To participate, please email Tommaso Cremaschi or James Farre.

In this expository talk, we discuss the basic properties and construction of lattices in the product of the automorphism groups of two trees. These groups were studied by Burger, Mozes, and others beginning in the 1990s. Using these techniques, one can construct groups that are finitely presented, torsion-free, simple, and split as a free product of free groups amalgamated along a subgroup of finite index. We also present some examples of these groups and analogies with Lie theory.