Research
My research interests are in the fields of hyperbolic geometry, low-dimensional topology, and Teichmüller theory. I'm particularly interested in topics concerning counting curves and geodesics on surfaces as well as geodesic currents.
All my papers are on the ArXiv
Papers
Book:
[*] Mirzakhani's Curve Counting and Geodesic Currents (with Juan Souto)
Birkhäuser's Progress in Mathematics series, volume 345, 2022
(See here for the first few pages and here for the published version)
Published/Accepted Papers:
[19] Counting and equidistribution of reciprocal geodesics and dihedral groups (with J. Souto)
International Mathematics Research Notices (IMRN), (2024) [ArXiv]
[18] Counting geodesics of given commutator length (with J. Souto)
Forum of Mathematics, Sigma, Volume 11, (2023), 47pp. (2023) [ArXiv]
[17] Mapping class group orbit closures for non-orientable surfaces (with M. Gendulphe, I. Pasquinelli, and J. Souto)
Geometric and Functional Analysis (GAFA), 33 (2023), 637-693 [ArXiv]
[16] Distribution in the unit tangent bundle of the geodesics of given type (with J. Souto)
Ergodic Theory and Dynamical Systems, 43 (2023), 887-903 [ArXiv]
[15] Ergodic invariant measures on the space of geodesic currents (with G. Mondello)
Annales l'Institut Fourier, 72 (2022), 2449-2513. [ArXiv]
[14] Hyperbolic cone metrics and billiards (with C. Leininger and C. Sadanand)
Advances in Mathematics, 409 (2022), 74p. [ArXiv]
[13] Counting curves on orbifolds (with J. Souto)
Trans. of the London Math. Soc., 9 (2022), 56-85 [ArXiv]
[12] You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces (with M. Duchin, C. Leininger, and C. Sadanand)
Commenttarii Mathematici Helvetici, 96 (2021), no. 3, 421-463 [ArXiv]
[11] Genericity of pseudo-Anosov mapping classes, when seen as mapping classes (with J. Souto and J. Tao)
L'Enseignement Mathématique, 66 (2020) , no 3-4, 419-439 [ArXiv]
[10] Short closed geodesics with self-intersections (with H. Parlier)
Math. Proceedings of the Cambridge Philosophical Soc. 169 (2020), no. 3, 623-638 [ArXiv]
[9] Length functions on currents and applications to dynamics and counting (with C. Uyanik)
In the Tradition of Thurston, Springer, (2020), 423-458 [ArXiv]
[8] Counting curves, and the stable length of currents (with H. Parlier and J. Souto)
Jour. of the Eur. Math. Soc. (JEMS), 22 (2020), no. 6, 1675-1702 [ArXiv]
[7] A remark on the word length in surface groups
Trans. of the Amer. Math. Soc. (TAMS), 327 (2019), no. 1, 441–455 [ArXiv]
[6] Simplicial embeddings of multicurve graphs (with F. Fanoni)
Michigan Math. Journal 66 (2017), no. 3, 549-567 [ArXiv]
[5] Counting Curves in Hyperbolic Surfaces (with J. Souto)
Geometric and Functional Analysis (GAFA) 26 (2016), no. 3, 729-777 [ArXiv]
[4] On Margulis cusps of hyperbolic 4-manifolds (with S. Zakeri)
Geometriae Dedicata 174 (2015) 75-103 [ArXiv]
[3] A discreteness criterion for groups containing screw translations (with S. Zakeri)
Contemporary Math. - Geometry Groups and Dynamics, 639 (2015) 235-242 [ArXiv]
[2] The Margulis region and screw parabolic elements of bounded type
Bull. of the London Math. Soc, 45 (2013), no. 6, 1209-1220 [ArXiv]
[1] Tame homomorphisms of polytopal rings
Beiträge zur Algebra und Geometrie, 49 (2008), no. 2, 315-323 [ArXiv]
PhD Thesis:
The Margulis region in hyperbolic 4-space (City University of New York, 2013)
Recent Invited Talks:
See here
Events I am/was co-organizing:
Surfaces, Manifolds, and Related Topics, March 18-20, 2024, Luxembourg
Group actions and low dimensional topology, July 3 - July 7, 2023, El Barco de Avíla, Spain
Two-day Geometry Meeting, May 22-23, 2023, University of Bristol, UK
HIMR-Clay Summer School, June 21- July 2, 2021, University of Bristol (virtually)
Interactions between Geometry, Dynamics, and Group Theory (LMS South West and South Wales regional meeting and workshop), January 15-17, 2020, University of Bristol
Geodesics on Real Hyperbolic Manifolds, Aug 9-11, 2018, Connecticut College, USA
Bristol Topology and Groups Meeting, June 28-29, 2018, University of Bristol, UK
Women in Mathematics: Opportunities for the Future, annual event 2017-2022, University of Bristol.