Ambidexterity

This page contains material for my lectures on ambidexterity at the Dualities in Topology and Algebra meeting at the ICTS in Bangalore.

Talks

Talk 1 (screen, print): Introduction, classical examples, first hints of recursion
Talk 2 (screen, print): $\infty$-categories, spectra
Talk 3 (screen, print): $G$-spectra, bordism and Morava theories, Tate vanishing
Talk 4 (screen, print): $K$-local spectra, classical and generalised characters, Morava theory of Eilenberg-MacLane spaces, Hopkins-Lurie ambidexterity.

Background

Introductory notes on spectra
Notes on formal group theory
An introductory talk about $\infty$-categories
An introductory talk about chromatic homotopy

Literature

The Tate spectrum of $v_n$-periodic complex oriented theories (Greenlees and Sadofsky 1996)
$K(n)$-local duality for finite groups and groupoids (Strickland 2000)
Tate cohomology and periodic localization of polynomial functors (Kuhn 2004)
Ambidexterity in $K(n)$-Local Stable Homotopy Theory (Hopkins and Lurie 2013)
Ambidexterity in Chromatic Homotopy Theory (Carmeli, Schlank and Yanovski 2018)