Cris Negron
University of Southern California, CA·Mathematics & Statistics·Early-career
Quantum field theories are among physicists' most effective tools for describing nature, but much of that theory still lacks a rigorous mathematical foundation. This project builds bridges between modern mathematics and quantum field theory.
- Fields
Mathematics & Statistics
Physics
- Topics
representation theory
homotopical algebra
homotopy theory
- Grants
- 1 known grant, through Jun 2028
What they work on
- 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.
- Describe topological field theories that arise as twists of supersymmetric quantum field theories in precise algebraic and geometric terms.
- Develop new relationships between representations of quantum groups, which are deformed symmetry structures, and the geometry of Springer resolutions.
More about the research
It uses recent advances in abstract algebra and geometry to describe these physical theories precisely in mathematical terms.
Why it matters
This is basic mathematics research. It aims to give rigorous mathematical footing to topological quantum field theories that physicists already use. Its new links between quantum groups and the geometry of Springer resolutions add understanding at the meeting point of algebra, geometry and physics. Its expository resources could help other mathematicians learn and apply these methods.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Chelsea Walton
Rice University, TX·Mathematics & Statistics
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.
Aaron Lauda
University of Southern California, CA·Mathematics & Statistics
Develop non-semisimple topological quantum field theories as a working framework for topological quantum computation, including density of braid group images in noncompact unitary groups and Hermitian forms on unrolled quantum group representation categories.
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.
The school
University of Southern California: 47 labs on PI Pages, $1.3B a year on research, 882 research doctorates a year.
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