Jonathan Leake

Contact

Email: jonathan@jleake.com
Location: Technische Universität Berlin, Germany
Physical location (COVID): Leake Family Residence, Mathematics Division, Granbury, TX

Teaching

Research

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.

CV

Recent

Publications

  1. Lower Bounds for Contingency Tables via Lorentzian Polynomials (with P. Brändén and I. Pak), Israel Journal of Mathematics (to appear). [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]

Preprints

  1. Lorentzian Polynomials on Cones and the Heron-Rota-Welsh Conjecture (with P. Brändén), 2021. [arXiv]
  2. On the Computability of Continuous Maximum Entropy Distributions: Adjoint Orbits of Lie Groups (with N. Vishnoi), 2020. [arXiv]
  3. On the Further Structure of the Finite Free Convolutions (with N. Ryder), 2018. [arXiv]

Invited Talks

Fellowships and Positions