Overview:

My primary research interests lie in developing theoretical/computational results that leverage tools from algebraic geometry and representation theory, to tackle inverse problems arising in data science and computational imaging. In particular, my doctoral work revolves around problems of the form:

Problem: Recover $x \in \mathbb{K}^n$ from indirect measurements $m(x)$ governed by algebraic relations on the entries of $x$.

Such problems naturally admit applications in molecular/tomographic imaging technologies like X-Ray crystallography, Computed Tomography (CT), and Cryo-electron microscopy (Cryo-EM). The techniques used in this line of work are broadly applicable to problems beyond molecular imaging. Some exciting applications of this work include: Invariant and equivariant machine learning [1], understanding the geometry of polynomial neural networks and neuromanifolds [2] [3], and problems in acoustic vision such as source localization and structure reconstruction [4].

My current publications are listed below. Publications marked with ($\dagger$) list author by contribution. Elsewhere author last names are listed alphabetically

In preparation

  • $O(n)$ Beltway problem with applications to cryo-EM and Euclidean Distance Geometry. (Joint with Dan Edidin)
  • ($\dagger$) The Direction and Rate of Spread of Chronic Wasting Disease via Spatiotemporal modeling. First author (Joint with Zoe Shanley, Ram K. Raghavan, Akila Raghavan, Levi Jaster and Shane Hesting).

Under review

Research Publications

Talks, Presentations and Recognition