Research

Quick Links

Preprints

  1. Tattwamasi Amrutam, David Jekel, and Mateusz Wasilewski. Simplicity of q-Gaussian \mathrm{C}^*-algebras. arXiv:2606.10723
  2. Ben Hayes, David Jekel, and Srivatsav Kunnawalkam Elayavalli. Questions on the structure of random embeddings of L(\mathbb{F}_2). arXiv:2606.02985
  3. David Jekel. Free information geometry and the model theory of noncommutative stochastic processes. arXiv:2604.12212
  4. David Jekel, Evangelos A. Nikitopoulos, and Félix Parraud. Asymptotic expansion for transport maps between laws of multimatrix models. arXiv:2604.03213
  5. David Gao, David Jekel, Srivatsav Kunnawalkam Elayavalli, and Greg Patchell. Exotic full factors via weakly coarse bimodules. arXiv:2602.00930
  6. Nicolas Gilliers and David Jekel. Bigraph independence: a mixture of the five natural independences. arXiv:2601.15215
  7. Wilfrid Gangbo, David Jekel, Kyeongsik Nam, and Aaron Z. Palmer. Large n-limit of matrix control problems and non-commutative controls. arXiv:2511.22804
  8. David Jekel, Yoonkyeong Lee, Brent Nelson, and Jennifer Pi. Strong convergence to operator-valued semicirculars. arXiv:2506.19940
  9. Ian Charlesworth and David Jekel. The atoms of graph product von Neumann algebras. arXiv:2506.09000
  10. Wilfrid Gangbo, David Jekel, Kyeongsik Nam, and Aaron Z. Palmer. Viscosity solutions in non-commutative variables. arXiv:2502.17329
  11. Ian Charlesworth and David Jekel. Operator models and analytic subordination for operator-valued free convolution powers. arXiv:2501.09190
  12. 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
  13. David Jekel, Juspreet Singh Sandhu, and Jonathan Shi. Potential Hessian ascent: The Sherrington-Kirkpatrick model. arXiv:2408.02360
  14. 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. 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
  2. Ilijas Farah, David Jekel, and Jennifer Pi. Quantum expanders and quantifier reduction for tracial von Neumann algebras. Journal of Symbolic Logic. 91.2:776-812 (2026). doi:10.1017/jsl.2025.10100, arXiv:2310.06197 
  3. David Gao and David Jekel. Elementary embeddings into ultrapower \mathrm{II}_1 factors without a UCP lift. Journal of Logic and Analysis 18.3:1-13 (2026). doi:10.4115/jla.2026.18.3, arXiv:2512.10129
  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. David Jekel. The unitary group of a \mathrm{II}_1-factor is SOT-contractible. Mathematische Annalen. 393:3109-3117 (2025). doi:10.1007/s00208-025-03297-1, arXiv:2508.05834
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. Isaac Goldbring, David Jekel, Srivatsav Kunnawalkam Elayavalli, and Jennifer Pi. Uniformly Super McDuff \mathrm{II}_1 factors. Mathematische Annalen 391: 2757-2781 (2025). doi:10.1007/s00208-024-02959-w, arXiv:2303.02809
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. Wilfrid Gangbo, David Jekel, Kyeongsik Nam, and Dimitri Shlyakhtenko. Duality for optimal couplings in free probability, Communications in Mathematical Physics 396:903-981 (2022), doi:10.1007/s00220-022-04480-0, arXiv:2105.12351
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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. The project will be published by Cambridge University Press. One of our translations was already published in the Leibniz Review:

G. W. Leibniz, David Jekel, and Matthew McMillan. English Translation of G. W. Leibniz, Specimen Analyseos Figuratae in Elementis Geometriae (1686) (LH XXXV, i, 14, Bd. 21–22). Leibniz Review 35:45-59 (2025). doi:10.5840/leibniz2025354

Selected conference talks

These talks include links to the PDF of slides (sometimes with corrections to the originals).

Expository Notes

Miscellaneous