This autumn school will take place during the week 14-18 September 2026 in a conference center close to Utrecht, The Netherlands.
Aims and Scope
The idea of this autumn school is to bring together a group of about 25 participants in a remote place in order to learn about advanced topics in Algebraic Topology. The talks are meant to be accessible to first or second year PhD students.
Lecture series
The following lecture series constitute the core program of the autumn school:
- Manuel Krannich: Embedding calculus from a higher-categorical perspective
Abstract Since its introduction by Goodwillie and Weiss, embedding calculus has grown into an indispensable homotopy-theoretic tool in the study of spaces of embeddings and diffeomorphisms of manifolds. Roughly, it approximates a manifold \(M\) by the homotopy type of the diagram of configuration spaces of framed points in \(M\) together with the natural point-forgetting and -splitting maps between them, and it approximates an embedding between manifolds by the induced derived map between these diagrams of configuration spaces.
In these lectures, I will give an introduction to embedding calculus and its applications from the perspective of higher category theory, in particular the theory of infinity-operads.
- Mona Merling: Equivariant algebraic \(K\)-theory and \(G\)-manifolds
Abstract Algebraic \(K\)-theory of smooth compact manifolds provides a homotopical lift of the classical \(h\)-cobordism theorem and serves as a critical link in the chain of homotopy theoretic constructions that show up in the classification of manifolds and their diffeomorphisms. This was the motivation behind Waldhausen's development of \(K\)-theory of ring spectra. The equivariant story for \(G\)-manifolds is far less understood. In this lecture series, I will first give an overview of the classical story. Then, I will give an overview of equivariant stable homotopy theory, and describe some recent progress on an equivariant homotopical lift of the \(h\)-cobordism theorem.
Registration
If you like to participate in the autumn school, please fill out the registration form. The deadline for registrations is 1 June 2026. Due to the limited capacity, we may not be able to admit all registered participants. The decisions will be made soon after the deadline.
We will be able to offer lodging and meals to accepted participants, but we cannot cover any travel expenses.
Travel Information
The autumn school starts Monday 14 September in the morning and ends Friday 18 September around noon, so it is recommended that you arrive already on Sunday 13 September. Travel details will be given in due time before the autumn school.
Organizers
The autumn school is organized by Gijs Heuts, Magdalena Kędziorek, Inbar Klang, and Steffen Sagave. It is an activity of the collaborative research grant Symmetry on the interface of topology and higher algebra that is funded by the Dutch Research Council (NWO) and has the above organizers as well as Renee Hoekzema and Lennart Meier as principal investigators.