Ron Donagi
University of Pennsylvania, PA·Mathematics & Statistics
Some of the deepest questions in modern mathematics come from physics. String theory and quantum field theory, the frameworks physicists use to describe fundamental particles and forces, keep suggesting surprising statements about geometric shapes defined by polynomial equations, a subject called algebraic geometry.
- Fields
Mathematics & Statistics
Physics
- Topics
algebraic geometry
string theory
quantum field theory
- Grants
- 2 known grants, through Jun 2028
What they work on
- Attack the geometric Langlands conjecture, a proposed deep link between areas of mathematics, using non-abelian Hodge theory and ideas from quantum field theory.
- Describe the physical theories of class S mathematically, using variations of Hitchin systems, which are geometric families linked to exactly solvable integrable systems.
- Apply supergeometry, a geometry that includes anticommuting quantities, to higher-loop calculations in string theory, and help establish rigorous mathematical foundations for F-theory.
- Study categorical symmetries and defect symmetry topological field theories, along with moduli questions about spaces that classify families of algebraic varieties.
- Develop variations of non-commutative Hodge structures based on Landau-Ginzburg singularity theory, giving non-commutative spectra that can block rationality of Fano varieties.
- Relate non-commutative spectra to R-charges of conformal field theories and to vertex operator algebras, and connect renormalization group flows with the Kähler-Ricci flow.
More about the research
This research works at that meeting point. It uses physical ideas to attack hard mathematical problems, and it uses rigorous mathematics to put physical theories on firm footing. The two projects share one main tool: Hodge theory, which studies how the shape of a geometric space is encoded in algebraic data.
Why it matters
This is basic mathematics. It could produce new tools for classifying geometric shapes defined by polynomial equations, and it could give firmer mathematical foundations to string theory and quantum field theory. Such shapes appear in physics, cryptography, control theory, robotics and computer vision. Over time, a better understanding of how to classify them could inform these fields, as well as future work in theoretical physics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Motohico Mulase
University of California-Davis, CA·Mathematics & Statistics
Develop complex Lagrangian geometry as a general framework for studying mirror symmetry, the hidden duality between symplectic geometry and complex algebraic geometry, and for studying quantization.
Laura Fredrickson
University of Oregon, OR·Mathematics & Statistics
Verify the Gaiotto–Moore–Neitzke conjectural description of the hyperkähler metric on Hitchin moduli spaces, especially near singular fibers, using constructive analytic techniques and geometric microlocal analysis.
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.
The school
University of Pennsylvania: 90 labs on PI Pages, $2.2B a year on research, 750 research doctorates a year.
Reach out
A start for your email. Fill in the brackets.