Research Interests(s)

My research is dedicated to understanding discrete infinite countable groups through their actions, primarily on nonpositively curved spaces and associated boundaries. The techniques involved are an interplay of geometry, analysis, and algebra.

Publications

The Semisimple Theory of Acylindricity in Higher Rank
Joint work with Sahana Balasubramanya, 63 pages, 7 figures, submitted

Le Conte de la Mesure Sur Les Complexes Cubiques CAT(0)
(In English) 11 pages, 11 figures
Topology at infinity of Discrete Groups Contemporary Mathematics–AMS, to appear

Homotopy equivalent boundaries of cube complexes
Joint work with David Futer and Mark Hagen
Geometriae Dedicata 218 (2024), no. 2, Paper No. 33, 83 pp. 82 pages

Contact Graphs, Boundaries, anda Central Limit Theorem for CAT(0) Cubical Complexes
Joint work with Jean L´ecur´eux and Fr´ed´eric Math´eus, 31 pages, Groups, Geometry, Dynamics, to appear

Effective Quasimorphisms on Right Angeled Artin Groups
Joint work with Jing Tao and Max Forester
Les Annales de L’Institut Fourier 69 (2019), no. 4, 1575–1626

Random Walks and Boundaries of CAT(0) Cubical Complexes
Joint work with Jean L´ecur´eux and Fr´ed´eric Math´eus
Commentarii Mathematici Helvetici, 93 (2018), no. 2, 291–333

The Poisson Boundary and Groups Acting on CAT(0) Cube Complexes
Ergodic Theory & Dynamical Systems, 38 (2018), no. 6, 2180–2223

The Mayer-Vietoris Sequence for Graphs of Groups, Property (T), and the First ℓ2-Betti Number
Joint work with Alain ValetteHomology, Homotopy, and Applications 19 (2017), no. 2, 251–274.

The Median Class and Superrigidity of Actions on CAT(0) Cube Complexes
Joint work with Indira Chatterji and Alessandra IozziWith an appendix by Pierre-Emmanuel Caprace
Journal of Topology, 9 (2016), no. 2, 349–400.

On Images of Real Representations of Special Linear Groupsover Complete Discrete Valuation Rings
Joint work with Pooja Singla
Glasgow Mathematical Journal, Volume 58, Number 1, (2016) 263–272

Reduced 1-cohomology and Relative Property (T)
Joint work with Alain Valette
Mathematische Zeitschrift, Volume 266, Number 4, (2010) 20 pages

Relative Property (T) and the Vanishing of the First ℓ2-Betti number
Bull. Belg. Math. Soc. Simon Stevin Volume 17, Number 5 (2010), 851-857

Relative Property (T) and Linear Groups
Les Annales de L’Institut Fourier
56 no. 6 (2006), p. 1767-1804