Svenja Huntemann (Carleton University)
Strong Placement Games: Connecting Commutative Algebra and Combinatorial GamesAffine planes with ovals for blocks

Combinatorial games are 2-player, perfect information games, for example Chess, Go, Nim, and Hex. Many combinatorial games consist of placing pieces on the board, following a set of rules to decide where to place. We are interested in a large subclass of these games, called strong placement games, which has many interesting properties. Among others, they are in a one-to-one correspondence with simplicial complexes and monomial ideals. After introducing all concepts, I will show how this connection between combinatorial games and commutative algebra works. I will also discuss how this link allows for new tools to study various game theoretic properties of strong placement games, as well as some interesting questions in algebra and combinatorics arising from it.