Srivatsav Kunnawalkam Elayavalli

Stefan E. Warschawski Assistant Professor
University of California at San Diego

Starting fall 2025 I will be tenure track assistant professor at University of Maryland, College Park.

skunnawalkamelayaval(at)ucsd(dot)edu

Published works

1. Strict comparison in reduced group C*-algebras (with T. Amrutam, D. Gao and G. Patchell). Preprint. December 2024. 

2. Simplices of maximally amenable extensions in II_1 factors (with G. Patchell). Preprint. October 2024.

3. General solidity phenomena and anticoarse spaces for type III_1 factors (with B. Hayes, D. Jekel, B. Nelson with an appendix by S. Vaes). Preprint. September 2024.

4. Sofic actions on graphs (with D. Gao and G. Patchell). Preprint. September 2024.  

5. On soficity for certain fundamental groups of graphs of groups (with D. Gao and M. Mj). Preprint. August 2024.

6. Soficity for group actions on sets and applications (with D. Gao and G. Patchell). Preprint. January 2024.  

7. Upgraded free independence phenomena for random unitaries (with D. Jekel). Preprint. May 2024. 

8. Strong 1-boundedness, L^2-Betti numbers, algebraic soficity, and graph products  (with AIM Square team). Preprint. May 2023. 

9. Internal sequential commutation and single generation (with D. Gao and G. Patchell and H. Tan). Preprint. April 2024.
   Int. Math. Res. Not. IMRN, in revision.

10. On the structure of graph product von Neumann algebras (with AIM Square team). Preprint. April 2024.
    Publ. Res. Inst. Math. Sci., to appear.

11. On conjugacy and perturbation of subalgebras (with D. Gao and G. Patchell and H. Tan).
    J. Noncommut. Geom., in revision.

12. Random permutation matrix models for graph products (with AIM Square team).
    Doc. Math., to appear.

13. Property T and strong 1-boundedness for von Neumann algebras (with B. Hayes and D. Jekel). Preprint. July 2021.
    J. Inst. Math. Jussieu., to appear.

14. Consequences of the random matrix solution to the Peterson-Thom conjecture (with B. Hayes and D. Jekel).
    Anal. PDE., to appear.

15. Uniformly super McDuff II_1 factors (with I. Goldbring, D. Jekel and J. Pi).
    Math. Ann., to appear.

16. Approximate homomorphisms and sofic approximations of orbit equivalence relations (with B. Hayes).  
    Ergodic Theory Dynam. Systems. 44 (2024), 3455–3480.

17. On sofic approximations of non amenable groups (with B. Hayes).
    Math. Z. 307, 38 (2024).

18. Sequential commutation in tracial von Neumann algebras (with G. Patchell).
    J. Funct. Anal. 288, (4) (2025).

19. Hyperfiniteness for group actions on trees (with K. Oyakawa, F. Shinko and P. Spaas).
    Proc. Amer. Math. Soc. 152 (2024), no. 9, 3657–3664.

20. Proper proximality for various families of groups (with C. Ding).
    Groups Geom. Dyn. 18 (2024), 921–938

21. On the structure of relatively biexact group von Neumann algebras  (with C. Ding).
    Comm. Math. Phys., 405, 104 (2024).

22. Cartan subalgebras in von Neumann algebras associated to graph product groups (with I. Chifan).
    Groups Geom. Dyn. 18 (2024), no. 2, 749–759

23. Vanishing first cohomology and strong 1-boundedness for von Neumann algebras (with B. Hayes and D. Jekel).
    J. Noncommut. Geom. 18 (2024), 383–409.

24. Properly proximal von Neumann algebras (with C. Ding and J. Peterson).
    Duke Math. J. (2023) 172(15):2821-2894.

25. Remarks on the diagonal embedding and strong 1-boundedness.
    Doc. Math. (2023) 28, no. 3, pp. 671–681.

26. Generic algebraic properties in spaces of enumerated groups (with I. Goldbring and Y. Lodha).
    Trans. Amer. Math. Soc. (2023) 376, 6245-6282.

27. An exotic II_1 factor without property Gamma (with I. Chifan and A. Ioana).
    Geom. Funct. Anal. (2023) 33, 1243–1265. 

28. Factorial relative commutants and the generalized Jung property for II_1 factors (with S. Atkinson and I. Goldbring).
    Adv. Math. (2022) 396, Paper No. 108107, 53 pp.

29. On ultraproduct embeddings and amenability for tracial von Neumann algebras (with S. Atkinson).
    Int. Math. Res. Not. IMRN (2021) 4, 2882–2918.

30. Free entropy theory and rigid von Neumann algebras.
    PhD Thesis, Vanderbilt University (2022 May).

I have in the past worked on, and presently continue to work on matters related to von Neumann algebras, C*-algebras, operator systems/spaces/bimodules, random matrix theory, free probability, continuous model theory, combinatorial and geometric group theory, analysis on groups and l^2 invariants, measured group theory, ergodic theory and dynamical systems, and descriptive set theory. A unifying trend in all of my research is my usage of ideas and techniques pertaining to "ultraproducts" to solve problems. 

Awards

1. NSF Standard grant: 2024 - 2027. DMS 2350049 "Entropy and boundary methods in von Neumann algebras". Total Award: $145,055.

2. AMS Simons grant: 2023- 2026. Total award: $9900. 

3. AIM Square grant: 2021-2024. "Classification of graph products from analytic and probabilistic viewpoints".

4. UCLA Chancellor's award for postdoctoral research. Total cash prize: $7,500. 

5. Founder's gold medal for first honors. 2022. The Graduate School of Vanderbilt University. Gold medal and cash prize: $3500.

6. Bjarni Jonsson prize for research. 2022. Department of Mathematics. Vanderbilt University. 

7. Russel G. Hamilton GLI Dissertation Enhancement Award. 2021. The Graduate School of Vanderbilt University.

8. Harold Stirling Vanderbilt Award. 2021. The Graduate School of Vanderbilt University.

9. University Graduate Fellowship and Russel G Hamilton Scholarship. 2018 - 2021. The Graduate School of Vanderbilt University.

10. Dorothea Klumpke Roberts Prize in Mathematics. 2018. Department of Mathematics. UC Berkeley. 

11. Magas Kitu ̆ntetessel Award. 2015. Budapest Semesters in Mathematics. 

``Time spent flying is not deducted from your lifespan.''

Notes

1. Sofic approximations of countable groups via graphs. January 2020. 

2. A remark on inclusions with factorial commutants. February 2023. 

3. Remarks on conjugacy classes of Haar unitaries (with D. Gao, G. Patchell and H. Tan). February 2024. 

4. A note on the Balachander Bani. English version. Tamil version (translated with the help of my parents). March 2024.

5. The life of a postdoctoral scholar in mathematics. English version. April 2024.

6. W. C. Thiruvengadam 6/9/1935 - 8/28/2017. English version. May 2024.

Thanks for visiting my website. I am Sri, a mathematician, carnatic musician and Veena player, a USHPA P3 certified paragliding pilot and I extremely enjoy petting dogs, cooking, eating, video games, Tamil literature and poetry, traveling and pretty much everything life has to offer. I grew up in Chennai, India. To get in touch write to me at skunnawalkamelayaval(at)ucsd(dot)edu or find me in AP&M1101 in the UCSD campus.