Jonathan Leake

Assistant Professor
Department of Combinatorics and Optimization
University of Waterloo

Contact

Email: jonathan@jleake.com
Office: MC 6008

Teaching

Research

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

Papers

  1. Optimal Trickle-Down Theorems for Path Complexes via C-Lorentzian Polynomials with Applications to Sampling and Log-Concave Sequences (with K. Lindberg and S. Oveis Gharan), FOCS (2025). [arXiv, STOC workshop on HDX]
  2. Inequalities Characterizing Distinguished Unipotent Orbits (with A. Bertoloni Meli and T. Koshikawa), preprint (2024). [arXiv, resources]
  3. Compatibility of Real-Rooted Polynomials with Mixed Signs (with N. Ryder), 2024. [arXiv]
  4. Capacity Bounds on Integral Flows and the Kostant Partition Function (with A. Morales), preprint (2024). [arXiv]
  5. From Trees to Polynomials and Back Again: New Capacity Bounds with Applications to TSP (with L. Gurvits and N. Klein), ICALP (2024). [arXiv, IAS talk]
  6. Lorentzian Polynomials on Cones (with P. Brändén), preprint (2023). [arXiv, talk+slides]
  7. Lower Bounds for Contingency Tables via Lorentzian Polynomials (with P. Brändén and I. Pak), Israel Journal of Mathematics (2023). [journal, arXiv, IPAM talk, slides]
  8. Deterministic Approximation Algorithms for Volumes of Spectrahedra (with M. L. Doğan and M. Ravichandran), preprint (2022). [arXiv]
  9. Lorentzian Polynomials on Cones and the Heron-Rota-Welsh Conjecture (with P. Brändén), 2021. [arXiv]
  10. A Representation Theoretic Interpretation of the Borcea-Brändén Characterization, Mathematische Zeitschrift (2021). [journal, arXiv, IPAM talk+slides]
  11. Capacity Lower Bounds via Productization (with L. Gurvits), STOC (2021). [conference, arXiv, Simons talk, STOC talk]
  12. 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, STOC talk, code]
  13. Counting Matchings via Capacity Preserving Operators (with L. Gurvits), Combinatorics, Probability, and Computing (2021). [journal, arXiv, Simons talk]
  14. Optimization and Sampling Under Continuous Symmetry: Examples and Lie Theory (with N. Vishnoi), 2021. [arXiv, Simons talk]
  15. Connecting the q-Multiplicative Convolution and the Finite Difference Convolution (with N. Ryder), Advances in Mathematics (2020). [journal, arXiv]
  16. On the Computability of Continuous Maximum Entropy Distributions: Adjoint Orbits of Lie Groups (with N. Vishnoi), preprint (2020). [arXiv]
  17. On the Computability of Continuous Maximum Entropy Distributions with Applications (with N. Vishnoi), STOC (2020), SIAM Journal on Computing (2022). [conference, arXiv, STOC talk]
  18. Mixed Determinants and the Kadison-Singer Problem (with M. Ravichandran), Mathematische Annalen (2020). [journal, arXiv]
  19. Generalizations of the Matching Polynomial to the Multivariate Independence Polynomial (with N. Ryder), Algebraic Combinatorics (2019). [journal, arXiv]
  20. On the Further Structure of the Finite Free Convolutions (with N. Ryder), preprint (2018). [arXiv, Simons talk]

Fellowships and Positions