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Kida Lab
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A lab exploring the orbit equivalence relations generated by group actions.
AboutAbout the lab
Measuring the difficulty of classification through equivalence relations.
The Kida Lab studies group actions on measure spaces and their orbit equivalence relations, in the fields of discrete groups and ergodic theory.
Whether a mathematical object can be classified is expressed concretely as a property of a certain equivalence relation.
The complexity of that equivalence relation is regarded as reflecting the complexity of the corresponding classification problem.
The lab is particularly interested in the connections between orbit equivalence relations and the functional-analytic and geometric properties of groups.
Key terms
- Ergodic theory
- Mathematics that studies a system evolving over time through its average behavior over the long run
- Orbit equivalence relations
- A relation that, when a group moves the points of a space, regards points that can be moved into one another as the same
- Operator algebras
- A system of algebras formed by linear maps (operators) acting on an infinite-dimensional space
ResearchResearch themes
The lab studies group actions on measure spaces and their orbit equivalence relations. In particular, it explores connections with the functional-analytic and geometric properties of groups.
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MembersFaculty
- ProfessorYoshikata KidaPublications ↗
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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: “Arnold's cat map” MathsPoetry / CC BY-SA 3.0 (cropped)
- Orbit Equivalence Relations, Amenability, and Rigidity: “F2 Cayley Graph” Jim.belk at English Wikipedia / Public domain (cropped)
- Related lab (Matui Lab): “Cantors cube” User:Solkoll / Public domain (cropped)
- Related lab (Takada Lab): “Kelvin-Helmholtz instability clouds” Brocken Inaglory / CC BY-SA 3.0 (cropped)
- Related lab (Shimomura Lab): “Traveling wave” P.wormer / CC BY-SA 3.0 (cropped)
- Related lab (Aida Lab): “BMonSphere” Thomas Steiner / CC BY-SA 2.5 (cropped)
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