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Ono Lab
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The lab studies the geometry of symplectic structures using Floer theory.
AboutAbout the lab
Exploring the geometric structure of space through the method of holomorphic curves.
The Ono Lab studies the geometric structure of space, especially the geometry of symplectic structures, in the fields of differential geometry and topology.
Floer theory arose by combining the variational framework for studying periodic solutions of Hamiltonian systems with the method of holomorphic curves introduced by Gromov.
With collaborators, the lab works on constructing Floer theory for Hamiltonian diffeomorphisms without technical conditions, and on Floer theory of Lagrangian submanifolds and homological mirror symmetry.
Key terms
- Symplectic structure
- A geometric structure on the space that combines the positions and momenta of objects (phase space)
- Floer theory
- A theory that combines holomorphic curves with the calculus of variations to summarize information about periodic solutions and intersections in homology
- Homological mirror symmetry
- A conjecture that two seemingly separate kinds of geometry, symplectic geometry and algebraic geometry, correspond to each other in pairs
ResearchResearch themes
The lab studies the geometric structure of space, especially the geometry of symplectic structures. It constructs Floer theory for Hamiltonian diffeomorphisms and Lagrangian submanifolds, and applies it to the Arnold conjecture and homological mirror symmetry.
*Illustrative imageConstruction of Floer Theory and the Arnold Conjecture
The lab has worked on constructing Floer theory for Hamiltonian diffeomorphisms without technical conditions. In joint work, it carried out the construction on general closed symplectic manifolds and proved the Betti number version of the Arnold conjecture.
*Illustrative imageFloer Theory of Lagrangian Submanifolds
The lab jointly studied the general theory for cases where Floer (co)homology of Lagrangian submanifolds can be defined. It is also publishing its results on homological mirror symmetry for toric manifolds in installments.
*Illustrative imageKuranishi Structures and Virtual Fundamental Classes
This research is founded on Kuranishi structures, introduced in a 1996 joint work, and on the theory of virtual fundamental classes and virtual fundamental chains. The lab is progressively publishing, together with collaborators, expository papers that include the details of this theory.
MembersFaculty
- ProfessorKaoru Ono
VoicesStudent voices
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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: “Torus vectors radial” RokerHRO / CC BY-SA 3.0 (cropped)
- Construction of Floer Theory and the Arnold Conjecture: “Arnold cat map” Jacopo Bertolotti / CC0 (cropped)
- Floer Theory of Lagrangian Submanifolds: “Clifford-torus-frame-25” Preimage / Public domain (cropped)
- Kuranishi Structures and Virtual Fundamental Classes: “Stef57 Cobordisme en dim 1” Stef57 / CC BY-SA 3.0 (cropped)
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（中西 賢次） ): “Korteweg-de Vries equation for solitons” Diederik Korteweg. Gustav de Vries. Sander Bais. Gijs Mathijs Ontwerpers, Amsterdam / Public domain (cropped)
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