Hamiltonian elements in algebraic K-theoryMPIM

by Yakov Savelyev

Thursday Jun 12, 2025, 12:45 PM → 1:45 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Bonn symplectic geometry seminar

I will explain how to associate elements in algebraic K-theory of a commutative ring, and some categorified analogues of the latter, using Hamiltonian fiber bundles and Floer theory. This is analogous to the classical story of complex K-theory elements induced by finite dimensional complex vector bundles. In particular, this produces non-trivial elements in categorified algebraic K-theory (Bertrand Toen's secondary K-theory). The story gives a path to generalizing homological mirror symmetry to algebraic K-theory context, using Langlands dual group formalism.