I am an Assistant Professor in the Department of Mathematics at The University of Texas at Austin.


My research interests include Hyperbolic Geometry, Kleinian Groups, Geometric Group Theory, Low Dimensional Topology and Teichmüller Theory.


Curriculum Vitae

Statement of Research



    Big Heegaard Distance implies finite mapping class group, Topology and Its Applications 154 (2007), no. 16, 2939--2949.

    Heegaard splittings and pseudo-Anosov Maps, with Juan Souto, Geometric and Functional Analysis 19 (2009), no. 4, 1195--1228.

    Quasi-convexity and Shrinkwrapping, Algebraic and Geometric Topology 9 (2009), 2443--2478.

    Non-realizability and ending laminations - Proof of the Density Conjecture, with Juan Souto, Acta. Math. 209 (2012), no. 2, 323--395.

    Distributional limits of Riemannian Manifolds and graphs with sublinear genus growth, with Pekka Pankka and Juan Souto, Geometric and Functional Analysis 24 (2014), 322--359.

A note on Thurston’s Uniform Injectivity Theorem, with Juan Souto, in preparation.

Splittings, models and bounds in hyperbolic geometry, with Jeff Brock, Yair Minsky and Juan Souto, in preparation.

Uniform models for hyperbolic structures, with Cyril Lecuire, in preparation.


Heegaard splittings and hyperbolic geometry (5/12/2005)



    Fall 2008: M328K - Introduction to Number Theory


    Fall 2009: M392C - The Curve Complex


    Spring 2012: M392C - Topics in Hyperbolic Geometry


    Fall 2012: M361C - Introduction to Real Analysis

    Spring 2013: M367K - Topology I


    Fall 2013: M408C - Differential and Integral Calculus

    Fall 2014: M367K - Topology I

                               TTh 12:30 - 2:00 in GDC 6.202

Office Hours:      T 11:00-12:00 and Th 2:00 - 3:00



E-Mail: my first name at math dot utexas dot edu

Office:     RLM 12.156

                (512) 471 - 1184

Mailing Address: Department of Mathematics, RLM 8.100, 2515 Speedway, Stop C1200, Austin, TX 78712-1202