Triangular Ice Combinatorics

Explore the fascinating world of triangular ice combinatorics in this 54-minute lecture from the Asymptotic Algebraic Combinatorics 2020 conference. Delve into the intricacies of Alternating Sign Matrices (ASM) and their connections to various combinatorial and algebraic problems. Discover the Triangular Lattice version of the Ice model, leading to an integrable 20 Vertex model and the introduction of Alternating Phase Matrices (APM). Learn about the generalization of the ASM-DPP correspondence and its relation to quarter-turn symmetric domino tilings. Examine the compact determinant formula for APM enumeration and explore conjectures for triangular Ice with different boundary conditions. Gain insights into the limit shape of large APM as presented by P. Di Francesco from the University of Illinois and IPhT Saclay.