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Gomi Lab
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The lab studies topology, the area of mathematics most closely tied to physics.
AboutAbout the lab
Topology that connects with physics.
The Gomi Lab studies topology, the area of mathematics that is closely tied to physics.
The lab has also written expository articles that introduce topological insulators from the viewpoint of topology, as well as an introduction to twisted K-theory.
Its papers include work on topology as it appears in condensed matter physics, such as topological insulators, and work on magnitude homology.
Key terms
- Topology
- A field of mathematics that studies the properties of shapes and spaces that do not change when they are stretched or bent
- Topological insulator
- A material that does not conduct electricity in its interior but does conduct it on its surface or edges. This property is explained by topology
- K-theory
- A tool for studying a space by organizing the vector bundles over it into a form that can be added and subtracted
ResearchResearch themes
*Illustrative imageDescribing the Topology of Matter in Mathematics
Some properties of matter, like those of topological insulators, are determined by how a shape is "connected." The lab describes and classifies the properties of systems with crystal symmetry or time-reversal symmetry using tools from topology such as K-theory and homology.
*Illustrative imageMeasuring the "Size" of Metric Spaces
Magnitude is a quantity that expresses how "large" a shape or a space with distances is. The lab studies magnitude homology, which builds this quantity as a homology theory, for geodesic spaces, in which any two points can be joined by a shortest path.
MembersFaculty
- ProfessorKiyonori Gomi
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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: “Klein bottle glass2” PaulT (Gunther Tschuch) / CC BY-SA 4.0 (cropped)
- Describing the Topology of Matter in Mathematics: “Möbius strip” David Benbennick / CC BY-SA 3.0 (cropped)
- Measuring the "Size" of Metric Spaces: “Shortest path example graph” Shirisha Gongati / CC0 (cropped)
- Related lab (カールマン研究室): “Trefoil knot build with trebl torus type construction set bricks” Dutchdudedesign / CC BY-SA 4.0 (cropped)
- Related lab (谷田川研究室): “Riemann surface sqrt” Jan Homann / Public domain (cropped)
- Related lab (大矢研究室): “E8Petrie” Jgmoxness / CC BY-SA 3.0 (cropped)
- Related lab (本多研究室): “Calabi yau” Jbourjai / Public domain (cropped)
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