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Room P3.10, Mathematics Building

Hisham Sati, University of Pittsburgh and New York University

M-theory via rational homotopy theory

M-theory has proven to be very rich both from physics and mathematics points of view. We explain how the fields and their dynamics in M-theory can be succinctly captured by the 4-sphere, viewed via spectra and via cohomotopy. Working rationally allows us to have a mathematical handle on the sphere and to bring in interesting techniques and results from rational homotopy theory. Using spheres, we also describe the dynamics arising from various special points in the moduli space of M-theory, including reduction to type IIA and to heterotic string theory, inclusion into the bounding theory, inclusion of M-branes, and lifts. The detailed agreement with the dynamics expected fromthese theories is tantalizing and suggests an emerging deep picture on the mathematical structure of M-theory. This is joint work with Domenico Fiorenza and Urs Schreiber.