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:

Publications

Selected Talks and Posters

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.