Probabilistic Operator Algebra Seminar: Free amalgamated graph products

Seminar | September 30 | 3-5 p.m. | 736 Evans Hall

 Archit Kulkarni and Jorge Garza Vargas, UC Berkeley

 Department of Mathematics

In the last two decades, tools from noncommutative probability theory have successfully been applied to study the spectra of graphs. In this direction, it has been shown that noncommutative notions of independence (classical, free, monotone and Boolean) correspond to previously studied graph products (Cartesian, free, comb and star, respectively). In this ongoing work, we introduce a new graph product to the dictionary, corresponding to the notion of freeness with amalgamation. On the one hand, we give a combinatorial description of our product, which allows us to construct infinite graphs of interest. On the other hand, we can analyse the spectra of these graphs using tools from operator valued free probability. As an application we obtain new results regarding the spectra of universal covers of graphs and Cayley graphs of amalgamated free products of groups.