Research
My research is in discrete, convex, and computational geometry.
I am currently working with Gregory Chambers on problems in polyhedral geometry, including unfoldings of convex polyhedra. My broader interests include:
- Blocking and covering numbers of convex bodies and the Hadwiger conjecture
- Rigidity theory and applications of algebraic methods such as the theory of places, a tool used, for example, in the proof of the Bellows Conjecture.
Publications
- On an Interesting Circle in a Triangle, with Andrey S. Shutov
Moscow Mathematical Conference of High School Students, 2019.
Best Paper Award.
Selected 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
Previous Research
Before joining the Department of Mathematics at Rice University, I worked with Matthias Heinkenschloss in Rice’s Department of Computational Applied Mathematics and Operations Research. My research focused on parameter identifiability and local solution manifolds of nonlinear least squares problems.
Undergraduate and Earlier Projects
Blocking Numbers of Convex Bodies
Bachelor’s thesis at the Moscow Institute of Physics and Technology, supervised by Alexander Polyanskii.Max-sum Matchings of Points
Undergraduate research project at MIPT, supervised by Alexander Polyanskii.
The project focused on the conjecture posed by Andy Fingerhut in 1995, concerning the intersection of ellipses induced by a maximal-sum matching of an even set of points in the plane. The conjecture 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
Research practicum thesis at MIPT, supervised by Alexander Polyanskii.
I studied applications of the theory of places, an algebraic tool used in the proof of the Bellows Conjecture, and applied it to obtain a new proof of the rigidity of Laman graphs.