Jonathan Leake

Assistant Professor
Department of Combinatorics and Optimization
University of Waterloo





My research interests lie mainly in combinatorics, polynomials, log-concavity, and entropy; especially analytic questions concerning linear operators and log-concave polynomials, discrete approximation via continuous optimization techniques, and applications to computer science.




  1. Lower Bounds for Contingency Tables via Lorentzian Polynomials (with P. Brändén and I. Pak), Israel Journal of Mathematics (2022). [journal, arXiv]
  2. A Representation Theoretic Interpretation of the Borcea-Brändén Characterization, Mathematische Zeitschrift (2021). [journal, arXiv]
  3. Capacity Lower Bounds via Productization (with L. Gurvits), STOC (2021). [conference, arXiv]
  4. Sampling Matrices from Harish-Chandra--Itzykson--Zuber Densities with Applications to Quantum Inference and Differential Privacy (with C. McSwiggen and N. Vishnoi), STOC (2021). [conference, arXiv]
  5. Counting Matchings via Capacity Preserving Operators (with L. Gurvits), Combinatorics, Probability, and Computing (2021). [journal, arXiv]
  6. Connecting the q-Multiplicative Convolution and the Finite Difference Convolution (with N. Ryder), Advances in Mathematics (2020). [journal, arXiv]
  7. On the Computability of Continuous Maximum Entropy Distributions with Applications (with N. Vishnoi), STOC (2020). [conference, arXiv]
  8. Mixed Determinants and the Kadison-Singer Problem (with M. Ravichandran), Mathematische Annalen (2020). [journal, arXiv]
  9. Generalizations of the Matching Polynomial to the Multivariate Independence Polynomial (with N. Ryder), Algebraic Combinatorics (2019). [journal, arXiv]


  1. From Trees to Polynomials and Back Again: New Capacity Bounds with Applications to TSP (with L. Gurvits and N. Klein), 2023. [arXiv]
  2. Lorentzian Polynomials on Cones (with P. Brändén), 2023. [arXiv]
  3. Deterministic Approximation Algorithms for Volumes of Spectrahedra (with M. L. Doğan and M. Ravichandran), 2022. [arXiv]
  4. Lorentzian Polynomials on Cones and the Heron-Rota-Welsh Conjecture (with P. Brändén), 2021. [arXiv]
  5. Optimization and Sampling Under Continuous Symmetry: Examples and Lie Theory (with N. Vishnoi), 2021. [arXiv]
  6. On the Computability of Continuous Maximum Entropy Distributions: Adjoint Orbits of Lie Groups (with N. Vishnoi), 2020. [arXiv]
  7. On the Further Structure of the Finite Free Convolutions (with N. Ryder), 2018. [arXiv]

Invited Talks

Fellowships and Positions