Groups and Graphs

ERC Consolidator Grant 648017

Asymptotic invariants of discrete groups, sparse graphs and locally symmetric spaces

Our research focuses on the following notions:

• Rank gradient, mod p and Q-homology growth, log torsion in homology, deficiency growth
• p.m.p. group actions, graphings, cost, weak containment, profinite actions
• Invariant random subgroups, measured groupoids of p.m.p. actions
• Local sampling convergence, unimodular random graphs, local-global convergence
• Stochastic processes on groups, graphs and symmetric spaces
• Sofic groups and actions
• Asymptotic invariants of locally symmetric spaces
• Cellular maps, factor of i.i.d. processes
• Ramanujan graphs, actions and manifolds
• Structure theory of random regular graphs
• Graph polynomials, matching and chromatic measures of graphs
• Statistical physics on finite graphs and their limits, sofic entropy