About me

Hello! I’m a postdoc in the math department at MIT working with Philippe Rigollet, and am also affiliated with IDSS. I obtained my PhD at the Courant Institute at NYU, where I worked with Jonathan Weare and Afonso Bandeira (now at ETH). I am interested in the application of probability and stochastic analysis to diverse problems ranging from the math of data science to interacting particle systems. See below for more on two of my research projects.

Low SNR Gaussian Mixture Models

EM trajectory moving along moment level sets

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With Afonso Bandeira, I studied 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 explored the surprising intimate connection between log likelihood maximization algorithms such as EM, and the method of moments, in this regime.

The Continuum Limit of Interacting Particle Systems

From microscopic to macroscopic

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Together with Jonathan Weare, Jeremy Marzuola at UNC Chapel Hill, and other collaborators, I studied interacting particle 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.