SEMINARIO Probabilita' Tyler Helmuth (University of Bristol) Titolo: Random spanning forests and hyperbolic symmetry Giovedi' 12 Dicembre 2019 ORE 10:00 Dipartimento di Matematica e Fisica Universita' degli Studi Roma Tre Largo San Leonardo Murialdo,1 - Pal.C - Aula 211 Abstract The arboreal gas is a probability measure that arises from conditioning the random subgraph given by Bernoulli(p) bond percolation to be a spanning forest, i.e., to contain no cycles. This conditioning makes sense on any finite graph G, and specializes to the uniform measure on spanning forests when p = 1/2. One is naturally lead to ask about the percolative properties of the arboreal gas, and this turns out to be a surprisingly rich question. I will discuss some results and conjectures about the arboreal gas, most of which are based on important relations between the arboreal gas and spin systems with hyperbolic symmetry. Based on joint work in progress with Roland Bauerschmidt, Nick Crawford, and Andrew Swan.