physics. In particular, it has recently been made apparent that Hopf Algebras play a crucial role in the study of renormalizations in quantum electrodynamics. On the other hand, in the realm of symmetric and quasisymmetric functions it also appears to play a very significant role, with surprising repercussions in representation theory, algebraic geometry, mathematical physics, and the combinatorics of Macdonald polynomials. From another perspective, there has been a lot of recent developments regarding combinatorial models for Macdonald polynomials and their link to diagonal coinvariant spaces.We expect to link these often complementary point of view.

This workshop is preceded by the School on Macdonald Polynomials.