Todd Kemp

  
 

Contact Info

Todd Kemp
Associate Professor, UC San Diego
Department of Mathematics
AP&M 5202
University of California, San Diego
La Jolla, CA 92093-0112

Phone: (858) 534-3985
Fax: (858) 534-5273
E-mail: tkemp@math.ucsd.edu

 

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).

My first former PhD student Natasha Blitvic (PhD from MIT, 2012) works in noncommutative probability and enumeratuve combinatorics. She is now Lecturer (tenure-track Assistant Professor) at Lancaster University. My second former PhD student David Zimmermann (PhD, 2015) works on log Sobolev inequalities and random matrices. He was a Dickson Instructor at the University of Chicago, and now works at Raytheon. I have two current PhD students: Ching Wei Ho (entering his fifth year) and Alice Chan (entering her fourth year), both of whom work on analysis and probability on high-dimensional Lie groups, random matrix theory, and free probability.

Here is a recent research statement: Kemp-Research-2016.pdf

Publications

Published work:

  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 (2010)    K-MZ-2010.pdf
  4. Hypercontractivity for log-subharmonic functions. J. Funct. Anal. 258, 1785-1805 (2010)   [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. Most Boson Quantum States are Almost Maximally Entangled. To appear in Proc. Am. Math. Soc. [With Shmuel Friedland] FK-Boson-Entanglement.pdf
  19. Fluctuations of Brownian Motions on GL(N). To appear in AIHP Probab. Stat. [With Guillaume Cébron] CeK-Fluctuations.pdf
  20. The Spectral Edge of Unitary Brownian Motion. To appear in Probab. Theory Related Fields. [With Benoit Collins and Antoine Dahlqvist] CDK-PTRF-2016.pdf

Preprints:

  1. The Complex Time Segal-Bargmann Transform. [With Bruce Driver and Brian Hall] DHK-C-Time-SBT.pdf
  2. Random Matrices with Log-Range Correlations, and Log-Sobolev Inequalities. [With David Zimmermann] KZ-Log-Correlations.pdf