Interests
Currently, I am either doing research in or learning about:
Properties of Cremona groups 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 algebraic geometry
Publications and Preprints
Cyclic Nielsen realization for del Pezzo surfaces,
(with Seraphina Lee and Tudur Lewis), In preparation.
Uniform estimates for random matrix products and applications, [pdf]
(with Omar Hurtado), Preprint.
(with Thomas Brazelton), Preprint.
(with Claudio Gómez-Gonzáles, Siddharth Viswanath, and Jesse Wolfson), MAA Focus, vol. 44, 2024, no. 4: 18-22. [Additional Materials]
J. Reine Angew. Math. (Crelle), to appear.
Translation from Russian.
Select Talks
Research Talks
Equivariant Monodromy and Moduli - Joint Math Meetings in Seattle, WA (January 2025)
Equivariant Monodromy and Moduli - Brown University Geometry/Topology Seminar (November 2024)
Uniform Central Limit Theorems on Lie Groups - UCSD Group Actions Seminar (October 2024)
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 in San Francisco, CA (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