RESEARCH INTERESTS
Operator Algebras (von Neumann algebras, C*-algebras),
Ergodic Theory (measured group theory, orbit equivalence),
Group Theory (analytic, geometric and representation theoretic aspects; group stability),
Logic (descriptive set theory, continuous model theory).
I am especially interested in classification and rigidity for von Neumann algebras and
equivalence relations arising from groups and their actions on measure spaces.
My research has been supported by: NSF Grant DMS #2153805, a Simons Fellowship, NSF FRG Grant #1854074, NSF Career Grant DMS #1253402, NSF Grant DMS #1161047, a Sloan Foundation Fellowship and a Clay Research Fellowship.
CO-AUTHORS
Remi Boutonnet,
Lewis Bowen,
Ionut Chifan,
Yoann Dabrowski,
Daniel Drimbe,
Damien Gaboriau,
Daniel Hoff,
Camille Horbez,
Cyril Houdayer,
Jingyin Huang,
Alekos S. Kechris,
Yoshikata Kida,
Srivatsav Kunnawalkam Elayavalli,
Denis Osin,
Jesse Peterson,
Sorin Popa,
Alireza Salehi Golsefidy,
Pieter Spaas,
Bin Sun,
Hui Tan,
Todor Tsankov,
Robin Tucker-Drob,
Stefaan Vaes.
Matthew Wiersma.
PAPERS AND PREPRINTS
52. Asymptotic freeness in tracial ultraproducts. With Cyril Houdayer. preprint 2023.
(arXiv)
51. Non-isomorphism of $A^*n,2\leq n\leq\infty$, for a non-separable abelian von Neumann algebra $A$.
With Remi Boutonnet, Daniel Drimbe, and Sorin Popa. Geometric and Functional Analysis, accepted.
(arXiv)
50. On existentially closed II_1 factors.
With Hui Tan. Journal of Functional Analysis, accepted.
(arXiv)
49. Small cancellation and outer automorphisms of Kazhdan groups acting on hyperbolic spaces.
With Ionut Chifan, Denis Osin and Bin Sun. preprint 2023.
(arXiv)
48. Wreath-like products of groups and their von Neumann algebras II: Outer automorphisms.
With Ionut Chifan, Denis Osin and Bin Sun. preprint 2023.
(arXiv)
47. Wreath-like products of groups and their von Neumann algebras I: W^*-superrigidity.
With Ionut Chifan, Denis Osin and Bin Sun.
Annals of Mathematics, accepted.
(arXiv)
46. Two non-elementarily equivalent II_1 factors without property Gamma. With Ionut Chifan and Srivatsav Kunnawalkam Elayavalli.
Geometric and Functional Analysis, accepted.
(arXiv)
45. An introduction to von Neumann algebras,
Model Theory of Operator Algebras, Volume 11 in the series De Gruyter Series in Logic and Its Applications, 43-82.
44. Tensor product indecomposability results for existentially closed factors. With Ionut Chifan and Daniel Drimbe.
Model Theory of Operator Algebras, Volume 11 in the series De Gruyter Series in Logic and Its Applications, 269-302.
(arXiv)
43. Embedding universality for II_1 factors with property (T). With Ionut Chifan and Daniel Drimbe.
Adv. Math. 417 (2023), Paper No. 108934, 24 pp.
(arXiv)
42. Orbit equivalence rigidity of irreducible actions of right-angled Artin groups. With Camille
Horbez and Jingyin Huang. Compos. Math. 159 (2023), no. 4, 860-887.
(arXiv)
41. Almost commuting matrices and stability for product groups.
preprint 2021, submitted. (arXiv)
40. On sofic approximations of F_2\times F_2.
Ergodic Theory Dynam. Systems 42 (2022), no. 7, 2333-2351. (arXiv).
39. Cohomological obstructions to lifting properties for full C*-algebras of property (T) groups. With Pieter Spaas and Matthew Wiersma.
Geometric and Functional Analysis 30 (2020), 1402-1438.
(arXiv) (correction)
38. Cocycle superrigidity for profinite actions of irreducible lattices.
With Daniel Drimbe and Jesse Peterson. Groups Geom. Dyn. 17 (2023), no. 1, 315-329.
(arXiv).
37. Stability for product groups and property (tau). Journal of Functional Analysis, 279, Issue 9, 15 November 2020, 108729 (arXiv).
36. II_1 factors with exotic central sequence algebras. With Pieter Spaas
(arXiv). J. Inst. Math. Jussieu 20 (2021), no. 5, 1671-1696.
35. Properly proximal groups and their von Neumann algebras. With Remi Boutonnet and Jesse Peterson.
Ann. Sci. Ec. Norm. Super. Volume 54, fascicule 2 (2021), 445-482.
(arXiv).
34. A class of II_1 factors with a unique McDuff decomposition. With Pieter Spaas. Math. Ann. 375 (2019), no. 1-2, 177-212.
(arXiv).
33. Compact actions whose orbit equivalence relations are not profinite. Adv. Math. 354 (2019), 106753, 19 pp. (arXiv).
32. Rigidity for von Neumann algebras.
Proceedings of the International Congress of Mathematicians-Rio de Janeiro 2018. Vol. III. Invited lectures, 1639-1672, World Sci. Publ.,
Hackensack, NJ, 2018. (arXiv).
31. Amalgamated Free Product Rigidity for Group von Neumann Algebras. Adv. Math. 329 (2018), 819-850.
With Ionut Chifan. (arXiv).
30. Local spectral gap in the group of Euclidean isometries. With Remi Boutonnet. Int. Math. Res. Not. IMRN 2020, no. 2, 466-486.
