Jonathan Leake
Assistant Professor
Department of Combinatorics and Optimization
University of Waterloo
Contact
Email: jonathan@jleake.com
Office: MC 6008
Teaching
Research
My research generally centers around log-concave polynomials and, broadly speaking, their various applications and connections in combinatorics and computer science.
Papers
- Inequalities Characterizing Distinguished Unipotent Orbits (with A. Bertoloni Meli and T. Koshikawa), preprint (2024). [arXiv, resources]
- Compatibility of Real-Rooted Polynomials with Mixed Signs (with N. Ryder), 2024. [arXiv]
- Capacity Bounds on Integral Flows and the Kostant Partition Function (with A. Morales), preprint (2024). [arXiv]
- From Trees to Polynomials and Back Again: New Capacity Bounds with Applications to TSP (with L. Gurvits and N. Klein), ICALP (2024). [arXiv, talk]
- Lorentzian Polynomials on Cones (with P. Brändén), preprint (2023). [arXiv, talk+slides]
- Lower Bounds for Contingency Tables via Lorentzian Polynomials (with P. Brändén and I. Pak), Israel Journal of Mathematics (2023). [journal, arXiv, talk, slides]
- Deterministic Approximation Algorithms for Volumes of Spectrahedra (with M. L. Doğan and M. Ravichandran), preprint (2022). [arXiv]
- Lorentzian Polynomials on Cones and the Heron-Rota-Welsh Conjecture (with P. Brändén), 2021. [arXiv]
- A Representation Theoretic Interpretation of the Borcea-Brändén Characterization, Mathematische Zeitschrift (2021). [journal, arXiv, talk+slides]
- Capacity Lower Bounds via Productization (with L. Gurvits), STOC (2021). [conference, arXiv, talk1, talk2]
- 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, talk, code]
- Counting Matchings via Capacity Preserving Operators (with L. Gurvits), Combinatorics, Probability, and Computing (2021). [journal, arXiv, talk]
- Optimization and Sampling Under Continuous Symmetry: Examples and Lie Theory (with N. Vishnoi), 2021. [arXiv, talk]
- 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: Adjoint Orbits of Lie Groups (with N. Vishnoi), preprint (2020). [arXiv]
- On the Computability of Continuous Maximum Entropy Distributions with Applications (with N. Vishnoi), STOC (2020), SIAM Journal on Computing (2022). [conference, arXiv, talk]
- 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]
- On the Further Structure of the Finite Free Convolutions (with N. Ryder), preprint (2018). [arXiv, talk]
Fellowships and Positions
- Assistant Professor, University of Waterloo (2022-now).
- 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).
- PhD Math, UC Berkeley (2014-2019).
- Developer, Teacher Retirement System of Texas (2012-2014).
- MS Math, Texas A&M University (2010-2012).
- BS Computer Engineering and Applied Math, Texas A&M University (2006-2010).