## Research:

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

## Events:

Asymptotic group theory, Aug 17-21, 2015, Renyi Institute, Budapest, Hungary (organizers: Miklos Abert and Laci Pyber)ESI Programme in Measured Group Theory, 18 Jan - 18 March, 2016, ESI, Viena, Austria (organizers: Miklos Abert, Goulnara Arzhantseva, Damien Gaboriau, Thomas Schick and Andreas Thom)

Measured group theory, 28 Aug - 3 September, 2016, MFO, Oberwolfach, Germany (organizers: Miklos Abert, Damien Gaboriau and Andreas Thom)

## Members of the group:

- Principal Investigator: Miklós Abért
- Endre Csóka (senior researcher)
- Viktor Harangi (Marie Curie Fellow)
- Ádám Timár (Marie Curie Fellow)
- Samuel Mellick (Phd student)
- László Márton Tóth (Phd student)
- András Mészáros (junior researcher)
- Péter Csikvári (postdoc, MIT)

## Visiting researchers:

- Balint Virág (University of Toronto)
- Tsachik Gelander (Weizmann Institute)
- Andrew Stewart (University of Toronto)
- Anatoly Vershik (Steklov Institute)
- Idan Perl (Ben Gurion University)
- Arie Levit (Weizmann Institute)
- Andrei Alpeev (Steklov Institute)

## Open positions:

A postdoctoral position is open, starting September 2016 or before. See Postdoctoral position for details.## Contact:

Email: invgrogra at renyi.hu