Interests
I am in the early stages of my mathematics career, so the things I like to think about are subject to a lot of change. Currently, I am either doing research in or learning about:
Properties of Cremona and mapping class groups
Hodge theory on arithmetic manifolds
Resolvent degree and essential dimension
Harmonic maps into singular spaces
Random walks and dynamics on groups
Real enumerative algebraic geometry
Preprints
A uniform central limit theorem for semisimple groups - with Omar Hurtado (In preparation)
Nielsen realization for rational 4-manifolds - with Seraphina Lee and Tudur Lewis (In preparation)
A smooth Birman-Hilden theory for hyperkähler manifolds (Submitted for publication) [arXiv] [pdf]
Translation from Russian: “On The Klein-Hilbert Resolvent Problem” by G.N. Chebotarev (Available upon request)
Select Talks
Research Talks
Moduli and 4-Manifold Mapping Class Groups - University of Notre Dame Topology Seminar (April 2024)
Moduli and 4-Manifold Mapping Class Groups - University of Michigan: Ann Arbor Topology Seminar (March 2024)
Birman and Hilden, Enriques and Torelli - UCLA Algebraic Topology Seminar (February 2024)
A Smooth Birman-Hilden Theory for 4-Manifolds - Joint Math Meetings (January 2024)
A Smooth Birman-Hilden Theory for 4-Manifolds - Texas Geometry and Topology Conference (November 2023)
The Geometry of Sextics and Resolvent Problems - Algebra, Geometry, and Topology Philadelphia Conference (May 2022)
Department Talks
Orbifolds and Their Applications to the SSH and Haldane Models - Condensed Matter Physics and Topology Seminar (Spring 2022)
Cohomology Computations for Condensed Matter Physicists - Condensed Matter Physics and Topology Seminar (Fall 2021)
Lectures
Department Lecture Series
Ratner's Theorems and Their Applications (Spring 2021 Lecture Series) - Ergodic Theory Seminar