Research

My research is in the field of functional analysis with an emphasis on the classification of group von Neumann algebras. My mathematical interests include operator algebras, ergodic theory, measured group theory, and fractal geometry.

Current PhD Students: Patrick DeBonis (Purdue University)

Previous Undergraduate Students: A. Meenakshi McNamara

Previous Postdocs: Krishnendu Khan

You can view a talk I gave at the Banff International Research Station as a participant in the "Classification Problems in von Neumann Algebras" in October 2019 here:

Publications and Preprints

• Quantum chromatic numbers of products of quantum graphs, with A. Meenakshi McNamara, preprint, (submitted)
• On the structure of graph product von Neumann algebras, with Ian Charlesworth, Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli Brent Nelson , preprint (to appear in Publications of the Research Institute for Mathematical Sciences)
• Random permutation matrix models for graph products, with Ian Charlesworth, Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli Brent Nelson , preprint, (to appear in Documenta Mathematica).
• McDuff and Prime von Neumann algebras arising from Thompson-Like Groups , with Patrick DeBonis and Krishnendu Khan, preprint , (submitted).
• Strong 1-boundedness, L2-Betti numbers, algebraic soficity, and graph products, with Ian Charlesworth, Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli Brent Nelson , preprint (submitted).
• Maximal rigid subalgebras of deformations and L²-cohomology, with B. Hayes, D. Hoff, and T. Sinclair, Analysis and PDE (2021 )Volume 14, No. 7, Pgs. 2269-2306, DOI: 10.2140/apde.2021.14.2269, preprint.
• R we living in the matrix?, with R. Araiza, Notices of the American Mathematical Society (2019) Volume 66, Number 8, Pgs. 1216-1224, pdf.
• Classification of tensor decompositions of II₁ factors associated with poly-hyperbolic groups, with S. Pant, (2018) preprint.
• Tensor product decompositions of I₁ factors arising from extension of amalgamated free product groups, with I. Chifan, and W. Sucpikarnon, Communications in Mathematical Physics (2018), 1-32, preprint.
• W ^* -rigidity for the von Neumann algebras of products of hyperbolic groups, with I. Chifan, T. Sinclair, Geometric and Functional Analysis 26 (2016), 136-159, preprint.
• Multifractal analysis via scaling zeta functions and recursive structure of lattice strings, with M. L. Lapidus, S. A. Roby, and J. A. Rock, Contemporary Mathematics, American Mathematical Society 600 (2013), 205-238,preprint.