# Arithmetic and Geometry

Hausdorff Trimester Program

January 2 - April 19, 2013

Organizers: Gerhard Faltings, Roger Heath-Brown, Yuri I. Manin, and Boris Moroz

The main theme of the trimester was the interplay of different methods used in modern number theory. We emphasised the new results and conjectures in arithmetic geometry, having direct bearing on the classical numbertheoretic problems. The proceedings volume, which we published, summarised investigations and discussions during the trimester. Two sessions, on the recently proved Serre conjecture from the 15th of January until the 14th of February (organisers: L. Dieulefait and J-P. Wintenberger) and on counting rational points on algebraic varieties from the 15th of March until the 14th of April (organiser: D.R. Heath-Brown), as well as a couple of shorter workshops, several seminars, and mini-courses were organised. The trimester culminated in a research conference from the 15th until the 19th of April.