Jonathan Leake

Assistant Professor
Department of Combinatorics and Optimization
University of Waterloo


Office: MC 6008



My research generally centers around log-concave polynomials and 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