Autumn school: computations in motivic homotopy theory

An autumn school on computations in motivic homotopy theory will be held at the University of Regensburg during September 16--20, 2019.

Lecture Series:

Motivic infinite loop spaces by Marc Hoyois

I will give an overview of the theory of framed correspondences in motivic homotopy theory. Motivic spaces with framed transfers are the analogue in motivic homotopy theory of E_∞-spaces in classical homotopy theory, and in particular they provide an algebraic description of infinite P^1-loop spaces. I will discuss the foundations of the theory (following Voevodsky, Garkusha, Panin, Ananyevskiy, and Neshitov), some applications such as the computations of the infinite loop spaces of the motivic sphere and of algebraic cobordism (following Elmanto, Hoyois, Khan, Sosnilo, and Yakerson), and some open problems.

Stable homotopy groups of motivic spheres by Oliver Röndigs & Markus Spitzweck

This lecture series will illustrate some techniques which are useful in computing within the Morel-Voevodsky motivic stable homotopy category SH(F) of a field F. In particular, several filtrations on SH(F) and their associated spectral sequences will be employed and analyzed. This information will be used to describe some stable homotopy groups of motivic spheres.

A^1-enumerative geometry by Kirsten Wickelgren

Classical enumerative geometry counts or describes the number of geometric objects satisfying certain conditions. In order to have an invariant count, one works over algebraically closed fields, e.g., a degree n polynomial has n solutions. A^1 homotopy theory provides an opportunity to count geometric objects over general fields. The counts are valued in the Grothendieck--Witt group of symmetric bilinear forms, as this is the target of Morel's A^1-Brouwer degree. In this lecture series, we will introduce A^1-enumerative geometry and discuss several examples. The main example is an enriched count of the degree d plane curves passing through 3d-1 points. This series will include work of Jesse Kass, Marc Levine, Jake Solomon, Padma Srinivasan, Matthias Wendt and the lecturer.

Schedule

The lectures will take place in the seminar room M 311 on the third floor of the math building.

The registration and the coffee breaks will be in M103. The registration starts from Monday 9:00 am.

Financial Support

Limited financial travel support is available. Please indicate in your registration if you wish to apply for financial support.

Registration

Please register under the following link via Google Forms. If you want to apply for financial support, please complete the registration before July 29th, 2019 (extended deadline!).

Organizers

Practical Information

MAP: Points of Interest.

City of Regensburg: Regensburg is a Unesco World Heritage site that is famous for its well preserved medieval city center and its beautiful Gothic cathedral. Further information can be found here.

PUBLIC TRANSIT: Local bus system. There are many useful buses typically, but the 6 will suffice for getting to and from the city center and the lecture hall.

ACCOMMODATION: Regensburg is a tourist destination and we encourage guests to book their rooms as early as possible. Here is a list of hotels in the area:

1. Hotel Kaiserhof am Dom (In the city center, must take a bus to the University.)

2. Hotel Muenchner Hof (In the city center, must take a bus to the University.)

3. Hotel Apollo (Near the University, but limited eating options.)

4. Hotel Jakob (In the center, must take a bus to the University.)

5. Hotel Central (In the city center, must take a bus to the University.)

One can also check the standard alternatives:

1. Hotels.com

2. Airbnb

TRAVEL: One can reach the university by following the instructions here.

INTERNET: Access to Wifi via eduroam is available throughout the mathematics building. We can also provide a temporary guest account through the university for those without eduroam access.

HomeAboutPeopleEventsResearchRTGPositionsGuest ProgrammeImpressum