Recorded 27 March 2024. Abhijit Champanerkar of College of Staten Island, CUNY, presents "Geometric bounds for spanning tree entropy of planar lattices" at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Abstract: A surprising fact about the spanning tree entropy for many planar lattices is that its value is closely related to hyperbolic geometry. We conjecture sharp upper and lower bounds for the spanning tree entropy of any planar lattice. These bounds come from volumes of associated hyperbolic alternating links, hyperbolic polyhedra and regular ideal bipyramids. We explain the context and recent progress on our conjecture, which lies at the intersection of hyperbolic geometry, number theory, probability and graph theory. This is joint work with Ilya Kofman. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-statistical-mechanics-and-discrete-geometry/