turkmath.org

Given prime $p$, one can define Frobenius operators on the commutative rings of characteristic $p$. This notion has generalizations in a larger class of rings and even in topological spaces and spectra. Spectra with circle actions and Frobenius operators are called cyclotomic spectra. A simple example is the free loop space. Major examples arise in algebraic and arithmetic geometry, as topological Hochschild homology of rings and categories, and many applications to these fields are found. By mirror symmetry, it is natural to expect the cyclotomic spectra to arise in symplectic topology. In this talk, we will explain how to obtain cyclotomic spectra using holomorphic cylinders in symplectic manifolds, i.e. by using Hamiltonian Floer theory. Joint work in progress with Laurent Cote.