Morse and symplectic invariants over spectra

We often convert intricate geometric data (such as counts of
holomorphic disks) into manipulable algebraic data (such as cochain
complexes). In this talk, we discuss joint work with Jacob Lurie
demonstrating that classical invariants can be upgraded to produce far
richer algebraic data (out of the same old geometry). More
specifically, we discuss a program to enrich Lagrangian Floer theory
over spectra in the sense of stable homotopy theory. Such a program
began in many ways with the work of Cohen-Jones-Segal in the 1990s; in
this talk, we will describe a new approach involving a moduli stack of
broken holomorphic strips on a point.