Research Interests: 

Entropy, boundary and ultraproduct methods in the structure theory of von Neumann algebras and related subjects.

My research program is supported by the NSF Analysis Research Grant DMS 2350049: Total Award: $145,055, Period: 2024-2027. 

Publications:

1. Internal sequential commutation and single generation (with D. Gao and G. Patchell and H. Tan). Preprint. April 2024.

2. On the structure of graph product von Neumann algebras (with AIM Square team). Preprint. April 2024. 

3. Random permutation matrix models for graph products (with AIM Square team). Preprint. April 2024. 

4. On conjugacy and perturbation of subalgebras (with D. Gao and G. Patchell and H. Tan). Preprint. March 2024.

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

6. Sequential commutation in tracial von Neumann algebras (with G. Patchell). Preprint. November 2023. 

7. Consequences of the random matrix solution to the Peterson-Thom conjecture (with B. Hayes and D. Jekel). Preprint. August 2023. 

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

9. Uniformly super McDuff II_1 factors (with I. Goldbring, D. Jekel and J. Pi). Preprint.  March 2023.

10. Property T and strong 1-boundedness for von Neumann algebras (with B. Hayes and D. Jekel). Preprint. July 2021.

11. On sofic approximations of non amenable groups (with B. Hayes).
    Math. Z., in revision.

12. Proper proximality for various families of groups (with C. Ding).
    Groups Geom. Dyn., to appear. 

13. On the structure of relatively biexact group von Neumann algebras  (with C. Ding).
    Comm. Math. Phys., to appear. 

14. Hyperfiniteness for group actions on trees (with K. Oyakawa, F. Shinko and P. Spaas).
    Proc. Amer. Math. Soc., to appear. 

15. Approximate homomorphisms and sofic approximations of orbit equivalence relations (with B. Hayes).  
    Ergodic Theory Dynam. Systems., to appear. 

16. Cartan subalgebras in von Neumann algebras associated to graph product groups (with I. Chifan).
    Groups Geom. Dyn., to appear. 

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

18. Vanishing first cohomology and strong 1-boundedness for von Neumann algebras (with B. Hayes and D. Jekel).
    J. Noncommut. Geom. (2023) 1-27.

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

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

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

22. 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.

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

PhD Thesis: 

Free entropy theory and rigid von Neumann algebras. 

Completed under the guidance of Jesse Peterson at Vanderbilt University in May 2022. 

Unpublished Research 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. 

Curriculum Vitae: 

(Last revised Feb 25th, 2024). Link.