Chromatic Homotopy Theory and Higher Algebra

 In the world of homotopy theory, there are analogs of abelian groups called Spectra. Spectra are extremely useful in algebraic topology, differential topology, algebraic K-theory, and more. According to the primary decomposition theorem,  Abelian groups decompose into parts according to different primes. One of the great insights in the study of spectra is that they decompose in an even richer way according to so-called “chromatic primes”. In the talk, we shall discuss some of the places where spectra appear in mathematics and how these extra primes arise, studied, and utilized. We also discuss “higher algebra”  – that is, algebra with spectra taking the role of abelian groups - and see how it sheds light back on the different mathematical fields in which spectra appear.