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
- The generic crystallographic phase retrieval problem. Applied and Computational Harmonic Analysis (Joint with Dan Edidin)
Research Publications
- A Transversality Theorem for Semi-Algebraic Sets with Application to Signal Recovery from the Second Moment and Cryo-EM. Foundations of Computational Mathematics , 2025. (Joint with Tamir Bendory, Nadav Dym and Dan Edidin)
- Phase Retrieval with Semialgebraic and ReLU Neural Network Priors SIAM Journal on Mathematics of Data Science , 2025. (Joint with Tamir Bendory, Nadav Dym and Dan Edidin)
- The generators, relations and type of the Backelin semigroup. Communications in Algebra , (Joint with Florian Enescu)