Jonathan Leake

Assistant Professor
Department of Combinatorics and Optimization
University of Waterloo


Office: MC 6008



My research generally centers around log-concave polynomials and, broadly speaking, their various applications and connections in combinatorics and computer science.


  1. Capacity Bounds on Integral Flows and the Kostant Partition Function (with A. Morales), preprint (2024). [arXiv]
  2. From Trees to Polynomials and Back Again: New Capacity Bounds with Applications to TSP (with L. Gurvits and N. Klein), ICALP (2024). [arXiv, talk]
  3. Lorentzian Polynomials on Cones (with P. Brändén), preprint (2023). [arXiv, talk+slides]
  4. Lower Bounds for Contingency Tables via Lorentzian Polynomials (with P. Brändén and I. Pak), Israel Journal of Mathematics (2023). [journal, arXiv, talk, slides]
  5. Deterministic Approximation Algorithms for Volumes of Spectrahedra (with M. L. Doğan and M. Ravichandran), preprint (2022). [arXiv]
  6. Lorentzian Polynomials on Cones and the Heron-Rota-Welsh Conjecture (with P. Brändén), 2021. [arXiv]
  7. A Representation Theoretic Interpretation of the Borcea-Brändén Characterization, Mathematische Zeitschrift (2021). [journal, arXiv, talk+slides]
  8. Capacity Lower Bounds via Productization (with L. Gurvits), STOC (2021). [conference, arXiv, talk1, talk2]
  9. 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, talk, code]
  10. Counting Matchings via Capacity Preserving Operators (with L. Gurvits), Combinatorics, Probability, and Computing (2021). [journal, arXiv, talk]
  11. Optimization and Sampling Under Continuous Symmetry: Examples and Lie Theory (with N. Vishnoi), 2021. [arXiv, talk]
  12. Connecting the q-Multiplicative Convolution and the Finite Difference Convolution (with N. Ryder), Advances in Mathematics (2020). [journal, arXiv]
  13. On the Computability of Continuous Maximum Entropy Distributions: Adjoint Orbits of Lie Groups (with N. Vishnoi), preprint (2020). [arXiv]
  14. On the Computability of Continuous Maximum Entropy Distributions with Applications (with N. Vishnoi), STOC (2020), SIAM Journal on Computing (2022). [conference, arXiv, talk]
  15. Mixed Determinants and the Kadison-Singer Problem (with M. Ravichandran), Mathematische Annalen (2020). [journal, arXiv]
  16. Generalizations of the Matching Polynomial to the Multivariate Independence Polynomial (with N. Ryder), Algebraic Combinatorics (2019). [journal, arXiv]
  17. On the Further Structure of the Finite Free Convolutions (with N. Ryder), preprint (2018). [arXiv, talk]

Fellowships and Positions