Bott periodicity from algebraic geometry

Abstract: A famous theorem in algebraic topology is Bott periodicity: the homotopy groups of the space of orthogonal matrices repeat with period 8: pi_k(O) = pi_{k+8}(O) . I will give an elementary overview of Bott periodicity and then I will explain how to formulate and prove a theorem in algebraic geometry which, when specialized to the field of complex numbers, recovers the usual topological Bott periodicity, but makes sense over any field. This is work in progress with Ravi Vakil.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

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