Research

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• ORCID: 0000-0002-8580-5064
• arXiv record

Preprints

1. David Gao, David Jekel, Srivatsav Kunnawalkam Elayavalli, and Greg Patchell. Exotic full factors via weakly coarse bimodules. arXiv:2602.00930
2. Nicolas Gilliers and David Jekel. Bigraph independence: a mixture of the five natural independences. arXiv:2601.15215
3. David Gao and David Jekel. Elementary embeddings into ultrapower \mathrm{II}_1 factors without a UCP lift. arXiv:2512.10129
4. Wilfrid Gangbo, David Jekel, Kyeongsik Nam, and Aaron Z. Palmer. Large n-limit of matrix control problems and non-commutative controls. arXiv:2511.22804
5. David Jekel, Yoonkyeong Lee, Brent Nelson, and Jennifer Pi. Strong convergence to operator-valued semicirculars. arXiv:2506.19940
6. Ian Charlesworth and David Jekel. The atoms of graph product von Neumann algebras. arXiv:2506.09000
7. Wilfrid Gangbo, David Jekel, Kyeongsik Nam, and Aaron Z. Palmer. Viscosity solutions in non-commutative variables. arXiv:2502.17329
8. Ian Charlesworth and David Jekel. Operator models and analytic subordination for operator-valued free convolution powers. arXiv:2501.09190
9. Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli, and Brent Nelson. General solidity phenomena and anti-coarse spaces for type \mathrm{III}_1 factors. arXiv:2409.18106
10. David Jekel, Juspreet Singh Sandhu, and Jonathan Shi. Potential Hessian ascent: The Sherrington-Kirkpatrick model. arXiv:2408.02360
11. 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. To appear in Kyoto Journal of Math, arXiv:2305.19463 

