Research interests: Classical & Quantum Spin Glasses, Random Optimization, Matrix Models, Asymptotic Combinatorics of the Hard-Core Model, 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 design spectral algorithms that optimize spin glasses, operator-valued polynomials (quantum spin glasses) & CSPs. This includes developing tools for the analysis & geometry of Gaussian processes on symmetric domains (such as compact Lie groups), and designing & analyzing sum-of-squares relaxations that 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 include information about higher moments of Gibbs measures, and study the implications of this on the hard-core model on explicit families of graphs.
  

Publications

Working Papers