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Geometric bounds for spanning tree entropy of planar lattices

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Ilya Kofman (CUNY)

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, right-angled hyperbolic
polyhedra and hyperbolic regular ideal bipyramids. In this talk, we
explain the context for our conjecture, which lies at the intersection
of hyperbolic geometry, number theory, probability and graph theory.
This is joint work with Abhijit Champanerkar.