Todd Kemp

Research

I work in probability theory (stochastic analysis, diffusion processes on Lie groups, random matrices, and free probability), mathematical physics (Yang-Mills theory, quantum information theory), and functional analysis (functional inequalities, heat kernel analysis, holomorphic and subharmonic function spaces).

I am a Founding Faculty member of the Halicioğlu Data Science Institute.

Mentoring

I have served as advisor to 7 PhD students:

• Natasha Blitvic (PhD: 2007-2012, MIT). Reader in Mathematical Sciences, Centre for Probability, Statistics and Data Science, Queen Mary University of London.
• David Zimmermann (PhD: 2010-2015, UCSD). Software Engineer at Google, in Sunnyvale, CA.
• Ching Wei Ho (PhD: 2013-2018, UCSD). Permanent faculty member at Acedemia Sinica (the National Academy of Taiwan).
• Alice Chan (PhD: 2014-2019, UCSD) Industry, Machine Learning.
• Evangelos (Vaki) Nikitopoulos (PhD: 2018-2024, UCSD). Co-advised with Bruce Driver. Lewis Research Assistant Professor at the University of Michigan.
• Zhichao Wang. (PhD: 2019-2024, UCSD). Co-advised with Ioana Dumitriu. Postdoctoral Researcher at UC Berkeley, in Statistics and the Simons Institute for Theory and Computing.
  
• Collin Cranston. (PhD: 2020- , UCSD).

• Ian Charlesworth (SEW: 2017-2018, UCSD). Lecturer (Assistant Professor), University of Cardiff.
• Benson Au (SEW: 2018-2021, UCSD), Co-mentored with Jon Novak. Postdoctoral Researcher in Statistics at UC Berkeley.
• Yuriy Nemish (SEW: 2019-2023, UCSD). Industry, ML.
• David Jekel (NSF: 2020-2023, UCSD). Postdoctoral Researcher, University of Copenhagen.
• Marco Carfagnini (SEW: 2022-2024, UCSD). Assistant Professor, University of Melbourne.
• Priyanga Ganesan (PPF: 2022-2024. SEW 2024- , UCSD) SEW Visiting Assistant Professor, UCSD.
• Akihiro Miyagawa (Postdoc: 2024 - 2026, UCSD). Postdoctoral Fellow, UCSD.

