Spectra in Khovanov and knot Floer theories

Abstract: These notes provide an introduction to the stable homotopy types in Khovanov theory (due to Lipshitz-Sarkar) and in knot Floer theory (due to Manolescu-Sarkar). They were written following a lecture series given by Sucharit Sarkar at the Renyi Institute during a special semester on "Singularities and low-dimensional topology", organised by the Erdos Center.