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Srivatsav Kunnawalkam Elayavalli

Assistant Professor
University of Maryland, College Park

sriva(at)umd(dot)edu (UMD)

Starting July 1, 2026 I will be Assistant Professor at the University of California, Berkeley.

I am a mathematician who likes to study operator algebras and find connections to other areas of mathematics including geometric group theory, random matrix theory, mathematical logic, topology and geometry, ergodic theory and dynamics.

Publications

Strongly converging unitary representations of extensions by exact groups (with D. Gao and M. Mj). to be announced, 2026.
Questions on the structure of random embeddings of L(F_2) (with B. Hayes and D. Jekel). to be announced, 2026.
Relative biexactness and mixing in von Neumann algebras (with Z. Yang). to be announced, 2026.
On free components of Artin and Coxeter groups (with G. Dumas, J. Huang and L. Teryoshin). April 2026.
Toeplitz exactness for strong convergence (with D. Gao). April 2026.
Selfless reduced amalgamated free products and HNN extensions (with D. Gao, G. Patchell and L. Teryoshin). April 2026.
A new source of purely finite matricial fields (with D. Gao, A. Manzoor and G. Patchell). April 2026.
Strongly 1-bounded inner amenable groups (with B. Hayes). March 2026.
Conjugacy co-amenability (with M. Kalantar). February 2026.
Non-isomorphism of reduced free group C*-algebras (with D. Gao). February 2026.
Exotic full factors via weakly coarse bimodules. (with D. Gao, D. Jekel and G. Patchell). January 2026.
50 Open Problems: Ultraproduct II_1 factors. November 2025.
Some remarks on decay in countable groups and amalgamated free products (with G. Patchell and L. Teryoshin). September 2025.
Selfless reduced free product C*-algebras (with B. Hayes and L. Robert). May 2025.
Negative resolution to the C*-algebraic Tarski problem (with C. Schafhauser). March 2025.
Sofic actions on graphs (with D. Gao and G. Patchell). September 2024.
Selfless inclusions of C*-algebras (with B. Hayes, G. Patchell and L. Robert). October 2025.
J. Funct. Anal., in revision.
3-handle construction on II_1 factors (with D. Gao and G. Patchell). April 2025.
Proc. Amer. Math. Soc., to appear.
On soficity for certain fundamental groups of graphs of groups (with D. Gao and M. Mj). Preprint. August 2024.
J. Top. Anal., to appear.
Simplices of maximally amenable extensions in II_1 factors (with G. Patchell). Preprint. October 2024.
Groups Geom. Dyn., to appear.
General solidity phenomena and anticoarse spaces for type III_1 factors (with B. Hayes, D. Jekel, B. Nelson with an appendix by S. Vaes). September 2024.
J. Funct. Anal., in revision.
Strong 1-boundedness, L^2-Betti numbers, algebraic soficity, and graph products (with AIM Square team). Preprint. May 2023.
Kyoto J. Math., to appear.
Strict comparison in reduced group C*-algebras (with T. Amrutam, D. Gao and G. Patchell). Preprint. December 2024.
Invent. Math. 242 (2025), no. 3, 639–657.
Upgraded free independence phenomena for random unitaries (with D. Jekel). Preprint. May 2024.
