Research Interests: 

Very broadly, my interests lie in the overlap of  operator algebras and geometric group theory. More precisely, I study the operator algebras (von Neumann algebras and C^*-algebras) of certain important classes of groups commonly studied in geometric group theory (e.g., Thompson-like groups, Houghton-like groups) with the goal of providing interesting new examples to test conjectures, answer open problems concerned with the construction of examples with certain desired properties, etc. I am also interested in noncommutative (real) algebraic geometry, specifically when the *-algebra is taken to be the (real or complex) group algebra of a noncommutative group. Keywords: von Neumann algebras, McDuff factors, property gamma, C^*-algebras, C^*-simplicity, (inner) amenability, property (T), Haagerup property, proper proximality, generalized Thompson groups, cloning systems, self-similar groups, generalized Houghton groups, shift-similar groups, various forms of stability of groups, hyperlinearity, soficity, character theory and rigidity

Papers:

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. Non-inner amenability of the Higman-Thompson groups, with Matthew Zaremsky.  (submitted) View on arXiv 

4. 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.

Papers in the works:

Von Neumann algebras of Houghton-like groups

C*-algebras of Thompson-like groups from cloning systems

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.  Functional Analysis Seminar, University of California San Diego, January 14th 2025, Presentation Title: TBD