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Kawasaki Lab
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Research that uses symplectic geometry to study the shape of transformation groups.
AboutAbout the lab
Measuring the shape of transformation groups by distance
Prof. Kawasaki specializes in symplectic geometry.
Symplectic geometry is a field rooted in the Hamiltonian systems of analytical mechanics, and in recent years it has drawn attention through its relationships with various other fields.
Of particular interest are the metric and group structures of the Hamiltonian diffeomorphism group, one of the transformation groups of a symplectic manifold.
As an application, non-displaceable fibers of integrable systems are also studied.
Key terms
- Symplectic geometry
- Geometry that studies spaces equipped with the structure needed to describe the motion of objects
- Hamiltonian system
- A mechanical framework in which motion is determined by a function representing energy
- Diffeomorphism group
- A group formed by collecting all the transformations that map a space onto itself smoothly
ResearchResearch themes
The lab specializes in symplectic geometry, a field rooted in the Hamiltonian systems of analytical mechanics. In recent years it has drawn attention through its relationships with various other fields.
*Illustrative imageHamiltonian Diffeomorphism Groups
The lab studies the metric and group structures of the Hamiltonian diffeomorphism group, one of the transformation groups of a symplectic manifold.
*Illustrative imageApplications to Integrable Systems
As an application of the study of metric and group structures, the lab also studies non-displaceable fibers of integrable systems (fibers that still overlap their original position even after being displaced).
*Illustrative imageExtending to Other Transformation Groups
The lab is interested in applying the group-theoretic arguments used for Hamiltonian diffeomorphism groups to other transformation groups, such as contact diffeomorphism groups and diffeomorphism groups.
MembersFaculty
- Associate ProfessorMorimichi Kawasaki
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: “Chaos Theory & Double Pendulum - 1” Cristian V. / CC BY-SA 4.0 (cropped)
- Hamiltonian Diffeomorphism Groups: “Cayley graph of quaternion group on torus” PSL27 / CC BY-SA 4.0 (cropped)
- Applications to Integrable Systems: “Clifford-torus-frame-50” Preimage / Public domain (cropped)
- Extending to Other Transformation Groups: “Overtwisted contact structure” Pmassot / CC BY-SA 3.0 (cropped)
- Related lab (Kasuya Lab): “Standard contact structure r 3” Pmassot / CC BY-SA 3.0 (cropped)
- Related lab (Algebra (Ouchi) Lab): “CalabiYau5” Andrew J. Hanson / CC BY-SA 3.0 (cropped)
- Related lab (Geometry Lab (Inoguchi)): “Hopf Fibration” Niles Johnson / CC BY 4.0 (cropped)
- Related lab (Analysis Lab (Hamamuki)): “Real snowflake macro photo” Alexey Kljatov / CC BY-SA 4.0 (cropped)
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