The stable homotopy groups of spheres can be thought of as a derived analogue of the integers, and
they encode deep information about algebraic and differential topology as well as arithmetic geometry.
Chromatic homotopy theory reveals this hidden information and provides a systematic approach to
the computation of these groups.
After a quick survey of the chromatic perspective, we explain recent joint work with Schlank and
Stapleton which implies that the chromatic approach is asymptotically algebraic. Our work is based
on a categorical generalization of ideas from mathematical logic which should be of interest beyond the
applications to stable homotopy theory.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3207