Publications

1. David Jekel. The unitary group of a \mathrm{II}_1-factor is SOT-contractible. Mathematische Annalen. To appear, published online. doi:10.1007/s00208-025-03297-1, arXiv:2508.05834
2. Ben Hayes, David Jekel, and Srivatsav Kunnawalkam Elayavalli, Property (T) and strong 1-boundedness for von Neumann algebras. J. Inst. Math. Jussieu. To appear, published online. doi:10.1017/S1474748024000446, arXiv:2107.03278
3. Ilijas Farah, David Jekel, and Jennifer Pi. Quantum expanders and quantifier reduction for tracial von Neumann algebras. Journal of Symbolic Logic. To appear, published online. doi:10.1017/jsl.2025.10100, arXiv:2310.06197 
4. David Jekel and Srivatsav Kunnawalkam Elayavalli. Upgraded free independence phenomena for random unitaries. Trans. Amer. Math. Soc. Ser. B 13:1-29 (2026). doi:10.1090/btran/244, arXiv:2404.17114
5. David A. Jekel, Todd A. Kemp, and Evangelos A. Nikitopoulos. A martingale approach to noncommutative stochastic calculus. Journal of Functional Analysis 290.2: 111200 (2026). doi:10.1016/j.jfa.2025.111200, arXiv:2308.09856
6. Ian Charlesworth, Rolando de Santiago, Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli, Brent Nelson. On the Structure of Graph Product von Neumann Algebras. Publ. Res. Inst. Math. Sci. 61.4:713-762 (2025). doi:10.4171/PRIMS/61-4-3, arXiv:2404.08150
7. David Jekel, Lahcen Oussi, and Janusz Wysoczański. General limit theorems for mixtures of free, monotone, and Boolean independence. Electron. J. Prob. 30: art. 145, 50pp. (2025). doi:10.1214/25-EJP1407, arXiv:2407.02276
8. David Jekel. Information geometry for types in the large-n limit of random matrices. Commun. Math. Phys. 406: art. 272 (2025). doi:10.1007/s00220-025-05451-x, arXiv:2501.00703
9. Anshu, David Jekel, and Therese Landry. Quantum Wasserstein distances for quantum permutation groups. Journal of Geometry and Physics 217: art. 105637 (2025). doi:10.1016/j.geomphys.2025.105637, arXiv:2505.19269
10. Ian Charlesworth, Rolando de Santiago, Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli, Brent Nelson. Random permutation matrix models for graph products. Documenta Mathematica 30.5: 1231-1269 (2025), doi:10.4171/dm/992, arXiv:2404.07350
11. David Gao and David Jekel. Elementary equivalence and disintegration of tracial von Neumann algebras. Forum of Mathematics, Sigma 13: e105 (2025), doi:10.1017/fms.2025.10066, arXiv:2410.05529
12. Ben Hayes, David Jekel, and Srivatsav Kunnawalkam Elayavalli. Consequences of the random matrix solution of the Peterson-Thom conjecture. Analysis and PDE 18.7: 1805-1834 (2025), doi:10.2140/apde.2025.18.1805, arXiv:2308.14109
13. David Jekel. Combinatorial aspects of Parraud’s asymptotic expansion for GUE matrices. ALEA, Lat. Am. J. Probab. Math. Stat. 22: 579-606 (2025). doi:10.30757/ALEA.v22-22, arXiv:2402.08024
14. Isaac Goldbring, David Jekel, Srivatsav Kunnawalkam Elayavalli, and Jennifer Pi. Uniformly Super McDuff II_1 factors. Mathematische Annalen 391: 2757-2781 (2025). doi:10.1007/s00208-024-02959-w, arXiv:2303.02809
15. David Jekel. Optimal transport for types and convex analysis for definable predicates in tracial $\mathrm{W}^*$-algebras. Journal of Functional Analysis 287.9: art. 110583 (2024). doi:10.1016/j.jfa.2024.110583, arXiv:2308.11058
16. David Jekel and Jennifer Pi. An elementary proof of the inequality \chi \leq \chi^* for conditional free entropy. Documenta Mathematica 29.5: 1085–1124 (2024). doi:10.4171/dm/969, arXiv:2305.02574
17. 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
18. David Jekel. Covering entropy for types in tracial \mathrm{W}^*-algebras, Journal of Logic and Analysis 15.2: 1-68 (2023). doi:10.4115/jla.2023.15.2, arXiv:2204.02582
19. Ben Hayes, David Jekel, and Srivatsav Kunnawalkam Elayavalli, Vanishing first cohomology and strong 1-boundedness for von Neumann algebras. J. Noncommut. Geom. 18.2: 383-409 (2024). doi:10.4171/JNCG/530, arXiv:2110.12324
20. 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
21. David Jekel, Wuchen Li, and Dimitri Shlyakhtenko, Tracial non-commutative smooth functions and the free Wasserstein manifold. Dissertationes Mathematicae 580: 1-150 (2022). doi:10.4064/dm843-10-2021 arXiv:2101.06572
22. 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: 1585-1623 (2021). doi:10.30757/ALEA.v18-58, arXiv:2102.01214
23. Terence Tao and Dimitri Shlyakhtenko, with an appendix by David Jekel, Fractional free convolution powers. Indiana Univ. Math. J.  71.6: 2551-2594 (2022). doi:10.1512/iumj.2022.71.9163, arXiv2009.08812
24. Ben Hayes, David Jekel, Brent Nelson, and Thomas Sinclair, A random matrix approach to absorption in free products, International Mathematics Research Notices, 2021.3: 1919–1979. doi:10.1093/imrn/rnaa191, arXiv:1912.11569
25. David Jekel, Conditional expectation, entropy, and transport for convex Gibbs laws in free probability, International Mathematics Research Notices, 2022.6: 4516-4619. doi:10.1093/imrn/rnaa181, arXiv:1906.10051
26. David Jekel and Weihua Liu, An operad of non-commutative independences defined by trees, Dissertationes Mathematicae 553: 1-100 (2020). doi:10.4064/dm797-6-2020, arXiv:1901.09158
27. David Jekel, An elementary approach to free entropy theory for convex potentials, Analysis & PDE 13.8: 2289-2374 (2020). doi:10.2140/apde.2020.13.2289, arXiv:1805.08814
28. David Jekel, Operator-valued chordal Loewner chains and non-commutative probability, Journal of Functional Analysis 278.10: 108452 (2020). doi:10.1016/j.jfa.2019.108452 arXiv:1711.02611
29. 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: 1040-1110 (2018).  Final Version PDF arXiv:1604.07075

Ph.D. Thesis

Evolution equations in non-commutative probability

Leibniz translation project

With Matthew McMillan, I am working on translating several unpublished works of Leibniz on geometry from Latin into English.

Selected conference talks

• Entropy and Wasserstein distance in free probability, at IPAM Noncommutative Optimal Transport, Workshop II, 2025-04-30 [slides] [video]
• Non-commutative transport of measure for operator algebras, at OTWIA, 2020-08-10.
• An operatorial viewpoint on Loewner chains in the upper half-plane at UCLA, 2020-04-17.
• 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, 2020-03-05.
• 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, 2019-07-25.
• Free Entropy for Free Gibbs Laws given by Convex Potentials at U of Virginia, 2019-04-23. (Medium length.)
• Free Entropy for Free Gibbs Laws given by Convex Potentials at UC Berkeley, 2019-01-28. (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