(arXiv).
29. Prime II_1 factors arising from irreducible lattices in products of rank one simple Lie groups.
With Daniel Drimbe and Daniel Hoff. J. Reine Angew. Math. 757 (2019), 197-246. (arXiv).
28. Cocycle superrigidity for translation actions of product groups.
With Damien Gaboriau
and Robin Tucker-Drob. Amer. J. Math. 141 (2019), no. 5, 1347-1374.
(arXiv).
27. von Neumann's problem and extensions of non-amenable equivalence relations.
With Lewis Bowen and Daniel Hoff. Groups Geom. Dyn. 12 (2018), no. 2, 399-448.
(arXiv).
26. II_1 factors with non-isomorphic ultrapowers.
With Remi Boutonnet and Ionut Chifan. Duke Math. J. 166 (2017), no. 11, 2023-2051.
(arxiv).
25. Weak containment rigidity for distal actions. Adv. Math. 302 (2016), 309-322. With Robin Tucker-Drob.
(arxiv),
(journal version).
24. Local spectral gap in simple Lie groups and applications. Invent. Math. 208 (2017), no. 3, 715-802.
With Remi Boutonnet
and Alireza Salehi Golsefidy.
(arXiv),(journal version).
23. Strong ergodicity, property (T), and orbit equivalence rigidity for translation actions.
J. Reine Angew. Math. 733 (2017), 203-250.
(arXiv),(journal version).
22. Orbit equivalence and Borel reducibility rigidity for profinite actions with spectral gap.
J. Eur. Math. Soc. (JEMS) 18 (2016), no. 12, 2733-2784.
(arXiv),(journal version).
21. W*-superrigidity for arbitrary actions of central quotients
of braid groups. With
Ionut Chifan and Yoshikata Kida. Math. Ann. 361(2015), 563-582.
(arXiv), (journal version).
20. Unbounded derivations, free dilations and indecomposability
results for II_1 factors. With Yoann Dabrowski. Trans. Amer. Math. Soc. 368 (2016), no. 7, 4525-4560.
(arXiv),(journal version).
19. Classification and rigidity for von Neumann algebras.
European Congress of Mathematics, EMS (2013), 601-625.
(arxiv),
(journal version).
18. Cartan subalgebras of amalgamated free product II_1 factors.
With an appendix joint with Stefaan Vaes. Ann. Sci. Ec. Norm. Super. (4) 48 (2015), no. 1, 71-130.
(arXiv),(journal version).
17. Compact actions and uniqueness of the group measure space
decomposition of
II_1 factors. J. Funct. Anal. 262 (2012), 4525-4533.
(arXiv),
(journal version).
16. Uniqueness of the group measure space decomposition for Popa's HT factors.
Geom. Funct. Anal. 22 (2012), no. 3, 699-732.
(arXiv),(journal version).
15. Rigidity for equivalence relations on homogeneous spaces. Groups. Geom. Dyn.,
7(2013), 403-417. With Yehuda Shalom.
(arXiv),(journal version).
14. A class of superrigid group von Neumann algebras. Ann. of Math. 178 (2013), 231-286.
With Sorin Popa and Stefaan Vaes.
(arXiv),(journal version).
13. Rigid actions need not be strongly ergodic. Proc. Amer. Math. Soc. 140 (2012), 3283-3288.
With Stefaan Vaes.
(arXiv),(journal version).
12. W*-superrigidity for Bernoulli actions of property (T) groups. J. Amer. Math. Soc. 24 (2011),
1175-1226.
(arXiv),(journal version).
11. On Relative property (T) and Haagerup's property.
Trans. Amer. Math. Soc., 363 (2011), 6407-6420.
With Ionut Chifan.
(arXiv),(journal version).
10. On a Question of D. Shlyakhtenko. Proc. Amer. Math. Soc. 139(2011), 1091-1093.
With Ionut Chifan.
(arXiv),(journal version).
9. Relative property (T) for the subequivalence relations induced by the action of SL_2(Z) on T^2. Adv. Math. 224
(2010), no. 4, 1589-1617.
(arXiv),(journal version).
8.
Subequivalence relations and positive-definite functions. Groups Geom. Dyn. 3 (2009), no. 4, 579-625.
With Alekos S. Kechris and Todor Tsankov.
(arXiv),(journal version).
7. Ergodic subequivalence relations induced by a Bernoulli action. Geom. Funct. Anal. 20 (2010), no. 1,
53-67. With Ionut Chifan. (arXiv),(journal version).
6. Cocycle superrigidity for profinite actions of property (T) groups. Duke Math. J. 157
(2011), no. 2, 337-367.
(arXiv),(journal version).
5. Orbit inequivalent actions for groups containing a copy of F_2. Invent. Math. 185 (2011), no. 1, 55-73.
(arXiv),(journal version).
4. Non-orbit equivalent actions of F_n. Ann. Sci. Ec. Norm. Super. (4) 42 (2009), no. 4, 675-696.
(arXiv),(journal version).
3. Rigidity results for wreath product II_1 factors. J. Funct. Anal. 252 (2007), no. 2, 763-791.
(arXiv),(journal version).
2. Amalgamated free products of weakly rigid factors and calculation of their symmetry groups. Acta Math. 200 (2008), no. 1, 85-153. With Jesse Peterson and Sorin Popa.
(arXiv),(journal version).
1. A relative version of Connes' \chi(M)
invariant and existence of orbit inequivalent actions. Ergodic Theory Dynam. Systems 27 (2007), no. 4, 1199-1213.
(arXiv),
(journal version)