About Me
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Welcome! My name is Eli. I successfully defended my thesis and obtained my PhD in mathematics at the University of Albany (UAlbany) in April of 2024. I won University at Albany’s 2023-2024 Distinguished Doctoral Dissertation Award, which is awarded to the best dissertation in any field in the College. In the summer of 2024, I will be starting a three-year a postdoctoral research associate position at the University of Utah. My advisors were Matthew Zaremsky (at UAlbany) and Jon Bannon (at Siena College). If you would like to get in contact with me, please do not hesitate to send an email to ebashwinger[at]albany[dot]edu.
Here is my curriculum vitae.
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:
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
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
Non-inner amenability of the Higman-Thompson groups, with Matthew Zaremsky. (submitted) View on arXiv
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:
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.
AMS Special Session on Recent Developments in Operator Algebras III March 26-27th 2022 Presentation Title: Group von Neumann Algebras from Thompson-like Groups
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
Algebra/Topology Seminar, at University at Albany November 9th 2023. Presentation Title: Von Neumann Algebras from Thompson-like Groups
Operator Algebras Seminar, at Purdue University, November 14th 2023, Presentation Title: Von Neumann Algebras of Thompson-like Groups
Analysis and Data Science Seminar, at University at Albany, Date TBD, Presentation Title: Von Neumann Algebras of Thompson-like Groups
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
Subfactor Seminar, Vanderbilt University, March 1st 2024, Presentation Title: Von Neumann Algebras from Thompson-like Groups