Parametrized higher category theory and higher algebra:
I am taking part in a project with Clark Barwick, Saul Glasman, Emanuele Dotto and Jay Shah whose aim is to provide common foundations for several different parts of homotopy theory, among which equivariant homotopy theory, parametrized homotopy theory and Goodwillie calculus. For a general introduction see this lecture by Clark Barwick.
Levine's Chow's moving lemma
Forthcoming. An exposition of Levine's proof of Chow's moving lemma for higher Chow groups.
Crossing Browder's bridge
Forthcoming. An explanation in modern language of Browder's original proof of his theorem relating the Kervaire invariant of framed manifolds and the 2-line of the Adams spectral sequence.