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Differential Geometry, Complex Geometry, Dynamical Systems, and Global Analysis Lab
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The lab studies the spaces formed by solutions of equations, using the viewpoint of infinite-dimensional geometry.
AboutAbout the lab
Asking about infinity, space, and complexity through mathematics
Prof. Matsuo studies geometric analysis and differential geometry.
The professor's three major research themes are "infinity, space, and complexity." From the viewpoint of infinite-dimensional geometry, the professor has studied the spaces formed by solutions of nonlinear partial differential equations.
Recently, the professor has become interested in the discretization of space and works on mathematics arising from lattice gauge theory.
In the master's program, to acquire the typical methods for nonlinear problems in geometric analysis, students begin by choosing one landmark paper and reading it thoroughly together.
Key terms
- Nonlinear partial differential equation
- Among equations involving derivatives with respect to several variables, a type for which the sum of solutions is not necessarily a solution.
- Moduli space
- A space obtained by collecting all objects of the same kind, such as shapes or solutions to an equation, and regarding the collection itself as a single space.
- Lattice gauge theory
- A method of treating gauge theory, which describes the forces between elementary particles, by dividing space into a lattice.
ResearchResearch themes
Under the three major themes of "infinity, space, and complexity," the lab studies spaces of solutions to equations of geometric origin from the viewpoint of infinite-dimensional geometry. Recently, as a new direction involving the discretization of space, it also works on mathematics arising from lattice gauge theory.
*Illustrative imageInfinite-dimensional moduli spaces
The lab has studied, from the viewpoint of infinite-dimensional geometry, moduli spaces of solutions to nonlinear partial differential equations that arise from finite-dimensional geometry. The current interest is complexity: the question of whether infinite-dimensional moduli spaces are complex.
*Illustrative imageMathematics arising from lattice gauge theory
This is research in a new direction, the discretization of space. In a co-authored paper, a formula expressing the Atiyah-Patodi-Singer index in terms of the η invariant of domain wall fermions was established with mathematical rigor.
MembersFaculty
- Associate ProfessorShinichiroh Matsuo
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: “Minimal surface curvature planes-nl” ChristiaanPR / CC BY-SA 4.0 (cropped)
- Infinite-dimensional moduli spaces: “CY5-6D-lattice” Andrew J. Hanson / CC BY-SA 3.0 (cropped)
- Mathematics arising from lattice gauge theory: “Jaguar Supercomputer ( )” Oak Ridge National Laboratory / CC BY 2.0 (cropped)
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