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Konno Lab
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A lab that explores the shapes of manifolds through four-dimensional gauge theory.
AboutAbout the lab
Exploring the shape of four dimensions through gauge theory
The Konno Lab works in geometry, studying the development of four-dimensional gauge theory and its applications to topology and differential geometry.
One central part of the lab's research is to formulate problems using ideas from topology and geometry in dimensions other than four, then build a gauge-theoretic framework suited to those problems and solve them.
For example, the lab has established the foundations of gauge theory for families of 4-manifolds and has shown that it can be used for purposes such as constructing characteristic classes of 4-manifold bundles.
The lab has a strong interest in using gauge theory to open up new research areas in differential topology.
Key terms
- Gauge theory
- A method of studying the shape of geometric objects using solutions of differential equations that originate in physics
- Manifold
- A shape that looks like ordinary space in the neighborhood of every point
- Characteristic class
- An algebraic quantity that expresses how twisted a bundle of shapes is
ResearchResearch themes
The lab studies the development of four-dimensional gauge theory and its applications to topology and differential geometry. It is interested in using gauge theory to open up new research areas in differential topology.
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MembersFaculty
- Associate ProfessorHokuto KonnoPublications ↗
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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: “Hopf Fibration” Niles Johnson / CC BY 4.0 (cropped)
- Gauge Theory and Topology: “Fibre bundle - Moebius strip” JozumBjada / CC BY-SA 4.0 (cropped)
- Related lab (Ueda Lab): “Quintic 1” The original uploader was Floriang at German Wikipedia. / CC BY-SA 3.0 (cropped)
- Related lab (Sakasai Lab): “Triple torus illustration” Oleg Alexandrov / Public domain (cropped)
- Related lab (Habiro Lab): “3D Borromean Rings” Jim.belk / Public domain (cropped)
- Related lab (Asuke Lab): “Reeb foliation half-torus POV-Ray” Ilya Voyager / CC0 (cropped)
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