Homotopy Theory and Arithmetic Geometry: Motivic and Diophantine Aspects

The focus of this research school is on three major advances that have emerged lately in the interface between homotopy theory and arithemic:  cohomological methods in intersection theory, with emphasis on motivic sheaves; homotopical obstruction theory for rational points and zero cycles; and arithmetic curve counts using motivic homotopy theory.  The emergence of homotopical methods in arithmetic represents one of the most important and exciting trends in number theory, and the lectures will give a gentle introduction to this highly technical area. 

The three main lecture course topics are:

Cohomological methods in intersection theory
Lecturer: Denis-Charles Cisinski (Regensburg)
Assistant: Chris Lazda (Amsterdam)

Homotopical manifestations of rational points and algebraic cycles
Lecturer: Tomer Schlank (HUJ)
Assistant: Ambrus Pal (Imperial)

Arithmetic enrichments of curve counts
Lecturer: Kirsten Wickelgren (Georgia Tech)
Assistant: Frank Neumann (Leicester)

The lecture courses will be supplemented by tutorial sessions and guest lectures by Paul Arne Østvær (Oslo), Jon Pridham (Edinburgh) and Vesna Stojanovska (Illinois at Urbana-Champaign)