Events

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The chain rule of Arone-Ching is a celebrated result in Goodwillie calculus, describing how the derivatives of a composite of two functors between spaces or spectra can be reconstructed from the derivatives of the individual functors. Based on this result, Lurie conjectured that such a chain rule should more generally hold for a large class of $\infty$-categories. In this talk, I will discuss recent joint work with Max Blans in which we give an affirmative answer to this conjecture.

I will discuss various localizations of unstable homotopy theory arising from the chromatic perspective, namely the v${}_n$-periodic localizations and the localizations with respect to T(n)-homology. There are many ways to approach these through "algebraic models". For example, the v${}_n$-periodic localizations can be studied via the theory of spectral Lie algebras. Quite orthogonally, p-finite spaces can be studied through their cochain algebras with values in Morava E-theory.

I will explain how to approach the question of $E_2$-formality of differential graded algebras over a prime field via obstruction theory. In particular, $E_2$-algebras whose cohomology ring is a polynomial algebra on even degree classes are intrinsically formal. As a consequence we can prove $E_2$-formality of the classifying space of some compact Lie group or of Davis-Januszkiewicz spaces.