The topic of the summer school is ``Generalized correspondences and motives". We will attempt to understand several approaches to the motivic stable homotopy category involving ``correspondences" equipped with additional structure. After reviewing Voevodsky's approach to the derived category of motives, we will discuss ``framed correspondences" after Voevodsky and Garkusha-Panin and ``Chow-Witt correspondences" after Calmes and Fasel.
Main references:
Lecture notes on motivic cohomology - C. Mazza, V. Voevodsky, C. Weibel
Framed Correspondences - G. Garkusha, I. Panin
Finite Chow-Witt correspondences - B. Calmes, J. Fasel
Supplementary references:
Framed Correspondences - V. Voevodsky
The organization of the summer school:
We (the organizers) will attempt to divide the proof into manageable chunks on which you (the participants) will lecture. The number of lectures to be given is still to be decided.
Ideally, each lecture will have a designated note-taker, and we will attempt to assemble a transcription of the proof by the end of the summer school.