# 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**

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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**

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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.