Preprints, Publications, and Awards

You can find my CV here. 

Awards and Honors:

2022-Presnt: NSF DMS-2144739 Research Grant CAREER: Invariants and Entropy of Square Integrable Functions

2020-Present: NSF DMS-2000105 Research Grant "Entropy methods in von Neumann algebras"

2018: Winner of the Samir Aldroubi and Amira Azhari Prize for Excellence in Postdoctoral Research at Vanderbilt.

February 2018-2019: NSF DMS-1827376 Research Grant “Aspects of Sofic Entropy and Algebraic Actions”.

June 2016-May 2018: NSF DMS-1600802 Research Grant “Aspects of Sofic Entropy and Algebraic Actions”.

2014: UCLA Heaviside Wealth Management Award.

2013-2014: UCLA Dissertation Year Fellowship.

Publications:

Journal Papers:

1. On sofic approximations of non amenable groups. joint with Srivatsav Kunnawalkam Elayavalli. arXiv link. To appear in Mathematische Zeitschrift

2. Co-spectral radius for countable equivalence relations. To appear in Ergodic Theory and Dynamical Systems.  joint with M. Abert, M. Fraczyk. arXiv link 

3. Approximate homomorphisms and sofic approximations of orbit equivalence relations. joint with Srivatsav Kunnawalkam Elayavalli. arXiv link. To appear in Ergodic Theory and Dynamical Systems. 

4. Vanishing first cohomology and strong 1-boundedness for von Neumann algebras, joint with David Jekel, and Srivatsav Kunnawalkam Elayavalli. To appear in the Journal of Noncommutative Geometry arXiv link 

5. B. Hayes. A random matrix approach to the Peterson-Thom conjecture. Indiana Universty Mathematics Journal  71 (2022),  1243-1297 l. arXiv link 

6. B. Hayes. Harmonic models and Bernoullicity. Compositio Mathematica, 157(10), 2021,2160--2198. arXiv link. 

7. L. Bowen, B. Hayes, F.Lin, A multiplicative ergodic theorem for von Neumann algebra valued cocycles. Communications in Mathematical Physics, 384,  2021, 1291--1350. arXiv link. 

8. B. Hayes, D. Jekel, B. Nelson, and T. Sinclair.  A Random matrix approach to absorption in free products. International Mathematics Research Notices, 3  (2021), 1919-1979, arXiv link

9. R. deSantiago, B. Hayes, D. Hoff, and T. Sinclair. Maximal rigid subalgebras of deformations and L2-cohomology. Analysis & PDE 14(7), (2021), 2269–2306 . arXiv link

10. B. Hayes. Max-Min theorems for weak containment, square summable homoclinic points, and completely positive entropy.  Indiana Univ. Math. J.  70 (2021),  1221-1266.  arXiv link

11. K. Hamm, B. Hayes, and A. Petrosyan, An Operator theoretic approach to the convergence of rearranged Fourier series. To appear in Journal d'Analyse Mathematique. arXiv link.

12. B. Hayes, Relative entropy and the Pinsker product formula for sofic groups. To appear in Groups, Geometry, and Dynamics. arxivlink

13. B. Hayes. Weak equivalence to Bernoulli shifts for some algebraic actions, Proc. Amer. Math. Soc. 147 (2019), 2021-2032 . arXivlink DOI: org/10.1090/proc/14063

14. B.Hayes and A. Sale, Metric approximations of wreath products, Annales de l'Institut Fourier 68(1), 423-455, 2018. arXivlink Journal Version

15. B. Hayes. Local and Doubly Empirical Convergence and the Entropy of Algebraic Actions of Sofic Groups, Ergodic Theory and Dynamical Systems. 39(4), 930-935, 2019. arXivlink DOI: 10.1017/etds.2017.69

16. B. Hayes. 1-Bounded entropy and regularity problems in von Neumann algebras, International Mathematics Research Notices, 1(3), 57-137, 2018. arXiv:1505.06682 DOI:org/10.1093/imrn/rnw237

17. B. Hayes. Fuglede-Kadison determinants and sofic entropy, Geometric and Functional Analysis, 26(2), 520-606, 2016 arXiv link, DOI: 10.1007/s00039-016-0370-y

18. B. Hayes, Indepdence tuples and Deninger's problem, Groups, Geometry and Dynamics, 2017, 11 (1), 245-289: arXiv:1502.03858

19. B. Hayes. Sofic entropy of Gaussian actions, Ergodic Theory and Dynamical Systems. 2017, 37 (7):2187-2222 arxiv:1509.07835 doi:10.1017/etds.2016.6

20. B. Hayes. Polish models and sofic entropy, Journal of the Institute of Mathematics Jussieu, 2018, 17(2):241-275. arXiv:1411.1510, DOI: 10.1017/S1474748015000468 

21. B. Hayes. Metric mean dimension for algebraic actions of sofic groups, Trans. Amer. Math. Soc. 369 (2017), 6853-6897 , 369 (10), 6853-6897. arXiv:1310.4126

22. B.Hayes. An $l^{p}$-version of von Neumann dimension For Banach Space representations of sofic groups II, Journal of Functional Analysis, 269(8), 2365–2426. 2015. arXiv:1302.2286

23. B.Hayes. An $ l^{p}$-version of von Neumann Dimension for Banach space representations of sofic groups, Journal of Functional Analysis, 266 (2), 989-1040, 2013. arXiv:1110.5390 

Conference Proceedings:

1. B. Hayes. Mixing and spectral gap relative to Pinsker factors for sofic groups, to appear in the Proceedings in honor of Vaughan F. R. Jones’ 60th birthday conferences. Proceedings of the 2014 Maui and 2015 Qinhuangdao conferences in honour of Vaughan F. R. Jones' 60th birthday, Proc. Centre Math. Appl. Austral. Nat. Univ., 46, 193–221, 2017. arxiv:1509.07839 

Submitted:

1. On the structure of graph product von Neumann algebras. arXiv link. joint with Ian Charlesworth, Rolando de Santiago, David Jekel, Srivatsav Kunnawalkam Elayavalli, and Brent Nelson 

2. Random permutation matrix models for graph products arXiv link.  joint with Ian Charlesworth, Rolando de Santiago, David Jekel, Srivatsav Kunnawalkam Elayavalli, and Brent Nelson  

3. Spectral non-concentration near the top for unimodular random graphs. arXiv link . joint with Mikolaj Fraczyk, Madhu Sudan, and Yufei Zhao 

4. Growth dichotomy for unimodular random rooted trees. arXiv link.  joint with Miklos Abert, Mikolaj Fraczyk.

5. Consequences of the random matrix solution to the Peterson-Thom conjecture. joint with  joint with David Jekel, and Srivatsav Kunnawalkam Elayavalli. arXiv link 

6. Strong 1-boundedness, L2-Betti numbers, algebraic soficity, and graph products. joint with Ian Charlesworth, Rolando de Santiago, David Jekel, Srivatsav Kunnawalkam Elayavalli, and Brent Nelson. arXiv link 

7. Property (T) and strong 1-boundedness for von Neumann algebras, joint with David Jekel, and Srivatsav Kunnawalkam Elayavalli. arXiv link. 

Preprints:

1. B. Hayes. Local weak∗-Convergence, algebraic actions, and a max-min principle. arXiv link.

2. B. Hayes and A. Sale. The wreath product of two sofic groups is sofic. arxivlink

3. B.Hayes. An $l^{p}$-Version of von Neumann Dimension For Representations of Equivalence Relations, arXiv:1302.2293