## Homotopy Theory and Arithmetic Geometry: Motivic and Diophantine Aspects

**Date:**
9 - 13 July 2018

**Location: ** Imperial College London

**Event type:**
CMI-LMS Research School

**Organisers: ** Frank Neumann (Leicester) and Ambrus Pál (Imperial)

The focus of this CMI-LMS 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)

Image: Wikimedia Commons, Man vyi

CMI Enhancement and Partnership Program