Motohico Mulase
University of California-Davis, CA·Mathematics & Statistics
Mirror symmetry, first found in theoretical physics more than thirty years ago, is a surprising hidden link between two kinds of geometry. One is symplectic geometry, the mathematical language of classical mechanics.
- Fields
Mathematics & Statistics
Physics
- Topics
mirror symmetry
symplectic geometry
complex algebraic geometry
- Grants
- 1 known grant, through Jun 2027
What they work on
- 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.
- Construct concrete models on Hitchin integrable systems, exactly solvable geometric systems, that display several faces of mirror symmetry together, including Langlands duality and links to three-manifold and quantum knot invariants.
- Use topological recursion, a generalization of the Laplace transform, to propose a new mechanism for holomorphic quantization, building quantum counterparts of complex integrable systems.
More about the research
The other is complex algebraic geometry, the study of shapes defined by polynomial equations. The link has since appeared across many areas of mathematics, but no one yet has a systematic explanation of it. This focused research group aims to build a general tool for studying mirror symmetry. It also aims to construct concrete examples in which every known side of mirror symmetry can be seen at once.
Why it matters
This is pure mathematics. Its contribution is a clearer, unified understanding of mirror symmetry and of how classical integrable systems are quantized. Ideas from this area connect to high-energy particle physics and string theory. In the long run, the work could inform how these theories are formulated mathematically, but the grant names no direct applications.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
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.
Christopher Rogers
University of Nevada-Reno, NV·Mathematics & Statistics
Gather evidence for the Alekseev-Torossian conjecture that the Kashiwara-Vergne group (KRV) equals the Grothendieck-Teichmueller group (GRT), by studying how both act on explicit geometric and topological objects.
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.
The school
University of California-Davis: 49 labs on PI Pages, $1.0B a year on research, 647 research doctorates a year.
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