Research

My research lies in discrete, convex, and computational geometry, with a current focus on polyhedral geometry and unfoldings of convex polyhedra.

Current Work

I am currently working with Gregory Chambers on problems in polyhedral geometry, especially unfoldings of convex polyhedra.

I am also interested in related problems in discrete and convex geometry, including:

• unfoldings of polyhedra
• blocking and covering numbers of convex bodies
• rigidity theory and applications of the theory of places (algebraic tool used, for example, in the proof of the Bellows Conjecture)

Previous Research

Before joining the Mathematics Department, I worked in the Department of Computational Applied Mathematics and Operations Research (CMOR) at Rice University with Matthias Heinkenschloss on parameter identifiability and local solution manifolds of nonlinear least squares problems.

As an undergraduate at the Moscow Institute of Physics and Technology, I worked with Alexander Polyanskii on problems in discrete and convex geometry. My bachelor’s thesis studied blocking numbers of convex bodies.

Talks and Posters

• Exploring Local Solution Manifolds of Nonlinear Least Squares Problems
  Poster presented at RTG NASC 2024, Rice University, and the SIAM TX/LA 2024 Section Annual Meeting, Baylor University.
  Poster · Abstract

Undergraduate and Earlier Projects

• Blocking Numbers of Convex Bodies
  Bachelor’s thesis, Moscow Institute of Physics and Technology, supervised by Alexander Polyanskii.

• Maximum-sum matchings of points
  Undergraduate research project at MIPT, supervised by Alexander Polyanskii.
  The project concerned maximum-sum matchings of points: given an even number of points in the plane, find a perfect matching maximizing the sum of lengths of edges connecting the matched pairs.
  A conjecture of Andy Fingerhut from 1995 about ellipses induced by such matchings was later resolved by P. Barabanshchikova and A. Polyanskii in Intersecting ellipses induced by a max-sum matching.

• Rigidity of Laman graphs and the Bellows conjecture
  Thesis for the Research Practicum at MIPT, supervised by Alexander Polyanskii.
  I studied applications of the theory of places used in the proof of the Bellows Conjecture. I was able to use this tool to find a proof of the rigidity of Laman graphs.