Date: 2 November 2018
Location: Hempfield High School, Room 213
 Speaker: Irina Bobkova, IAS Princeton
   Title: Decomposition and duality in stable homotopy theory

Abstract: Computation of the stable homotopy groups of spheres is
a long-standing open problem in algebraic topology. This important
problem has connections to many other areas of modern mathematics,
including differential geometry, number theory and derived algebraic
geometry. I will explain how chromatic homotopy theory allows to split
this problem into easier pieces, which can be understood using the
theory of formal group laws. I will talk about recent results, and work
in progress, at the second chromatic level. I will describe a local
version of Spanier--Whitehead duality and how the sphere spectrum at the
second chromatic level can be decomposed in terms of simpler objects and
their Spanier--Whitehead duals.