Winter School: $\mathbb{A}^1$-Homotopy Theory

We are pleased to announce a winter school on $\mathbb{A}^1$-Homotopy Theory in Freiburg from February 5 to 9, 2018.


The school will cover the basic constructions of the unstable and stable $\mathbb{A}^1$-homotopy categories, along with the relevant category-theoretic methods, such as model structures, left Bousfield localization and symmetric spectra. These constructions will be applied to more recent developments, such as the questions of $\mathbb{A}^1$-contractibility and the minus-part of the stable $\mathbb{A}^1$-homotopy category.


There will be a total of twelve talks, six of which will be devoted to the introduction of fundamental definitions, constructions and results in $\mathbb{A}^1$-homotopy theory, and the other six of which will explore more advanced topics in the field. Participants will be responsible for giving the six elementary talks. Abstracts for individual talks and a list of relevant references to the literature are available here. All the elementary talks have been attributed by now.

On a practical note, the first talk will start at 13:30 on Monday, 5 February, so participants have the option of arriving Monday morning without missing any talks.
The last talk will end at 16:30 on Friday, 9 February. A detailed schedule is found here.


Registration is now closed.


  • Frédéric Déglise (CNRS – Université Bourgogne)
  • Brad Drew (Universität Freiburg)
  • Matthias Wendt (Universität Freiburg)


The list of registered participants is located here.

Local information

All talks will take place in the lecture hall of the FRIAS, which is located at Albertstr. 19 as indicated on this campus map.

If you arrive by plane at the EuroAirport Basel Mulhouse Freiburg, there is regular bus service to the Freiburg Hauptbahnhof. Walking directions from the train station to the FRIAS can be found here.

Support of the summer school

The school is part of the FRIAS program Cohomology in Algebraic Geometry and Representation Theory, supported by the FRIAS. It is also supported by the Graduirtenkolleg 1821 (University of Freiburg), the grant SPP 1786 (University of Essen, M. Levine) and the Eureopean grant ERC Nedag (Betrand Toën).