Trans. Amer. Math. Soc. Ser. B 13 (2026), 1–29.
On the structure of graph product von Neumann algebras (with AIM Square team). Preprint. April 2024.
Publ. Res. Inst. Math. Sci. 61 (2025), 713–762.
On conjugacy and perturbation of subalgebras (with D. Gao and G. Patchell and H. Tan).
J. Noncommut. Geom. (2025).
Soficity for group actions on sets and applications (with D. Gao and G. Patchell). Preprint. January 2024.
Res. Math. Sci. 12, 48 (2025).
Random permutation matrix models for graph products (with AIM Square team).
Doc. Math. 30 (2025), no. 5, pp. 1231–1269.
Property T and strong 1-boundedness for von Neumann algebras (with B. Hayes and D. Jekel). Preprint. July 2021.
J. Inst. Math. Jussieu. (2025) pp. 1 - 34.
Consequences of the random matrix solution to the Peterson-Thom conjecture (with B. Hayes and D. Jekel).
Anal. PDE., 18, 7, (2025) 1805–1834.
Uniformly super McDuff II_1 factors (with I. Goldbring, D. Jekel and J. Pi).
Math. Ann., 391, 2757–2781, (2025).
Finite index subfactors of super McDuff II_1 factors (with D. Gao). February 2025.
J. Log. Anal., 17, 5, (2025) 1–8.
Internal sequential commutation and single generation (with D. Gao and G. Patchell and H. Tan). Preprint. April 2024.
Int. Math. Res. Not. IMRN, (2025) 8 2025.
Approximate homomorphisms and sofic approximations of orbit equivalence relations (with B. Hayes).
Ergodic Theory Dynam. Systems. 44 (2024), 3455–3480.
On sofic approximations of non amenable groups (with B. Hayes).
Math. Z. 307, 38 (2024).
Sequential commutation in tracial von Neumann algebras (with G. Patchell).
J. Funct. Anal. 288, (4) (2025).
Hyperfiniteness for group actions on trees (with K. Oyakawa, F. Shinko and P. Spaas).
Proc. Amer. Math. Soc. 152 (2024), no. 9, 3657–3664.
Proper proximality for various families of groups (with C. Ding).
Groups Geom. Dyn. 18 (2024), 921–938.
On the structure of relatively biexact group von Neumann algebras (with C. Ding).
Comm. Math. Phys., 405, 104 (2024).
Cartan subalgebras in von Neumann algebras associated to graph product groups (with I. Chifan).
Groups Geom. Dyn. 18 (2024), no. 2, 749–759
Vanishing first cohomology and strong 1-boundedness for von Neumann algebras (with B. Hayes and D. Jekel).
J. Noncommut. Geom. 18 (2024), 383–409.
Properly proximal von Neumann algebras (with C. Ding and J. Peterson).
Duke Math. J. (2023) 172(15):2821-2894.
Remarks on the diagonal embedding and strong 1-boundedness.
Doc. Math. (2023) 28, no. 3, pp. 671–681.
Generic algebraic properties in spaces of enumerated groups (with I. Goldbring and Y. Lodha).
Trans. Amer. Math. Soc. (2023) 376, 6245-6282.
An exotic II_1 factor without property Gamma (with I. Chifan and A. Ioana).
Geom. Funct. Anal. (2023) 33, 1243–1265.
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.
On ultraproduct embeddings and amenability for tracial von Neumann algebras (with S. Atkinson).
Int. Math. Res. Not. IMRN (2021) 4, 2882–2918.
Free entropy theory and rigid von Neumann algebras.
PhD Thesis, Vanderbilt University (2022).

