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Algebraic approximations to stable homotopy theory

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Tobias Barthel
Universität Kopenhagen
Tue, 2018-01-09 11:15 - 12:00
MPIM Lecture Hall
Parent event: 
Extra talk

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.

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