Research                

Publications

The semi-simple theory of higher rank acylindricity 

Joint work with Sahana Balasubramanya 

In honor of Bhama Srinivasan

76 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, February 2025

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. 

Contact Graphs, Boundaries, and a Central Limit Theorem for CAT(0) Cubical Complexes

Joint work with Jean Lécuréux and Frédéric Mathéus 

31 pages, Groups, Geometry, Dynamics, 18(2024), no.2, 677–704

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 Lécuréux and Frédéric Mathéus 

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 Valette 

Homology, 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 Iozzi With an appendix by Pierre-Emmanuel Caprace 

Journal of Topology, 9 (2016), no. 2, 349–400.

On Images of Real Representations of Special Linear Groups over 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 With an appendix by Florian Martin and 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), Linear Groups, and Applications

University of Illinois, Chicago

ProQuest LLC, Ann Arbor, MI, 2006, 105 pp. ISBN: 978-0542-86795-8

Relative Property (T) and Linear Groups

Les Annales de L’Institut Fourier 56 no. 6 (2006), p. 1767-1804

OTHER PUBLICATIONS:

El premio Abel reconoce a dos pioneros de la interacción entre probabilidad y álgebra

 Joint with Yago Antolín, outreach newspaper article in spanish

Café y teoremas, El País March 24, 2020

PhD Supervision:

Jennifer Beck 2024 – PhD in Computational Mathematics 

Automaticity and Products of Hyperbolic Spaces

The University of North Carolina at Greensboro 

ProQuest LLC, Ann Arbor, MI, 2024. 91 pp. 

ISBN:979-8383-70084-6