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 career 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 fundamental 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. 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 set up a framework to study sofic approximations of orbit equivalence relations. Together with David Gao and Gregory Patchell, we introduced a new theory of soficity for actions of groups on sets and graphs, with various applications including proving soficity for generalized wreath products. I also studied, in the above AIM square project, the weak convergence of random permutation models in the framework of epsilon-free independence. I also studied much earlier, with Isaac Goldbring and Yash Lodha, a Baire category theoretical approach to several algebraic properties in spaces of countable groups. 

In 2024, much of my attention turned towards 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. 

More recently, my attention has been focused on 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.