陈绿洲博士,Purdue University

Several topological optimization problems involving surfaces can be turned into linear programming problems. In the case of stable commutator length, this was first discovered by Danny Calegari in the case of free groups. I later generalized this to a much broader class of graphs of groups. In this talk, I will explain the idea of turning such topological optimization problems into linear programming problems, and how linear programming duality can be used to obtain sharp lower bounds of stable commutator length (or similar invariants) as a replacement of Bavard's duality.