Research
With the help of Dr. Remus Nicoară, I am working on research involving von Neumann algebras. Von Neumann algebras are a certain type of algebra of operators on a Hilbert space, and they are useful for modeling certain aspects of quantum mechanics. They are named after John von Neumann, who discovered them in the 1930s. More specifically, Remus and I work on the theory of subfactors, which looks at inclusions of von Neumann algebras. This area was originally studied by Vaughan Jones in the early 1980s, and it is a significant branch of the theory of operator algebras in its own right, with applications in knot theory, representation theory, quantum groups, etc. We focus on an invariant for subfactors called commuting squares, along with a particular class of subfactors coming from complex Hadamard matrices (these matrices are interesting themselves, with important applications in quantum information theory, operator algebras, error correcting codes, and other areas). Commuting squares naturally show up in an important invariant for subfactors called the Standard Invariant; this invariant was studied and axiomatically described through the work of Sorin Popa.
I completed my oral exam at the University of Tennessee in Spring 2024, where I presented on the paper Subalgebras of a Finite Algebra by Dr. Erik Christensen. The slides that I used for the presentation can be found here.
