My research lies in ergodic theory, geometric group theory, and operator algebras. These areas draw on tools from functional analysis, probability, combinatorics, and graph theory and share a common program involving the study of dynamics and symmetry in spaces and algebras with measure-theoretic or topological structure. For some flavour of their interaction see my Oberwolfach Snapshot.

PHD STUDENTS

Miguel Donoso-Echenique (current)
Spyridon Petrakos (PhD 2025)
Petr Naryshkin (PhD 2024)
James O'Quinn (PhD 2024)
Xin Ma (PhD 2019)
March Boedihardjo (coadvisor, PhD 2016)
Timothy Rainone (PhD 2015)
Mitchell Hitchcock (PhD 2010)

EDITORIAL WORK

Transactions of the American Mathematical Society (2022-)
Memoirs of the American Mathematical Society (2022-)
Journal de l'Ecole polytechnique - Mathématiques (2025-)
Groups, Geometry, and Dynamics, Managing Editor (2014-2025)

CONFERENCE ORGANIZATION
Groups and Dynamics: Topology, Measure, and Borel Structure
Oberwolfach, Germany, April 12–17, 2026
Probability, Dynamics, and the Geometry of Groups
University of Münster, September 9-13, 2024
Group Actions: Dynamics, Measure, Topology
University of Múnster, Germany, November 28 – December 2, 2022
Groups and Dynamics: Topology, Measure, and Borel Structure
Oberwolfach, Germany, January 16–22, 2022
SUMIRFAS
Texas A&M University, July 26-28, 2019
Great Plains Operator Theory Symposium
Texas A&M University, May 28 - June 1, 2019
SUMIRFAS
Texas A&M University, August 17-19, 2018
Operator Algebras, Geometry, and Actions
Banach Center, Warsaw, Sep 29 - Oct 1, 2017
SUMIRFAS
Texas A&M University, July 21-23, 2017
Ergodic Theory and Operator Algebras
Texas A&M University, June 5-9, 2017
SUMIRFAS
Texas A&M University, July 29-31, 2016
Groups, Dynamics, and Operator Algebras
Queen Mary University of London, July 18-22, 2016
SUMIRFAS
Texas A&M University, July 31 - August 2, 2015
SUMIRFAS
Texas A&M University, July 25-27, 2014
Concentration Week on Groups, Groupoids, and Dynamics
Texas A&M University, June 9-13, 2014
Arbeitsgemeinschaft: Sofic Entropy
Oberwolfach, October 6-12, 2013
Dynamics, Geometry, and Operator Algebras
Texas A&M, August 5-9, 2013
SUMIRFAS
Texas A&M, August 2-4, 2013
SUMIRFAS
Texas A&M, August 3-5, 2012
Larsonfest
Texas A&M, July 20-22, 2012
Groups, Geometry, and Random Structures
Texas A&M, March 22-25, 2012
Set Theory and C*-Algebras
American Institute of Mathematics, January 22-26, 2012
Session on Dynamical Systems and Operator Algebras
AMS Sectional Meeting, University of Nebraska, October 14-16, 2011
Group Actions on Measure Spaces
Texas A&M, March 24-27, 2011
Set Theory and Functional Analysis
Texas A&M, July 26-30, 2010
East Coast Operator Algebras Symposium
Texas A&M, October 24-25, 2009