Research Interests: 

Very broadly, my research lies at the intersection of geometric group theory and operator algebras, with a focus on von Neumann algebras. Group-theoretic methods and constructions have been fruitfully and successfully applied in operator algebras since its inception. My goal is to continue this tradition of using group-theoretic methods and constructions to uncover novel phenomena at this interface, to construct exotic examples to test conjectures, and to prove classification results for group-related constructions. I am interested in various types of group and operator-algebraic rigidity. Specifically, I am interested in properties like inner amenability, proper proximality, property Gamma, the (super) McDuff factor property, primeness, solidity, and related structural invariants, along with mixing properties of subgroup/algebras, their normalizers, and associated normalizer algebras. The various families of groups I study include Thompson-like groups, self-similar groups, Houghton-like groups, shift-similar groups, and asymptotically rigid mapping class groups of infinite-type surfaces.

Publications & Preprints:

1. The correlation numerical range and trace-positive complex polynomials, with Jon Bannon and Mohammad Javaheri (Sept. 2016), Operators and Matrices 10(3):625-630. View here 

2. Von Neumann algebras of Thompson-like groups from cloning systems, with Matthew Zaremsky, J. Operator Theory. Vol. 89 (2023), No. 1, 23-48. View on arXiv 

3. Von Neumann algebras of Thompson-like groups from cloning systems II. (submitted) View on arXiv. Note: I have an updated version which is available upon request.

4. Non-inner amenability of the Higman-Thompson groups, with Matthew Zaremsky, Int. J. Algebra Comput. Vol. 35 (2025), No. 8, 1123-1134. View on arXiv. 

5.   On Similarity Structure Groups and their $W^*$ and $C^*$-algebras, with Patrick Debonis (2026), To appear in Algebraic & Geometric Topology. View on arXiv. 

Works in progress:

1. Property Gamma Factors from Shift-similar and Houghton-like Groups.

2. Bimodules, Groupoids, and $C^*$-algebras of Shift-similar and Houghton-like groups.

Conferences, Talks, and Presentations:

1. Fall Western Sectional Meeting California State University, Fullerton, Fullerton, CA October 24-25, 2015 (Saturday - Sunday) Meeting #1114, Title: The correlation numerical range and trace-positive complex polynomials. Attended but Jon Bannon presented our paper.

2. AMS Special Session on Recent Developments in Operator Algebras III March 26-27th 2022 Presentation Title: Group von Neumann Algebras from Thompson-like Groups

3. Workshop Series in von Neumann Algebras and Geometric Group Theory at The University of Iowa April 13-16th 2023 Presentation Title: Von Neumann Algebras from Thompson-like Groups

4. Algebra/Topology Seminar, at University at Albany November 9th 2023. Presentation Title: Von Neumann Algebras from Thompson-like Groups

5. Operator Algebras Seminar, at Purdue University, November 14th 2023, Presentation Title: Von Neumann Algebras of Thompson-like Groups

6. Analysis and Data Science Seminar, at University at Albany, Date TBD,  Presentation Title: Von Neumann Algebras of Thompson-like Groups

7.  Max Dehn Seminar on Geometry, Topology, Dynamics, and Groups at University of Utah, February 7th 2024 Presentation Title: Von Neumann Algebras from Thompson-like Groups

8.  Subfactor Seminar, Vanderbilt University, March 1st 2024, Presentation Title: Von Neumann Algebras from Thompson-like Groups

9. The 46th Annual Great Plains Operator Theory Symposium (GPOTS 2026) at University of Iowa, Presentation Title: Similarity Structure Groups and Their W* and $C^*$-algebras

10. Conference on MASAs, Nests, and Free Semigroup Algebras (in honor of David Pitts) at University of Nebraska–Lincoln, Presentation Title: Similarity Structure Groups and Their W* and $C^*$-algebras

11. AMS Special Session on Advances in Operator Algebras and Noncommutative Geometry, IV at McCormick Place convention center in Chicago, Presentation Title: Property Gamma Factors from Shift-similar and Houghton-like Groups