Jonathan Leake

Contact

Email: jonathan@jleake.com

Teaching

• Winter 2020-2021 (TU Berlin): Polynomial Capacity: Theory, Applications, Generalizations

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

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

• Lorentzian polynomials on cones and the Heron-Rota-Welsh conjecture, Combinatorics and Geometry Seminar, University of Washington, Seattle, WA (October 2021).
• Optimization and Sampling Under Symmetry (Part 2), Geometric Methods in Optimization and Sampling Boot Camp, Simons Institute, UC Berkeley (September 2021).
• Transportation Polytope Volume Bounds via Lorentzian Polynomials, Real Algebraic and Convex Geometry Conference, TU Braunschweig, Germany (July 2021).
• Capacity Lower Bounds via Productization, STOC 2021, Online (June 2021).
• Sampling Matrices from Harish-Chandra–Itzykson–Zuber Densities with Applications to Quantum Inference and Differential Privacy, STOC 2021, Online (June 2021).
• Flow/Transportation Polytope Volume Bounds via Polynomial Capacity, Polytopics, Max Planck Institute, Leipzig, Germany (April 2021).
• Capacity Bounds via Productization, Geometry of Polynomials Reunion, Simons Institute, UC Berkeley (September 2020).
• Approximate Counting via Polynomial Capacity, Online Applied Algebra and Analysis Seminar, TU Braunschweig, Germany (July 2020).
• On the Computability of Continuous Maximum Entropy Distributions with Applications, STOC 2020, Chicago, IL (June 2020).
• Approximate Counting via Polynomial Capacity, Unimodality, Log-concavity, and Beyond, Institut Mittag-Leffler, Stockholm (March 2020).
• Counting Matchings via the Capacity Method, Deterministic Counting, Probability, and Zeros of Partition Functions, Simons Institute, UC Berkeley (March 2019).
• On the Further Structure of Finite Free Convolutions, Beyond Randomized Rounding and the Probabilistic Method, Simons Institute, UC Berkeley (February 2019).
• Capacity Preserving Operators, Hausdorff Geometry of Polynomials and Polynomial Sequences, Institut Mittag-Leffler, Stockholm (May 2018).
• Extending the Borcea-Brändén Characterization, Expected Characteristic Polynomial Techniques and Applications, IPAM, UCLA (April 2018).

Fellowships and Positions

• Dirichlet Postdoctoral Fellowship, TU Berlin (2020-2022).
• Postdoc Fellowship (Algebraic and Enumerative Combinatorics), Institut Mittag-Leffler, Stockholm (Spring 2020).
• Postdoc, KTH, Stockholm (Fall 2019).
• James H. Simons Fellowship, Simons Institute, UC Berkeley (Spring 2019).