Publications and Preprints

1. Hypercontractivity in non-commutative holomorphic spaces. Commun. Math. Phys. 259 no. 3, 615-637 (2005)    K-CMP-2005.pdf
2. Strong Haagerup inequalities for free R-diagonal elements. J. Funct. Anal. 251, 141-173 (2007)   [With Roland Speicher]    KS-JFA-2007.pdf
3. R-diagonal dilation semigroups. Math. Z. 264, 111-136 (2008)    K-MZ-2010.pdf
4. Hypercontractivity for log-subharmonic functions. J. Funct. Anal. 258, 1785-1805 (2009)   [With Piotr Graczyk and Jean-Jacques Loeb].    GKL-JFA-2010.pdf
5. Resolvents of R-diagonal operators. Trans. Amer. Math. Soc. 362, 6029-6064 (2010)   [With Uffe Haagerup and Roland Speicher]    HKS-TAMS-2010.pdf
6. Enumeration of non-crossing pairings on bitstrings. J. Comb. Theory A. 118, 129-151 (2011)   [With Karl Mahlburg, Amarpreet Rattan, and Cliff Smyth]    KMRS-JCTA-2011.pdf
7. Duality in Segal-Bargmann Spaces. J. Funct. Anal. 261, 1591-1623 (2011)   [With Will Gryc]    GK-JFA-2011.pdf
8. Wigner Chaos and the Fourth Moment. Ann. Prob. 40, 1577-1635 (2012)   [With Ivan Nourdin, Giovanni Peccati, and Roland Speicher]    KNPS-AoP-2012.pdf
9. The Large-N Limit of the Segal-Bargmann Transform on U(N). J. Funct. Anal. 265, 2585-2644 (2013)   [With Bruce Driver and Brian Hall] DHK-JFA-2013.pdf
10. Liberation of Projections. J. Func. Anal. 266, 1988-2052 (2014) [With Benoit Collins] CK-JFA-2014.pdf
11. On Sharp Constants in Dual Segal-Bargmann L^p Spaces. J. Math. Anal. Appl. 424, 1198-1222 (2015) [With Will Gryc] GK-JMAA-2015.pdf
12. Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions. Canad. J. Math. 67 (6), 1384-1410 (2015) [With Piotr Graczyk and Jean-Jacques Loeb] GKL-CJM-2015.pdf
13. The Large-N Limits of Brownian Motions on GL(N). Int. Math. Res. Not. IMRN, no. 13, 4012-4057 (2016) K-BM-GLN.pdf
14. Heat Kernel Empirical Laws on U(N) and GL(N). J. Theoret. Probab. 30, no. 2, 397-451 (2017) K-Heat-Kernel-Empirical-Laws.pdf
15. Three proofs of the Makeenko-Migdal equation for Yang-Mills theory on the plane. Commun. Math. Phys. 351 no. 2, 741-774 (2017) [With Bruce Driver and Brian Hall] DHK-MM-plane.pdf
16. The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces. Comm. Math. Phys. 352, no. 3, 967-978 (2017) [With Bruce Driver, Franck Gabriel, and Brian Hall] DGHK-MM-surfaces.pdf
17. The Minimum Renyi Entropy Output of a Quantum Channel is Locally Additive. Lett. Math. Phys. 107, no. 6, 1131-1155 (2017) [With Gilad Gour] GK-Renyi.pdf
18. The Spectral Edge of Unitary Brownian Motion. Probab. Theory Related Fields 170, no. 1-2, 49-93 (2018) [With Benoit Collins and Antoine Dahlqvist] CDK-PTRF-2016.pdf
19. Most Boson Quantum States are Almost Maximally Entangled. Proc. Am. Math. Soc. 146, no. 12, 5035-5049 (2018) [With Shmuel Friedland] FK-Boson-Entanglement.pdf
20. Corrigendum to "On Sharp Constants for Dual Segal-Bargmann L^p Spaces". J. Math. Anal. Appl. 475, no. 2, 1992-1995 (2019) [With Will Gryc] GK-JMAA-2019.pdf
21. Brown Measure Support and the Free Multiplicative Brownian Motion. Adv. Math. 355, 106771, 36 pp. (2019) [With Brian Hall] HK-Brown-Measure-Support.pdf
22. The Complex Time Segal-Bargmann Transform. J. Funct. Anal. 278, no. 1, 108303, 42 pp. (2020) [With Bruce Driver and Brian Hall] DHK-C-Time-SBT.pdf
23. Random Matrices with Log-Range Correlations, and Log-Sobolev Inequalities. Ann. Math. Blaise Pascal 27, no. 2, 207-232 (2020) [With David Zimmermann] KZ-Log-Correlations.pdf
24. Fluctuations of Brownian Motions on GL(N). Ann. Inst. Henri Poincare Probab. Stat. 58, no. 1, 524-547 (2022) [With Guillaume Cébron] CeK-Fluctuations.pdf
25. Stochastic Networks and Reflecting Brownian Motion: the Mathematics of Ruth Williams Notices Amer. Math. Soc. 69, no. 3, 363-374 (2022) [With Ioana Dumitriu and Kavita Ramanan] DRK-Williams-Feature.pdf
26. The Brown Measure of the Free Multiplicative Brownian Motion. Probab. Theory Related Fields 184 no. 102, 209-273 (2022) [With Bruce Driver and Brian Hall] DHK-Brown-Measure.pdf
27. A Martingale Approach to Noncommutative Stochastic Calculus. J. Funct. Anal. 290, no 2., 117 pp. (2026) [With David A. Jekel and Evangelos A. Nikitopoulos] JKN-NCSC.pdf
28. The Strong Haagerup Inequality for q-Circular Systems. To Appear in Int. Math. Res. Not. IMRN. arXiv:2409.03177 (2026) [With Akihiro Miyagawa] KM-q-Haagerup.pdf
29. Bias and Division in the Free World. arXiv:2403.19860 (2025) [With Larry Goldstein] GK-Bias.pdf
30. Matrix Random Walks and the Lima Bean Law. arXiv:2510.10712 (2025) [With Bruce K. Driver, Brian C. Hall, Ching Wei Ho, Yuriy Nemish, Evangelos A. Nikitopoulos, and Felix Parraud] Lima-Bean-Law.pdf
31. Eigenvalues of Brownian Motion on GL(N,C). arXiv:2511.10535 (2025) [With Tatiana Brailovskaya, Nickolas A. Cook, and Felix Parraud] GLBM-Eig.pdf
32. Double q-Wigner Chaos and the Fourth Moment. arXiv:2511.20875 (2025) [With Akihiro Miyagawa] KM-q-Fourth-Moment.pdf