Introduction to Equivariant Homotopy Theory
- Magdalena Kędziorek:
Unstable case
2 May 2023, 11:00, aula T1
- Magdalena Kędziorek: Stable case: basics
4 May 2023, 11:00, aula T1
- Magdalena Kędziorek: Stable case: modern approach
9 May 2023, 11:00, aula T1
- Miguel Barrero: Global setting
11 May 2023, 11:00, aula T1
Lectures were given by Magdalena Kędziorek and Miguel Barrero, from Radboud Universiteit.
Equivariant homotopy theory has a long tradition and the homotopy theoretic foundations of the subject were developed by tom Dieck, Segal, May and their many students and collaborators in the 1960s and 1970s. More recently, equivariant homotopy theory has provided instrumental tools for solving computational and conceptual problems in algebraic topology and algebraic geometry among other parts of mathematics. New developments in the field in the last decades created an incredible amount of activity. We mention just a few: the Hill-Hopkins-Ravenel solution to the Kervaire invariant problem, Hausmann's understanding of the equivariant bordism using global setting, or the classification of different levels of commutativity (by several groups of authors including Gutiérrez-White).
In this series of lectures we will give a gentle introduction to equivariant homotopy theory —unstable, stable and global. We will set up foundations which will allow people to start working in the setting of equivariant homotopy theory, but at the same time we will focus on presenting a modern perspective on several more classical phenomena. We hope this approach will make the vast amount of material in this subject conceptually easier to organise.
For this lecture series we assume knowledge of basic algebra, topology, category theory and homotopy theory (including model categories).