Research

My work can also be found on arXiv and Google Scholar. Some videos by collaborators.

Probability

• A Constructive Proof of the Spherical Parisi Formula
  With Mark Sellke.
  Preprint 2023. [arXiv]

• Strong Topological Trivialization of Multi-Species Spherical Spin Glasses
  With Mark Sellke.
  Preprint 2023. [arXiv] [slides]

• Optimization Algorithms for Multi-Species Spherical Spin Glasses
  With Mark Sellke.
  Preprint 2023. [arXiv]

• Algorithmic Threshold for Multi-Species Spherical Spin Glasses
  With Mark Sellke.
  Preprint 2023. [arXiv] [video] [slides]

• Tight Lipschitz Hardness for Optimizing Mean Field Spin Glasses
  With Mark Sellke.
  FOCS 2022. [arXiv] [video] [slides]

• The Algorithmic Phase Transition of Random k-SAT for Low Degree Polynomials
  With Guy Bresler.
  FOCS 2021. [arXiv] [video] [slides]

• Convergence of Maximum Bisection Ratio of Sparse Random Graphs
  Electronic Communications in Probability, 23 (2018) paper no. 51. [arXiv]

Statistical Inference and Learning

• Threshold for Detecting High Dimensional Geometry in Anisotropic Random Geometric Graphs
  With Matthew Brennan and Guy Bresler.
  Random Structures & Algorithms 64 (2024), 125-137. [arXiv]

• When Does Adaptivity Help for Quantum State Learning?
  With Sitan Chen, Jerry Li, Allen Liu, and Mark Sellke.
  FOCS 2023. [arXiv] [video]
  (Earlier version: Tight Bounds for State Tomography with Incoherent Measurements, QIP 2023)

• Tight Bounds for Quantum State Certification with Incoherent Measurements
  With Sitan Chen, Jerry Li, and Allen Liu.
  FOCS 2022. [arXiv] [video]

• De Finetti-Style Results for Wishart Matrices: Combinatorial Structure and Phase Transitions
  With Matthew Brennan and Guy Bresler.
  Preprint 2021. [arXiv]

Combinatorics

• Improved Lower Bound for Frankl's Union-Closed Sets Conjecture
  With Ryan Alweiss and Mark Sellke.
  Preprint 2022. [arXiv]

• Cyclic Descents for General Skew Tableaux
  Journal of Combinatorial Theory, Series A 169 (2020). [arXiv]

• On the Local Geometry of Graphs in Terms of Their Spectra
  With Mustazee Rahman.
  European Journal of Combinatorics 81 (2019), 378-393. [arXiv]

• An Upper Bound on the Number of (132,213)-Avoiding Cyclic Permutations
  Discrete Mathematics 342(6) (2019), 1762-1771. [arXiv]

• Monomization of Power Ideals and Generalized Parking Functions
  Preprint 2015. (Don't intend to publish) (pdf)

Thesis

• Computational Hardness in Random Optimization Problems from the Overlap Gap Property
  S.M. thesis (2022). Ernst A. Guillemin Award for Best Master's Thesis (2023). (pdf)