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Topology and Differential Geometry Lab
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Research in geometry centered on symplectic geometry, which grew out of mechanics.
AboutAbout the lab
Exploring geometry born from mechanics
Prof. Ohta studies geometry, centered on symplectic geometry, which has its origins in analytical mechanics.
The lab investigates the relationship between singularities and symplectic and contact geometry, as well as Floer cohomology, from the viewpoint of homotopy algebraic structures.
Together with collaborators, Prof. Ohta has worked on giving mathematical foundations, from the symplectic geometry side, to the mirror symmetry conjecture predicted by string theory.
Key terms
- Symplectic geometry
- Geometry that grew out of analytical mechanics. It studies manifolds equipped with a nondegenerate closed differential 2-form.
- Floer cohomology
- An important invariant in symplectic geometry, defined using solutions of certain nonlinear partial differential equations.
- Mirror symmetry
- A conjecture that the symplectic geometry of one space is "equivalent" to the complex geometry of another space.
ResearchResearch themes
The lab studies geometry centered on symplectic geometry, which has its origins in analytical mechanics. It works on the relationship with singularities, as well as on Floer cohomology and mirror symmetry.
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MembersFaculty
- ProfessorHiroshi Ohta
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Schwarz P Surface” Anders Sandberg / CC BY-SA 3.0 (cropped)
- Symplectic Geometry and Floer Theory: “Chaos Theory & Double Pendulum - 3” Cristian V. / CC BY-SA 4.0 (cropped)
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