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Algebra (Daisuke Matsushita) Lab
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Research that builds a new kind of geometry from symplectic manifolds over the complex numbers.
AboutAbout the lab
Rich symmetry that appears only over the complex numbers.
Prof. Matsushita studies symplectic manifolds defined over the field of complex numbers.
The definition is just that of an ordinary symplectic manifold, with the number system changed to the complex numbers.
Even so, these manifolds are known to have rich symmetries not seen in the real case.
Prof. Matsushita's goal is to follow this phenomenon and build “holomorphic symplectic geometry.”
Key terms
- Field of complex numbers
- The set of all numbers that can be written as a+bi, using the number i whose square is −1. The four arithmetic operations can be carried out freely.
- Symplectic manifold
- A geometric object, modeled on the space formed by position–momentum pairs in mechanics, equipped with a mechanism for measuring area-like quantities.
- Analytic function
- A function that is differentiable over the complex numbers. It is known to be far better behaved than in the real case.
ResearchResearch themes
The lab studies symplectic manifolds defined over the field of complex numbers, investigating the rich symmetries not seen in the real case. Its aim is to pursue this phenomenon and construct “holomorphic symplectic geometry.”
*Illustrative imageComplex symplectic manifolds
The lab studies symplectic manifolds defined over the field of complex numbers. They are characterized by rich symmetries not found in symplectic manifolds over the real numbers.
*Illustrative imageHolomorphic symplectic geometry
When differentiability is considered over the complex numbers, well-behaved objects called analytic functions appear. The same situation is seen in symplectic geometry, and the lab pursues this phenomenon, aiming to construct “holomorphic symplectic geometry.”
MembersFaculty
- Associate ProfessorDaisuke Matsushita
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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: “K3 surface” BTotaro / CC BY-SA 4.0 (cropped)
- Complex symplectic manifolds: “Goursat” Mike Williams / CC BY 2.5 (cropped)
- Holomorphic symplectic geometry: “Color complex plot2” Jan Winnicki / CC BY-SA 3.0 (cropped)
- Related lab (Algebra (Ouchi) Lab): “CalabiYau5” Andrew J. Hanson / CC BY-SA 3.0 (cropped)
- Related lab (Kawasaki Lab): “Chaos Theory & Double Pendulum - 1” Cristian V. / CC BY-SA 4.0 (cropped)
- Related lab (Kasuya Lab): “Standard contact structure r 3” Pmassot / CC BY-SA 3.0 (cropped)
- Related lab (Furuhata Lab): “Canal-helix” Ag2gaeh / CC BY-SA 3.0 (cropped)
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