Publications & Preprints

1.  Peripheral Poisson boundaries and jointly bi-harmonic functions,
   arXiv preprint, arxiv:2307.11295
   
   In this paper we answer a question of Vadim Kaimanovich from 1992 by completely classifying all bounded jointly bi-harmonic functions on groups. We also study the notion of Peripheral Poisson boundaries in this context, and provide a solution of a related conjecture due to R. Bhat, B. Talwar and S. Kar.
   
   

2. Invariant subalgebras of von Neumann algebras arising from negatively curved groups,
   joint with Ionut Chifan and Bin Sun.
   Journal of Functional Analysis, 285, Issue 9, 2023.
   
   In this  paper we  explore the notion of the Invariant Subalgebras Rigidity (ISR) property . A group von Neumann algebra has the ISR property if every von Neumann subalgebra that's normalized by the group unitaries arises from a normal subgrop. We prove that the ISR property holds for group algebras arising from a large class of icc groups, including acylindrically hyperbolic groups, and various groups admitting nontrivial cohomology. Our paper positively answers open questions by T. Amrutam and Y. Jiang.
   
   

3.  Poisson boundaries of  II_1 factors,
   joint with Jesse Peterson,
   Compositio Mathematica, 158, 1746--1776 , 2022.
   
   In this paper we study the notion of noncommutative Poisson boundaries.  We answer a question of Prof. Sorin Popa on Mean-Value Property of II_1 factors. This has applications towards Popa's tightness conjecture, which in turn is related to the famous free group factor problem. For a beautiful exposition, see this write-up in S. Popa's blog.
   
   

4.   Examples of Property (T) II_1 Factors with Trivial Fundamental Group
   joint with Ionut  Chifan, Cyril  Houdayer and Krishnendu Khan,
   To appear in American Journal of Mathematics,  December 2023.
   
   In this paper we provide the first examples of property (T) factors with trivial fundamental group. This is the first class of examples satisfying the strong form of Connes' rigidity conjecture due to Prof. Sorin Popa.
   
   

5.  Some Applications of Group Theoretic Rips Constructions to the Classification of von Neumann Algebras,
   joint with Ionut Chifan and Krishnendu Khan,
   Analysis and PDE,  16,  no. 2, 433-476, 2023
   
   Motivated by the famous Connes' Rigidity Conjecture, in this paper we study the problem of reconstruction of  property (T) groups from their group von Neumann algebras. We show that the semidirect product feature is remembered by the group von Neumann algebra arising from a large class of groups with property (T).  These group factors were later shown to have trivial fundamental group by I. Chifan, C. Houdayer, K. Khan and myself.
   
   

6.  New examples of Property (T) factors with trivial fundamental group and unique prime factorization,
   arXiV preprint, 2020

In this paper we provide examples of property (T) factors with trivial fundamental group. These group factors were constructed using previous joint works of the author.

7.   Semidirect product rigidity of group von Neumann algebras arising from class S, inductive limits and fundamental group,
   joint with K. Khan, arXiv:2202.04280.
   
   In this work we provide more examples of property (T) group factors with trivial fundamental group.
   
   

8. [CD19] Rigidity results for von Neumann algebras arising from mixing extensions of profinite actions of groups on probability spaces,
   joint with Ionut Chifan,
   Math. Ann.  (378), 907-950 (2020) .
   
   In this paper we relate the study of conjugacy of  group actions on probability spaces  with the study of the inclusion of the group von Neumann algebra inside the crossed product von Neumann algebra.  We  formulate an extended version of Neshveyev-Stormer rigidity question, and show that many natural class of actions satisfy this rigidity phenomenon.
   
   

9. [CD18] A remark on the ultrapower algebra of the hyperfinite factor,
   joint with Ionut Chifan,
   Proceedings of the American Mathematical Society 146 (2018), 5289-5294.
   
   In this paper we answer a question by S. Popa from 1983, using a synthesis of Popa's deformation/rigidity theory with Jones' subfactor theory.
   
   

10. [BDLR19] An angle between intermediate subfactors and its rigidity,
    joint with Keshab Bakshi, Zhengwei Liu and Yunxiang Ren,
    Transactions of the American Mathematical Society 371 (8), 5973-5991.
    
    In this paper we introduce a new notion of angle between intermediate subfactors. We use this notion to answer a question due to R. Longo from 2003.