Research

Seminar Organization

• I am coorganizing with Anshu the Model Theory of C*-algebras Reading Seminar at the Fields Institute for Fall 2023. This is part of the long program in operator algebras.
• I organized the UCSD Functional Analysis Seminar for 2021-2022.
• During 2022-2023, I was a coorganizer with Priyanga Ganesan (details can be found here).

Papers and Preprints

1. Ian Charlesworth, Rolando de Santiago, Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli, Brent Nelson. On the structure of graph product von Neumann algebras. arXiv:2404.08150
2. David Jekel. Combinatorial aspects of Parraud’s asymptotic expansion for GUE matrices. arXiv:2402.08024
3. Ilijas Farah, David Jekel, and Jennifer Pi. Quantum expanders and quantifier reduction for tracial von Neumann algebras. arXiv:2310.06197 
4. Ben Hayes, David Jekel, and Srivatsav Kunnawalkam Elayavalli. Consequences of the random matrix solution of the Peterson-Thom conjecture. arXiv:2308.14109
5. David Jekel. Optimal transport for types and convex analysis for definable predicates in tracial $\mathrm{W}^*$-algebras. arXiv:2308.11058
6. David A. Jekel, Todd A. Kemp, and Evangelos A. Nikitopoulos. A martingale approach to noncommutative stochastic calculus. arXiv:2308.09856
7. Ian Charlesworth, Rolando de Santiago, Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli, Brent Nelson. Strong 1-boundedness, L^2-Betti numbers, algebraic soficity, and graph products. arXiv:2305.19463 
8. Ian Charlesworth, Rolando de Santiago, Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli, Brent Nelson. Random permutation matrix models for graph products. arXiv:2404.07350
9. David Jekel and Jennifer Pi. An elementary proof of the inequality chi <= chi* for conditional free entropy. arXiv:2305.02574
10. Isaac Goldbring, David Jekel, Srivatsav Kunnawalkam Elayavalli, and Jennifer Pi. Uniformly Super McDuff II_1 factors. arXiv:2303.02809 
11. David Jekel. Free probability and model theory of tracial W*-algebras. Chapter 6 of Model Theory of Operator Algebras, ed. Isaac Goldbring. De Gruyter, Berlin, Boston. doi:10.1515/9783110768282-006 arXiv:2208.13867
12. David Jekel. Covering entropy for types in tracial W*-algebras, Journal of Logic and Analysis 15.2 (2023), pp. 1-68, doi:10.4115/jla.2023.15.2, arXiv:2204.02582
13. Ben Hayes, David Jekel, and Srivatsav Kunnawalkam Elayavalli, Vanishing first cohomology and strong 1-boundedness for von Neumann algebras, J. Noncommut. Geom. 18 (2024), no. 2, pp. 383–409, doi:10.4171/JNCG/530, arXiv:2110.12324
14. Ben Hayes, David Jekel, and Srivatsav Kunnawalkam Elayavalli, Property (T) and strong 1-boundedness, arXiv:2107.03278
15. Wilfrid Gangbo, David Jekel, Kyeongsik Nam, and Dimitri Shlyakhtenko, Duality for optimal couplings in free probability, Communications in Mathematical Physics, 2022, doi:10.1007/s00220-022-04480-0, arXiv:2105.12351
16. David Jekel, Wuchen Li, and Dimitri Shlyakhtenko, Tracial non-commutative smooth functions and the free Wasserstein manifold. Dissertationes Mathematicae 580 (2022), pp. 1-150. doi:10.4064/dm843-10-2021 arXiv:2101.06572
17. Ethan Davis, David Jekel, and Zhichao Wang, Tree convolution for probability distributions with unbounded support, Latin American Journal of Probability and Mathematics Statistics 18.2 (2021), pp. 1585-1623. doi:10.30757/ALEA.v18-58, arXiv:2102.01214
18. Terence Tao and Dimitri Shlyakhtenko, with an appendix by David Jekel, Fractional free convolution powers. To appear in Indiana University Math Journal, arXiv2009.08812
19. Ben Hayes, David Jekel, Brent Nelson, and Thomas Sinclair, A random matrix approach to absorption in free products, International Mathematics Research Notices, 2021.3, pp. 1919–1979. doi:10.1093/imrn/rnaa191, arXiv:1912.11569
20. David Jekel, Conditional expectation, entropy, and transport for convex Gibbs laws in free probability, International Mathematics Research Notices, 2022.6, pp. 4516-4619. doi:10.1093/imrn/rnaa181, arXiv:1906.10051
21. David Jekel and Weihua Liu, An operad of non-commutative independences defined by trees, Dissertationes Mathematicae 553 (2020), pp. 1-100, doi:10.4064/dm797-6-2020, arXiv:1901.09158
22. David Jekel, An elementary approach to free entropy theory for convex potentials, Analysis & PDE 13.8 (2020), pp. 2289-2374, doi:10.2140/apde.2020.13.2289, arXiv:1805.08814
23. David Jekel, Operator-valued chordal Loewner chains and non-commutative probability, Journal of Functional Analysis 278.10, 108452, doi:10.1016/j.jfa.2019.108452 arXiv:1711.02611
24. David Jekel, Avi Levy, Will Dana, Austin Stromme, and Collin Litterell, Algebraic properties of generalized graph Laplacians: Resistor networks, critical groups, and homological algebra, SIAM J. Discrete Math 32.2 (2018),  pp. 1040-1110.  Final Version PDF arXiv:1604.07075

Ph.D. Thesis

Evolution equations in non-commutative probability

Talk Slides

• Non-commutative transport of measure for operator algebras, at OTWIA, 2020 August 10.
• An operatorial viewpoint on Loewner chains in the upper half-plane at UCLA, 2020 April 17.
• Results and Questions about Entropy and Transport for Non-commutative Laws at Oberwolfach Real Algebraic Geometry with a View toward Hyperbolic Programming and Free Probability, 2020 March 5.
• Non-commutative Transport of Measure and Free Complementation of Certain Subalgebras of $L(\mathbb{F}_d)$ at Oberwolfach $C^*$-algebras, 2019 August.
• Operator-valued Loewner Chains and Non-commutative Probability at IWOTA in Lisbon, 2019 July 25.
• Free Entropy for Free Gibbs Laws given by Convex Potentials at U of Virginia, 2019 April 23. (Medium length.)
• Free Entropy for Free Gibbs Laws given by Convex Potentials at UC Berkeley, 2019 January 28. (Long.)

Expository Notes

• Operator-valued Non-commutative Probability (165 pages).
• Aleksandrov and Peller’s results on Operator Modulus of Continuity

Miscellaneous

• (with Will Dana) Critical Groups of Graphs with Dihedral Symmetry