Putting mathematics at the
center of innovation
My research lies at the interface of numerical analysis and quantum dynamics. I develop and analyse numerical methods for the time-dependent Schrödinger equation and for mixed quantum-classical systems, aiming to bridge rigorous mathematics with applied sciences such as quantum chemistry and quantum computing. Across these projects, I pair theoretical error analysis with numerical experiments to establish both the correctness and the practical performance of new methods. My work spans the following areas:
Geometric and variational methods, including hybrid wavefunctions and particle closures, with applications to nonadiabatic dynamics and physical systems such as Rashba spin-orbit coupling
Error analysis and numerical simulation of methods for the linear and nonlinear Schrödinger equation
Analysis of the approximation of wave functions via Fourier analysis, frozen and thawed Gaussian propagation for the linear Schrödinger equation
Structure-preserving time integrators for differential equations based on operator splitting
Compressed representations for high-dimensional quantum dynamics and optimization
Variational methods for near-term quantum computing
with W. Bauer, F. Gay-Balmaz, C. Tronci
SIAM Multiscale Model. Simul., 22(4):1365-1401
with C. Lasser
Numer. Math., 152, 511-551
with M. B. Soley, A. Gorodetsky, V. S. Batista
J. Chem. Theory Comput., 18, 25-36