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Geometry 2 Lab (Differential Geometry; Tsuyoshi Kato)
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A lab that studies gauge theory and geometric analysis on noncompact spaces.
AboutAbout the lab
Exploring the geometry of spaces that extend without bound.
The Tsuyoshi Kato Lab studies gauge theory and differential topology within differential geometry.
Its research themes also include geometric analysis on noncompact spaces, noncommutative geometry, and tropical geometry and dynamical systems.
Through collaborative research, the lab investigates Seiberg-Witten theory for 4-manifolds and the properties of noncompact manifolds.
Key terms
- Gauge theory
- A theory that uses equations arising from field theory in physics to study the properties of shapes (manifolds).
- Noncompact
- Extending without bound, so that it does not fit within a finite size.
- Seiberg-Witten theory
- A theory that studies the space of solutions of a certain equation in order to distinguish the shapes of 4-dimensional manifolds.
ResearchResearch themes
The lab studies gauge theory, differential topology, and geometric analysis on noncompact spaces. It also works on noncommutative geometry and on tropical geometry and dynamical systems.
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MembersFaculty
- ProfessorTsuyoshi Kato
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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: “3D-Leveltorus-Reebgraph” 3D-Leveltorus.png: Kieff derivative work: Ilya Voyager (talk) / Public domain (cropped)
- Geometry of noncompact manifolds: “TiltedTorusFlowLines” Sam Derbyshire / CC BY-SA 3.0 (cropped)
- Related lab (Algebra 2 and Geometry 2 Lab (Complex Geometry, Algebraic Geometry, Differential Geometry; Kenichi Yoshikawa)): “Espace de Calabi-Yau” Rogilbert / Public domain (cropped)
- Related lab (Geometry 1 and Analysis 2 (Topology, Operator Algebras) Lab (Kubota)): “Topological insulator band structure” A13ean / CC BY-SA 4.0 (cropped)
- Related lab (Algebra 1 (Number Theory) Lab (Atobe)): “Bruhat-Tits-tree-for-Q-2” 부고 / CC BY-SA 4.0 (cropped)
- Related lab (Geometry 1 (Low-Dimensional Topology, Gauge Theory) Lab): “Superfície não orientável - Bordo trifólio” Object made by MockUp Company, photo by Rodrigo.Argenton / CC BY-SA 4.0 (cropped)
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