Laura Fredrickson
University of Oregon, OR·Mathematics & Statistics
Theoretical physicists studying certain quantum systems at low energies have made detailed predictions about the shapes of key mathematical spaces. Turning those predictions into proven theorems is difficult, and proofs would both confirm the physics and deepen our understanding of the geometry.
- Fields
Mathematics & Statistics
Physics
- Topics
Hitchin moduli space
K3 surfaces
elliptic fibration
- Grants
- 1 known grant, last ended Sep 2026
What they work on
- 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.
- Verify the Kachru–Tripathy–Zimet conjectural description of hyperkähler metrics on elliptically fibered K3 surfaces, analyzing the singular differential operators that appear near singular fibers.
- Determine the asymptotic geometry of algebraic completely integrable systems fibered by abelian varieties, extending geometric analysis tools to settings where current methods reach their limits.
More about the research
This project focuses on two such objects: Hitchin moduli spaces and K3 surfaces. Hitchin moduli spaces sit where several fields meet, including algebraic geometry, differential geometry, representation theory, and geometric analysis.
Why it matters
This is basic research in pure mathematics. Proving these physics-inspired conjectures would place predictions about low-energy quantum systems on rigorous footing. It would also clarify the asymptotic geometry of Hitchin moduli spaces and K3 surfaces, which could inform algebraic geometry, differential geometry, representation theory, and mathematical physics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Xuwen Zhu
Northeastern University, MA·Mathematics & Statistics
Study how gravitational instantons, four-dimensional spaces that solve Einstein's equations, degenerate and how their moduli spaces are structured, using geometric microlocal analysis and PDE techniques.
Jian Song
Rutgers University-New Brunswick, NJ·Mathematics & Statistics
Study the Yau-Tian-Donaldson conjecture for constant scalar curvature Kahler metrics on projective manifolds, testing uniform K-stability for models as a sufficient condition for existence.
Ron Donagi
University of Pennsylvania, PA·Mathematics & Statistics
Attack the geometric Langlands conjecture, a proposed deep link between areas of mathematics, using non-abelian Hodge theory and ideas from quantum field theory.
The school
University of Oregon: 14 labs on PI Pages, $175M a year on research, 219 research doctorates a year.
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