**Email:** jonathan at jleake dot com

**Location:** Technische Universität Berlin, Germany

**Physical location (COVID):** Leake Family Residence, Mathematics Division, Katy, TX

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

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.

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

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

**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).

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