I primarily work in number theory but have broad interests. Take a look at my CV to get a sense of some of the things I’ve done.

Research

Publications

• B. Matschke, A. S. Mudigonda. Quadratic Fields Admitting Elliptic Curves with Rational $j$-Invariant and Good Reduction Everywhere. Journal of Number Theory. Volume 247, June 2023, Pages 162-210
• A. S. Mudigonda, R. R. Williams. Time-Space Lower Bounds for Simulating Proof Systems with Quantum and Randomized Verifiers. ITCS 2021: 50:1-50:20.

Miscellaneous

• A. S. Mudigonda. _An Efficient Reduction from QMATIME[n] to the k-Local Hamiltonians Problem_.
• D. Gutfreund, Q. Fan, A. Mudigonda. Restructuring Deep Neural Networks to Reduce the Number of Parameters. (U.S. Patent 1166344382)

Expository Writing

Here are some things I wrote as an undergraduate student.

• Profinite Groups, Infinite Galois Theory, and an application to Kummer Theory: Term paper for 18.704 (Seminar in Algebra), taught by Prof. Bjorn Poonen.
• Sphere Packing in 8 Dimensions: Written for 18.786 (Number Theory II), taught by Prof. Wei Zhang, and loosely following [this][cohn-spheres] survey by Henry Cohn
• Towards Quantum PCP: A Proof of the NLETS Theorem: Written for CS 229 (Physics and Computation), taught by Prof. Boaz Barak. We also wrote a corresponding blog post.
• The official course notes to 18.218 (Combinatorics of the Grassmannian), taught by Prof. Alex Postnikov. There are a lot of edits to be made and proofs to be filled in.
• An Algebraic Approach to the Dirac Equation: Term paper for 8.06 (Quantum Physics III).
• Structure Determination of a Suzuki-Miyaura Coupling Product: Term paper for 5.36 (Biochemistry and Organic Lab).