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

Recent

• Deterministic Approximation Algorithms for Volumes of Spectrahedra (with M. L. Doğan and M. Ravichandran), 2022. [arXiv]

Publications

1. Lower Bounds for Contingency Tables via Lorentzian Polynomials (with P. Brändén and I. Pak), Israel Journal of Mathematics (2022). [journal, 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. Deterministic Approximation Algorithms for Volumes of Spectrahedra (with M. L. Doğan and M. Ravichandran), 2022. [arXiv]
2. Lorentzian Polynomials on Cones and the Heron-Rota-Welsh Conjecture (with P. Brändén), 2021. [arXiv]
3. Optimization and Sampling Under Continuous Symmetry: Examples and Lie Theory (with N. Vishnoi), 2021. [arXiv]
4. On the Computability of Continuous Maximum Entropy Distributions: Adjoint Orbits of Lie Groups (with N. Vishnoi), 2020. [arXiv]
5. 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).