Professor, UC San Diego
Department of Mathematics
University of California, San Diego
La Jolla, CA 92093-0112
Phone: (858) 534-3985
Fax: (858) 534-5273
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.
I have served as advisor to 4 former and 2 current PhD students:
- Natasha Blitvic (PhD: 2007-2012, MIT).
After a Zorn postdoctoral fellowship at Indiana University, she moved to Lancaster University (in the UK) where she is currently a
Lecturer (US equivalent: Associate Professor) in Pure Mathematics.
- David Zimmermann (PhD: 2010-2015, UCSD)
After an appointment as a Dickson Instructor at U Chicago, he went into industry.
He currently works for Google, in Sunnyvale, CA.
- Ching Wei Ho (PhD: 2013-2018, UCSD).
After a Zorn postdoctoral felowship at Indiana University, he became a permanent faculty member at Acedemia Sinica (the National Academy of Taiwan).
- Alice Chan (PhD: 2014-2019, UCSD)
Currently looking for industry positions related to ML.
- Evangelos (Vaki) Nikitopoulos (PhD: 2018- , UCSD).
Co-advised with Bruce Driver.
- Zhichao Wang. (PhD: 2019- , UCSD). Former Masters student of Michael Anshelevich.
I have mentored 2 former and 4 current postdocs (SEW = Stefen E. Warschawski Visiting Assistant Professor; NSF PDF = National Science Foundation Postdoctoral Research Fellow; PPF = President's Postdoctoral Fellow):
- Hypercontractivity in non-commutative holomorphic spaces. Commun. Math. Phys. 259 no. 3, 615-637 (2005) K-CMP-2005.pdf
- Strong Haagerup inequalities for free R-diagonal elements. J. Funct. Anal. 251, 141-173 (2007) [With Roland Speicher] KS-JFA-2007.pdf
- R-diagonal dilation semigroups. Math. Z. 264, 111-136 (2008) K-MZ-2010.pdf
- Hypercontractivity for log-subharmonic functions. J. Funct. Anal. 258, 1785-1805 (2009) [With Piotr Graczyk and Jean-Jacques Loeb]. GKL-JFA-2010.pdf
- Resolvents of R-diagonal operators. Trans. Amer. Math. Soc. 362, 6029-6064 (2010) [With Uffe Haagerup and Roland Speicher] HKS-TAMS-2010.pdf
- 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
- Duality in Segal-Bargmann Spaces. J. Funct. Anal. 261, 1591-1623 (2011) [With Will Gryc] GK-JFA-2011.pdf
- Wigner Chaos and the Fourth Moment. Ann. Prob. 40, 1577-1635 (2012) [With Ivan Nourdin, Giovanni Peccati, and Roland Speicher] KNPS-AoP-2012.pdf
- 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
- Liberation of Projections. J. Func. Anal. 266, 1988-2052 (2014) [With Benoit Collins] CK-JFA-2014.pdf
- 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
- 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
- The Large-N Limits of Brownian Motions on GL(N). Int. Math. Res. Not. IMRN, no. 13, 4012-4057 (2016) K-BM-GLN.pdf
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Brown Measure Support and the Free Multiplicative Brownian Motion. Adv. Math. 355, 106771, 36 pp. (2019) [With Brian Hall] HK-Brown-Measure-Support.pdf
- 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
- 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
- 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
- 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
- The Brown Measure of the Free Multiplicative Brownian Motion. To Appear in Probab. Theory Related Fields [With Bruce Driver and Brian Hall] DHK-Brown-Measure.pdf