My research is in infinite type surfaces, their hyperbolic geometry and big mapping class groups.

Publications and Preprints

  1. A Moduli Space of Marked Hyperbolic Structures for Big Surfaces.
    [preprint pdf updated 16 July 2024] [arXiv] [2-minute video abstract] [slides for a lightning talk] [ abstract▾ ]
    We introduce the moduli space of marked, complete, Nielsen-convex hyperbolic structures on a surface of negative, but not necessarily finite, Euler characteristic. The emphasis is on the case in which the surface is of infinite type, the aim being to study the mapping class group of such a surface via its action on this marked moduli space. We define a topology on the marked moduli space and prove that it reduces to the usual Teichm\"uller space in case the surface is of finite type. We prove that the action of the mapping class group on this marked moduli space is continuous.

Invited Talks

  1. Oct 19, 2024: TBA. 2024 AMS Fall Eastern Sectional Meeting.
  2. Aug 12, 2024: A Moduli Space of Marked Hyperbolic Structures for Big Surfaces. IISc Geometry and Topology seminar.
  3. Apr 09, 2024: A Moduli Space of Marked Hyperbolic Structures for Big Surfaces. CUNY Hyperbolic Geometry Seminar.
  4. Mar 12, 2024: A Moduli Space of Marked Hyperbolic Structures for Big Surfaces. Brandeis Topology Seminar.
  5. Nov 20, 2023: Mapping Class Group acts continuously on the marked moduli space. University at Buffalo Discourses of Graduates.
  6. Apr 21, 2022: Mapping Class Group acts continuously on the marked moduli space. Binghamton University Geometry and Topology Seminar.
  7. Mar 29, 2022: Mapping Class Group acts continuously on the marked moduli space. Cornell Topology and Geometric Group Theory Seminar.
  8. Nov 18, 2020: Classification of Infinite Type Surfaces. Virtual Geometric Structures seminar.