Research summary

I began my graduate work at the Vanderbilt University under the supervision of Jesse Peterson. My initial research interest was to study to large scale approximation properties of von Neumann algebras, in particular, the analytic structure of ultrapowers. This interest has also broadly impacted and informed my research program thus far.

In early articles joint with Scott Atkinson and Isaac Goldbring, we studied ultrapower characterizations of amenability motivated by Jung, and settled some questions of Popa concerning ultrapower embeddings. Then, together with Adrian Ioana and Ionut Chifan, we settled the long standing question concerning the existence of a pair of full II_1 factors with nonisomorphic ultrapowers. Building on this, with Gregory Patchell, and further with David Gao, we emphasized a new approach based on sequential commutation to study ultrapowers, and opened up various questions around elementary equivalence. One of the key components of the resolution to the above problem was Voiculescu's free entropy theory. My own motivation to arrive at this came from independent work I was involved in jointly with Ben Hayes and David Jekel concerning strong 1-boundedness. We settled the long standing question of Jung and Shlyakhtenko, proving that all II_1 factors with Kazhdan's property T are strongly 1-bounded. In this line, David Jekel and myself later obtained a strengthening of Voiculescu's free independence result, and used it to discover vast levels of free independence inside ultrapowers of von Neumann algebras.

In parallel I was also involved in the development of a new boundary theory for von Neumann algebras, jointly with Changying Ding and Jesse Peterson. We introduced a natural notion of Ozawa's small-at-infinity compactification of a von Neumann algebra, the existence of which was fundamentally unclear owing to obstructions from vanishing cohomology results of Johnson-Parrot and Popa. Using these new techniques we settled the long standing problems of Anantharaman-delaroche regarding the compact approximation property for II_1 factors, and of Popa concerning non-embeddability in free group factors. Changying Ding and myself also studied these relative boundaries in free products of von Neumann algebras, gaining new generalizations on Ozawa's Kurosh theorem. Later with Zhiyuan Yang, we developed a new technique upgrading relative boundaries in setting of biexact von Neumann algebras, yielding new examples and classification results.

I have at various points been interested in the structure of graph products, both in the categories of von Neumann algebras and countable groups. Together with Ian Charlesworth, Ben Hayes, David Jekel, Brent Nelson, and Rolando de Santiago, we ran an AIM square to investigate graph products, yielding results on free probabilistic and rigidity aspects of their structure. For instance, we proved the weak convergence of random permutation models in the framework of epsilon-free independence. I have also studied Gromov's notion of soficity in geometric group theory, using operator algebraic methods. With Ben Hayes, we studied uniqueness of embeddings upto conjugacy in the universal sofic group, and also studied a framework to study sofic approximations of orbit equivalence relations. Together with David Gao and Gregory Patchell, we filled a well known gap in the literature and found a natural theory of soficity for actions of groups on sets and graphs, with various applications including proving soficity for generalized wreath products. I studied much earlier, with Isaac Goldbring and Yash Lodha, a Baire category theoretical approach to several algebraic properties in spaces of countable groups. Between 2023 and early 2024, I was investigating, with David Gao, Isaac Goldbring, Gregory Patchell, Hui Tan and Jenny Pi, several miscellaneous matters in II_1 factor theory around single generation, maximal amenability, perturbations of subalgebras, and existentially closed factors, and the super McDuff property.

Starting in late 2024, much of my attention was focused on the structure and classification C*-algebras. Together with Tattwamasi Amrutam, David Gao and Gregory Patchell, we settled the long standing open problem of Blackadar from 1989, proving strict comparison for the free groups, and more generally all acylindrically hyperbolic groups with rapid decay. This reinforced the prospects of enlarging the classification program to the setting of non-nuclear C*-algebras. Since this work, several results, including those of Ozawa, have appeared in quick succession, yielding rapid progress in the understanding of strict comparison in C*-algebras, via Leonel Robert's intrinsic free independence property known as selflessness. Together with Leonel Robert and various other co-authors including Ben Hayes, Gregory Patchell, David Gao, Lizzy Teryoshin and Marius Junge, we discovered this phenomena in various new settings and built unifying frameworks. In parallel, with Chris Schafhauser, we settled the long standing C*-algebraic analogue of Tarski's elementary equivalence problem, surprisingly in the negative. Later with David Gao, we found a conceptually new and short proof of the seminal nonisomorphism result of Pimsner-Voiculescu from 1981, using methods from II_1 factors. Currently with David Gao, Marius Junge, Gregory Patchell and Leonel Robert, we are involved in developing an overarching theory of selflessness for C*-correspondences, with several new applications.

In early spring 2026, my attention turned towards the program of strong convergence, initiated in the seminal work of Haagerup and Thorbjornsen. Together with David Gao, Aareyan Manzoor and Gregory Patchell, we discovered a C*-algebraic approach to prove strong convergence of unitary representations in vast generality. In particular, we proved strong convergence of unitary representations with finite images, for all fundamental groups of closed hyperbolic 3-manifolds, settling an open problem in the field with important ramifications to Yau's conjectures in minimal surface theory via Antoine Song's work. Then with David Gao, we developed a new Toeplitz exactness machine that upgrades strong convergence in the setting of C*-correspondences. This recovered and generalized with a new approach the free exactness results of Pisier-Skoufranis, in the setting of amalgamated free products. Currently, I am involved in proving strong convergence of unitary representations of extensions by exact groups, with Mahan Mj and David Gao.

My long term interest is to settle the free group factor isomorphism problem. I hope I can do it some day.

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

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