Jonathan Leake

Contact

Email: jonathan at jleake dot com
Location: Technische Universität Berlin, Germany
Physical location (COVID): Leake Family Residence, Mathematics Division, Katy, TX

Teaching

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

Research

My research interests lie mainly in polynomials and combinatorics; especially analytic questions concerning linear operators and zeros of polynomials, discrete approximation, and applications to computer science.

CV

Preprints

1. Lower Bounds for Contingency Tables via Lorentzian Polynomials (with P. Brändén and I. Pak), 2020. [arXiv]
2. Capacity Lower Bounds via Productization (with L. Gurvits), 2020. [arXiv]
3. On the Further Structure of the Finite Free Convolutions (with N. Ryder), 2018. [arXiv]
4. A Representation Theoretic Interpretation of the Borcea-Brändén Characterization, 2017. [arXiv]

Publications

1. Connecting the q-Multiplicative Convolution and the Finite Difference Convolution (with N. Ryder), Advances in Mathematics (2020). [journal, arXiv]
2. On the Computability of Continuous Maximum Entropy Distributions with Applications (with N. Vishnoi), STOC (2020). [conference, arXiv]
3. Counting Matchings via Capacity Preserving Operators (with L. Gurvits), accepted by Combinatorics, Probability, and Computing (2020). [arXiv]
4. Mixed Determinants and the Kadison-Singer Problem (with M. Ravichandran), Mathematische Annalen (2020). [journal, arXiv]
5. Generalizations of the Matching Polynomial to the Multivariate Independence Polynomial (with N. Ryder), Algebraic Combinatorics (2019). [journal, arXiv]

Invited Talks

• 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).

Awards

• James H. Simons Fellowship, Simons Institute, UC Berkeley (Spring 2019).