Research

My research interests are in the fields of hyperbolic geometry, low-dimensional topology, and Teichmüller theory. Lately, I've been particularly interested in topics concerning curves on surfaces and geodesic currents.

All my papers are on the ArXiv

Preprints:

[-] Mirzakhani's Curve Counting (with J. Souto)

(preprint, 2019) [ArXiv]

[-] Ergodic invariant measures on the space of geodesic currents (with G. Mondello)

(preprint, 2018) [ArXiv]

[-] You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces (with M. Duchin, C.J. Leininger, and C. Sadanand)

(preprint, 2018) [ArXiv]

[-] Short closed geodesics with self-intersections (with H. Parlier)

(preprint, 2016) [ArXiv]

Publications:

[9] Length functions on currents and applications to dynamics and counting (with C. Uyanik)

to appear as a chapter in the forthcoming book "In the tradition of Thurston" [ArXiv]

[8] Counting curves, and the stable length of currents (with H. Parlier and J. Souto)

to appear in the Journal of the European Math. Soc. [ArXiv]

[7] A remark on the word length in surface groups

Trans. Amer. Math. Soc. 327 (2019) 441–455 [ArXiv]

[6] Simplicial embeddings of multicurve graphs (with F. Fanoni)

Michigan Math. J. 66 (2017), 549-567 [ArXiv]

[5] Counting Curves in Hyperbolic Surfaces (with J. Souto)

Geom. Funct. Anal. 26 (2016), no. 3, 729-777 [ArXiv]

[4] On Margulis cusps of hyperbolic 4-manifolds (with S. Zakeri)

Geom. Dedicata 174 (2015) 75-103 [ArXiv]

[3] A discreteness criterion for groups containing screw translations (with S. Zakeri)

Contemporary Mathematics 639 (2015) 235-242 [ArXiv]

[2] The Margulis region and screw parabolic elements of bounded type

Bull. London Math. Soc. 45 (2013), 1209-1220 [ArXiv]

[1] Tame homomorphisms of polytopal rings

Beitr. Algebra Geom. 49 (2008) 315-323 [ArXiv]

PhD Thesis:

The Margulis region in hyperbolic 4-space (City University of New York, 2013)