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Homma Lab
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A lab that explores the essence of geometry and physics through Dirac operators.
AboutAbout the lab
Exploring geometry through Dirac operators.
The Homma Lab studies spin geometry from the perspectives of differential geometry and global analysis.
The lab studies the Dirac operator, a differential operator, from various angles, including differential geometry, global analysis, and representation theory.
Specifically, it works on topics such as spin geometry, gauge theory, twistor theory, and index theorems.
Another aim of the lab is to understand the geometric and analytic properties of differential operators determined by geometric structures on Riemannian manifolds.
Key terms
- Spin geometry
- A branch of geometry that studies shapes using special quantities called spinors
- Dirac operator
- A differential operator that acts on quantities called spinors
- Gauge theory
- A theory that treats the field theories of physics using the language of geometry
ResearchResearch themes
The lab studies Dirac operators and spin geometry from the perspectives of differential geometry and global analysis. It also works on a variety of related topics, such as gauge theory, twistor theory, and index theorems.
*Illustrative imageSpin Geometry and Dirac Operators
The lab studies Dirac operators from the perspectives of differential geometry, global analysis, and representation theory, and works on topics such as spin geometry, gauge theory, and index theorems.
*Illustrative imageDifferential Operators on Riemannian Manifolds
Beyond Dirac operators, the lab studies the properties of differential operators determined by geometric structures on Riemannian manifolds, using examples such as Einstein manifolds.
MembersFaculty
The members of the Homma Lab consist of faculty members and students at the doctoral, master's, and undergraduate levels.As of 2024
- ProfessorYasushi Homma
- Lecturer (Fixed-Term)Makoto Udagawa
VoicesStudent voices
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Write a lab reviewAnonymous · Your draft is saved if you stopRelatedLabs similar to Homma Lab
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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: “Spinning top shadow” Armenak Margarian / CC BY-SA 4.0 (cropped)
- Spin Geometry and Dirac Operators: “Spiral tendril of Passiflora caerulea” Franz van Duns / CC BY-SA 4.0 (cropped)
- Differential Operators on Riemannian Manifolds: “Coral cerebro (Platygyra daedalea), parque nacional Ras Muhammad, Egipto, , DD 80” Diego Delso / CC BY-SA 4.0 (cropped)
- Related lab (Kaji Lab): “Modell einer Kubik mit vier Doppelpunkten -Schilling VII, 5 - 48” Oliver Zauzig / CC BY-SA 3.0 (cropped)
- Related lab (Nagai Lab): “Klein bottle glass2” PaulT (Gunther Tschuch) / CC BY-SA 4.0 (cropped)
- Related lab (Ikeda Lab): “Mathematisches-Gipsmodell.Fläche3.Ordnung - Kopie” Museopedia / CC BY-SA 4.0 (cropped)
- Related lab (Kanazawa Lab): “CalabiYau5” Andrew J. Hanson / CC BY-SA 3.0 (cropped)
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