ACADEMIC INTERESTS

• My Academic Interests lie at the intersection of Theoretical Computer Science and Mathematical Physics. I want to understand the average-case complexity landscape of different families of optimization problems. Currently, I am thinking about:
  • Quantum inapproximability on various models in Spin-Glass Theory. I am interested in exploring the duality between diluted spin-glass models and random CSPs via the Parisi Variational Principle and the Overlap/RSB structure of these problems, with implications on algorithmic hardness.
  • Possible connections between Wigner Function negativity & Sum-of-Squares pseudodistributions, particularly in the Unique-Games Conjecture regime. Generically, any connections between RS/RSB ansatzen and SoS pseudo-distributions pique my interest.
  • The use of High-Dimensional Expanders in the creation of better Quantum-Error Correction Codes and for provable speed-ups in approximate sampling & optimization algorithms.
• More broadly, I am excited about the intersections between Spin-Glass Theory, Quantum Inapproximability, Convex Analysis, Combinatorial Optimization, Spectral Graph Theory and Stochastic Geometry.
• I am fortunate to have some great collaborators. I primarily work very closely on many problems with the wonderful duo of Antares Chen and Jonathan Shi. I have also worked on some exciting projects with Chi-Ning Chou, Emil Khabiboulline and Jonathan Wurtz.