Corey Jones
North Carolina State University, NC·Mathematics & Statistics
Symmetry is central to how mathematics describes the physical world, from particle physics to the physics of solids. Traditionally, symmetries are described by mathematical objects called groups, in which every symmetry can be undone.
- Fields
Mathematics & Statistics
Physics
- Topics
operator algebras
tensor categories
fusion categories
- Grants
- 1 known grant, through Jul 2027
What they work on
- Classify approximately finite-dimensional actions of amenable tensor categories on approximately finite-dimensional C*-algebras using K-theoretic invariants, extending earlier results for fusion categories.
- Apply these classification results to obtain new classifications of topologically ordered one-dimensional quantum spin systems.
- Generalize the categorical chi invariant for von Neumann algebras to group actions, and use it to distinguish group actions on McDuff factors.
More about the research
Some recently discovered quantum theories, however, have symmetries that cannot be reversed. These require a broader idea of symmetry. Quantum theories can be written in the language of operator algebras. The new symmetries can then be described by tensor categories acting on those algebras. This project aims to classify such categorical symmetries, focusing on cases relevant to quantum spin systems, which are models of interacting quantum particles on a lattice. The results should help give a rigorous understanding of topologically ordered phases of matter.
Why it matters
This is basic mathematics. Classifying symmetries that cannot be reversed in operator algebras adds rigorous understanding of quantum spin systems and topologically ordered phases of matter. That understanding could eventually inform how physicists describe and distinguish exotic quantum phases.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
David Penneys
Ohio State University, OH·Mathematics & Statistics
Develop an operator-algebra description of topologically ordered quantum spin systems, using nets of von Neumann algebras to study superselection sectors, the distinct types of particle-like excitations.
Srivatsav Kunnawalkam Elayavalli
University of Maryland, MD·Mathematics & Statistics
Apply Voiculescu's free entropy theory, a measure of size for noncommuting variables, to determine the structure of free products and ultrapowers of finite von Neumann algebras.
Tao Mei
Texas A&M University-College Station, TX·Mathematics & Statistics
Determine the Lp-approximation properties of group von Neumann algebras, which are operator algebras built from discrete groups, that is, how well these infinite-dimensional objects can be approximated by simpler pieces.
The school
North Carolina State University: 40 labs on PI Pages, $717M a year on research, 603 research doctorates a year.
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