I am Assistant Professor in Applied Mathematics at Virginia Tech.
My research broadly deals with multiscale phenomena in mathematical physics, homogenization theory, and numerical methods for high-dimensional problems.

My current research interests include:

Randomized numerical methods for tensor computations. The tensor-train (TT) format — originally introduced in physics as Matrix Product States — provides an efficient low-rank representation for high-dimensional data, with applications ranging from parametrized PDEs and uncertainty quantification to quantum chemistry. A core computational bottleneck is rank reduction (TT rounding), which must be performed repeatedly in TT arithmetic. I develop and analyze structured random sketches for this task that are computationally efficient and come with rigorous theoretical guarantees, including recent results achieving linear scaling in tensor order.

Mathematical modeling of 2D materials. I study layered heterostructures — stacked 2D materials such as graphene and boron nitride — whose remarkable physical properties arise from the interplay between atomic-scale structure and mesoscopic moiré patterns. A fundamental mathematical challenge is that incommensurate stackings lack a periodic unit cell, making standard Bloch theory inapplicable; Non-Commutative Algebras provide the right framework to analyze their mechanical and electronic properties. My work spans the rigorous derivation of continuum models from atomistic descriptions and the study of topological transport phenomena in twisted bilayer systems.

Quantum algorithms for scientific computing. A central challenge in quantum simulation is the preparation of ground states of many-body Hamiltonians. Open quantum systems provide a natural framework for algorithm design, mimicking how quantum systems cool down through non-unitary interactions with their environment. I am developing and rigorously analyzing a randomized algorithm in this spirit, targeting the cold start regime where — unlike phase estimation — no initial state with large overlap with the ground state is required. This direction grew out of participation in a 2023 long program at IPAM on mathematical and computational challenges in quantum computing.