The connections between these overlapping subjects are central to the CAAC workshop’s traditional thematic aims. They were emphasised in a series of expository lectures which were given by Tony Geramita and François Bergeron in January 2004 at Queen’s University, Kingston, ON. Through these lectures, it became evident that interesting special cases of Macaulay’s inverse systems, a fundamental concept in commutative algebra, are essentially the coinvariant spaces which arise in algebraic combinatorics and representation theory. These connections led to collaborative interdisciplinary research among two historically disjoint groups.

The CAAC meeting has been held annually since 2004. It focuses on the continually evolving interactions between combinatorial algebra and algebraic combinatorics. The most recent 2021 (virtual) meeting was hosted by the Université du Québec à Montréal. It featured invited talks which involved the theory of Hessenberg varieties (Megumi Harada), the Macdonald symmetric functions (Olya Mandelshtam, Anton Mellit, Luc Lapointe), q-Whittaker symmetric functions and nilpotent endomorphisms over finite fields (Steven Karp), Hilbert Schemes (Greg Smith) and syzygies of monomial ideals (Sara Faridi).  In particular, they highlighted the interactions among combinatorics, equivariant (toric) geometry, probability theory and mathematical physics (including the quantum field theories).

More information about the workshop can be found at: https://garsia.math.yorku.ca/CAAC_2022/

Finally, additional information on past activities can be found here: https://www.mathstat.dal.ca/~faridi/research/inverse_systems/workshop.html.