Chelsea Walton
Rice University, TX·Mathematics & Statistics
For nearly two centuries, algebra has given mathematicians a language for symmetry, the ways an object can be transformed while keeping its essential shape. Category theory takes a broader view: it studies objects together with the maps that carry one object to another.
- Fields
Mathematics & Statistics
Physics
- Topics
category theory
monoidal categories
tensor categories
- Grants
- 1 known grant, through Apr 2027
What they work on
- Extend classical properties of algebras over a field to algebras in monoidal categories, and identify properties that carry significant meaning only in the categorical setting.
- Study Frobenius algebras and other algebraic structures in monoidal categories, especially those tied to topological quantum field theories (TQFTs).
- Investigate representations of modular tensor categories, which are central to 2-dimensional conformal field theory and correspond to 3d TQFTs, building on canonical representations of braided monoidal categories.
More about the research
Recasting classical algebra in this setting can reveal structure that was hidden before, with significant consequences in quantum physics. This project works within monoidal categories, which are categories that come with a built-in way to combine objects, and to combine the maps between them.
Why it matters
This is basic mathematics. Upgrading classical algebra to the setting of monoidal categories deepens the mathematical description of symmetry, and because these structures underlie topological and conformal quantum field theories, the results could eventually inform mathematical physics. A planned textbook series aims to make quantum algebra accessible to more students.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Cris Negron
University of Southern California, CA·Mathematics & Statistics·Early-career
Build rigorous mathematical realizations of topological quantum field theories whose spaces of lowest-energy states (moduli of vacua) are non-compact, using homotopical methods in representation theory.
David Carchedi
George Mason University, VA·Mathematics & Statistics
Build a theory of integration on quasi-smooth derived higher stacks, which are spaces that can handle non-smooth intersections, by developing a six-functor formalism within derived differential supergeometry.
Corey Jones
North Carolina State University, NC·Mathematics & Statistics
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.
The school
Rice University: 24 labs on PI Pages, $278M a year on research, 267 research doctorates a year.
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