Research interests: High-Dimensional Optimization & Sampling, Classical & Quantum Spin Glasses, Matrix Models, Phase Transitions in Gibbs measures, Analysis & Geometry of Gaussian Processes, Gaussian Free Field, Liouville Quantum Gravity.

My papers can be found on Google Scholar or DBLP. I (primarily) work with:

• David Jekel and Jonathan Shi to optimize spin glasses, operator-valued functions & CSPs, analyze Gaussian processes on symmetric domains (ex: Lie groups), and design sum-of-squares hierarchies to certify algorithmic thresholds in random optimization.
• Saeed Mehraban to develop & extend probabilistic techniques from mathematical spin-glass theory with complex-analytic ideas to study mathematical and algorithmic questions surrounding the random-permanent problem.
• Ewan Davies to extend the theory of local occupancy to higher moments of Gibbs measures, and study the implications of this on the hard-core model on explicit families of graphs (including phase transitions).
  

Publications

Working Papers