Research

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Preprints

  1. David Gao and David Jekel. Elementary equivalence and disintegration of tracial von Neumann algebras. arXiv:2410.05529
  2. Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli, and Brent Nelson. General solidity phenomena and anti-coarse spaces for type III_1 factors. arXiv:2409.18106
  3. David Jekel, Juspreet Singh Sandhu, and Jonathan Shi. Potential Hessian ascent: The Sherrington-Kirkpatrick model. arXiv:2408.02360
  4. David Jekel, Lahcen Oussi, and Janusz Wysoczański. General limit theorems for mixtures of free, monotone, and boolean independence. arXiv:2407.02276
  5. David Jekel and Srivatsav Kunnawalkam Elayavalli. Upgraded free independence phenomena for random unitaries. arXiv:2404.17114
  6. 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
  7. David Jekel. Combinatorial aspects of Parraud’s asymptotic expansion for GUE matrices. arXiv:2402.08024
  8. Ilijas Farah, David Jekel, and Jennifer Pi. Quantum expanders and quantifier reduction for tracial von Neumann algebras. arXiv:2310.06197 
  9. David A. Jekel, Todd A. Kemp, and Evangelos A. Nikitopoulos. A martingale approach to noncommutative stochastic calculus. arXiv:2308.09856
  10. 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 
  11. Ian Charlesworth, Rolando de Santiago, Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli, Brent Nelson. Random permutation matrix models for graph products. arXiv:2404.07350

Publications

  1. Ben Hayes, David Jekel, and Srivatsav Kunnawalkam Elayavalli, Property (T) and strong 1-boundedness, arXiv:2107.03278 To appear in J. Inst. Math. Jussieu.
  2. Isaac Goldbring, David Jekel, Srivatsav Kunnawalkam Elayavalli, and Jennifer Pi. Uniformly Super McDuff II_1 factors. arXiv:2303.02809  To appear in Mathematische Annalen.
  3. Ben Hayes, David Jekel, and Srivatsav Kunnawalkam Elayavalli. Consequences of the random matrix solution of the Peterson-Thom conjecture. arXiv:2308.14109 To appear in Analysis and PDE.
  4. David Jekel. Optimal transport for types and convex analysis for definable predicates in tracial $\mathrm{W}^*$-algebras. Journal of Functional Analysis 287.9:110583 (2024). doi:10.1016/j.jfa.2024.110583, arXiv:2308.11058
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. Terence Tao and Dimitri Shlyakhtenko, with an appendix by David Jekel, Fractional free convolution powers. Indiana Univ. Math. J.  71.6 (2022),  2551-2594, doi:10.1512/iumj.2022.71.9163, arXiv2009.08812
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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

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