Department of Mathematics

Many phenomena in mathematics and science can be modeled by drawing finite graphs whose nodes are connected by edges with specified lengths.  The set of all such models forms a geometric space, with one point for each possible model.  The topological structure of this space is still quite mysterious and is the focus of current activity in several different fields, including  perturbative quantum field theory, number theory and  tropical algebraic geometry.  In this talk I will describe spaces of graphs,  explain why they are of particular interest in geometric group theory, then highlight some recent results (joint with M. Borinsky) on their Euler characteristics (Contact: Spencer Dowdall)