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Kelly Lab
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The lab is extending topological methods to algebraic geometry.
AboutAbout the lab
Bringing topological methods to algebraic geometry
Kelly Lab studies motivic homotopy theory and algebraic K-theory in the field of algebraic geometry.
Recently, the lab has been working on generalizing the topological methods in algebraic geometry developed by Voevodsky and others.
The lab also targets objects that Voevodsky's methods could not capture, such as non-reduced schemes, additive groups, and wild ramification in number theory.
The lab applies topological methods to frameworks that can handle these objects, such as modulus pairs and derived schemes.
Key terms
- Motivic homotopy theory
- A theory that brings the ideas of topology, which studies continuous deformations of shapes, into algebraic geometry
- Algebraic K-theory
- A theory that studies rings and algebraic varieties by associating to them groups built from objects such as vector bundles
- Scheme
- A generalization of the notion of an algebraic variety that lets the solution sets of more general equations be treated as geometric objects
ResearchResearch themes
The lab studies motivic homotopy theory and algebraic K-theory, along with their representation theory. It works on generalizing topological methods in algebraic geometry, and applications to birational geometry and class field theory are also among its research themes.
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MembersFaculty
- Associate ProfessorShane KellyPublications ↗
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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: “Spectral Sequence Visualization” L.penguu / CC BY-SA 4.0 (cropped)
- Motivic Homotopy Theory: “Blowup” Robx / Public domain (cropped)
- Related lab (Ito Lab): “Tetrahedroid” Salix alba / CC BY-SA 4.0 (cropped)
- Related lab (Oguiso Lab): “Calabi yau” Jbourjai / Public domain (cropped)
- Related lab (Kawakami Lab): “BarthSextic” Mike Williams / Public domain (cropped)
- Related lab (Gongyo Lab): “Mathematisches-Gipsmodell.Fläche3.Ordnung - Kopie” Museopedia / CC BY-SA 4.0 (cropped)
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