Research

Published papers

1. Joint with Richard Canary and Andrew Zimmer, "Patterson-Sullivan measures for transverse subgroups" arXiv:2304.11515, to appear in Journal of Modern Dynamics.

2. Joint with Andrew Zimmer, "Regularity of limit sets of Anosov representations" arXiv:1903:11021, to appear in Journal of Topology.

3. Joint with Gye-Seon Lee, "Cusped Borel Anosov representations with positivity" Geometriae Dedicata 218, 54 (Francois Labourie’s 60th birthday special edition). 

4. Joint with Zhe Sun, ''The Goldman symplectic form on the PGL(V)-Hitchin component'' arXiv:1709.03589, to appear in Memoirs of the American Mathematical Society.

5. Joint with Sungwoon Kim and Ser Peow Tan, "Weakly positive and directed Anosov representations" Advances in Mathematics 408 (2022) 108611.

6. Joint with Richard Canary and Andrew Zimmer, "Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups" Advances in Mathematics 404 (2022), 108439.

7. Joint with John Loftin, "Coordinates on the augmented moduli space of convex RP^2 structures" Journal of the London Mathematical Society 104 (2021), 1930-1972.

8. Joint with Anna Wienhard and Zhe Sun, ''Flows on the PGL(V)-Hitchin component'' Geometric and Functional Analysis 30 (2020), 588-692.

9. Joint with Jeffrey Danciger, "Affine actions with Hitchin linear part" Geometric and Functional Analysis 29 (2019), 1369-1439.

10. Joint with Giuseppe Martone, "Positively ratioed representations" Commentarii Mathematici Helvetici 94 (2019), 273-345.

11. Joint with Anna Wienhard, "Deforming convex real projective structures" Geometriae Dedicata 192 (2018), 327-360. (Bill Goldman’s 60th birthday special edition). 

12. Joint with Gye-Seon Lee, "Collar lemma for Hitchin representations" Geometry & Topology 21 (2017), 2243-2280.

13. "Degeneration of Hitchin representations along internal sequences" Geometric and Functional Analalysis 25 (2015), No. 5, 1588-1645.

14. "The degeneration of convex RP^2 structures on surfaces" Proceedings of the London Mathematical Society 111 (2015), Issue 5, 967-1012.

15. "Geometry of the Hitchin component" PhD thesis (2015).

Preprints

1. Joint with Richard Canary and Andrew Zimmer, "Entropy rigidity for cusped Hitchin representations" arXiv:2201:04859, preprint (2022).

2. Joint with Sara Maloni, Giuseppe Martone, and Filippo Mazzoli, "d-pleated surfaces and their shear-bend coordinates" arXiv:2305.11780, preprint (2023).

3. Joint with Richard Canary and Andrew Zimmer, "Patterson-Sullivan measures for relatively Anosov subgroups" arXiv:2308:04023, preprint (2023). 

Expository articles

1. Introduction to Lie groups. (2015)

2. Domains of discontinuity for Anosov representations. (2013) 

3. Freudenthal suspension theorem. (2009)

Presentation slides and posters

1. Young Mathematician Forum 2016 presentation slides.

2. AMS Fall Eastern Sectional Meeting presentation slides on Collar Lemma.

3. AMS Fall Eastern Sectional Meeting presentation slides on Anosov representations.

4. Joint Mathematics Meetings 2014 presentation slides.

5. GEAR Retreat 2014 poster.

6. Ahlfors-Bers 2014 presentation slides.

7. Geometry on groups and spaces 2014 (ICM satellite conference) presentation slides.

Videos

1. Lecture 1, Lecture 2, Lecture 3 at Homogeneous Dynamics and Geometry in Higher-Rank Lie Groups at IHES, June 2023.

2. Talk at Workshop on discrete subgroups of Lie groups, Banff International Research Station, December 2019.

3. Lecture 1, Lecture 2, Lecture 3 at Discussion meeting on surface group representations and projective structures at ICTS, December 2018.

4. Talk at Discussion meeting on surface group representations and geometric structures at ICTS, November 2017.

5. Talk at Teichmuller Theory seminar at Rutgers-Newark, November 2017.

6. Talk at GEAR retreat 2017 at Stanford, August 2017.

7. Talk at Workshop on Geometric Group Theory and Low Dimensional Topology at ICTP, June 2016.

8. Talk at MSRI workshop for the semester long program on dynamics on moduli spaces, April 2015.

A cute (unpublished) paper I wrote as an undergraduate.