About me

Hello! I’m a math PhD candidate at New York University’s Courant Institute. I am interested in the application of probability and stochastic analysis to diverse problems. So far, this interest has taken me in two research directions.

The Continuum Limit of Interacting Particle Systems

From microscopic to macroscopic

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Together with Jonathan Weare (my advisor at Courant), Jeremy Marzuola at UNC Chapel Hill, and other collaborators, I have been studying interacting particle system models for particle diffusion on a crystal surface. The overarching question is the following: given a stochastic process governing this diffusion on a microscopic level, can we derive an equation for the collective, macroscopic motion of particles by "zooming out" on this microscopic dynamics? We have approached this problem using a blend of numerical simulation and probabilistic analysis.

Low SNR Gaussian Mixture Models

EM trajectory moving along moment level sets

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My second research direction is in the mathematics of data science. Afonso Bandeira (my second advisor, now at ETH) and I study statistical inference for Gaussian mixture models in the regime of vanishing separation between mixture centers. This regime is of particular interest in applications such as cryo-electron microscopy, in which the mixture centers are known to enjoy additional structure: they are related to each other by the action of a group. We have been exploring the surprising intimate connection between log likelihood maximization algorithms such as EM, and the method of moments, in this regime.