This autumn school will take place during the week 16-20 September 2024 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:
- Bjørn Ian Dundas: Trace methods in algebraic K-theory and equivariant stable homotopy theory
Abstract Quillen's algebraic K-theory was a revolutionary invention opening a coherent and structural approach to a wide array of mathematical phenomena spanning from number theory to manifolds and beyond. Naturally, the wider the scope and the deeper the grasp, the harder it is to obtain information about an invariant. Algebraic K-theory turned out to be very hard indeed. It started out very promising with Quillen himself providing the first calculations relevant for the Adams conjecture. Bright brains like Suslin and Thomason's made tremendous contributions, but for twenty years calculations of even the simplest cases seemed far out of reach.
However, two major breakthroughs came towards the end of the millennium. First it was realized that given the right target, trace methods could expand the already existing calculations enormously and secondly the motivic program finally succeeded.
Since then our understanding of algebraic K-theory has expanded beyond anyone’s wildest expectation. Not only have we successfully calculated K-theory in key situations, the methods have shed light on central aspects of fields not immediately associated with algebraic K-theory, as for instance in the disproof of the telescope conjecture.
These talks aim at exploring trace methods spanning from the very first calculations to the most recent applications. This will have to include introductions to
- algebraic K-theory
- topological cyclic homology
- Markus Hausmann: Equivariant homotopy theory
Abstract Equivariant topology and the study of symmetries of spaces has a long history. The aim of these lectures will be to give an overview of classical and modern aspects of the theory. In particular, I aim to cover the following:
- Bredon homology, Smith theory and the localization theorem
- Modern approaches to the homotopy theory of G-spectra and their relationship: Inverting representation spheres, spectral Mackey functors, Tate gluing
- Complex bordism with reality MR vs. equivariant complex bordism MUG: The role of the former in Hill-Hopkins-Ravenel's solution to the Kervaire invariant one problem, and the role of the latter for an equivariant version of chromatic homotopy theory
Registration
If you like to participate in the autumn school, please
fill out the the registration form. The
deadline for registrations is 2 June 2024. 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 16 September in the morning and ends Friday 20 September around noon, so it is recommended that you arrive already on Sunday 15 September. Travel details will be given in due time before the autumn school.
Organizers
The autumn school is organized by Gijs Heuts, Lennart Meier, Ieke Moerdijk, and Steffen Sagave.