Geometric Bounds for Spanning Tree Entropy of Planar Lattices

Explore the fascinating intersection of hyperbolic geometry, number theory, probability, and graph theory in this 43-minute lecture presented by Abhijit Champanerkar at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Delve into the surprising relationship between spanning tree entropy of planar lattices and hyperbolic geometry. Examine conjectured sharp upper and lower bounds for spanning tree entropy, derived from volumes of hyperbolic alternating links, hyperbolic polyhedra, and regular ideal bipyramids. Gain insights into recent progress on this conjecture and its implications across multiple mathematical disciplines. Recorded on March 27, 2024, this talk offers a deep dive into cutting-edge research at the College of Staten Island, CUNY, in collaboration with Ilya Kofman.