## Organizers:

*Ivan Fesenko (Nottingham), Yakov Kremnitzer (Oxford),*

Sir Martin Taylor (Oxford), Boris Zilber (Oxford)

Sir Martin Taylor (Oxford), Boris Zilber (Oxford)

Symmetries and correspondences play the most central role in modern number theory. One-dimensional class field theory, the cornerstone of algebraic number theory of the 20th century, has been generalised in many directions, each of which has merits and drawbacks. Langlands type correspondences are complemented by other powerful theories such as arithmetic noncommutative class field theories, a variety of higher class field theories, anabelian geometry, mean-periodicity correspondence for zeta functions of arithmetic schemes. Recent work in arithmetic, functional, geometric Langlands correspondences, noncommutative summation formulas, new developments in anabelian geometry, higher adeles and zeta integrals for arithmetic schemes, dualities on arithmetic surfaces, higher commutative summation formulas, as well as related work in representation theory, algebraic analysis, geometry, K-theory, model theory, archimedean L-functions and integrable systems, the study of interaction with mirror symmetry, TQFT and quantum computation reveal new intra-disciplinary fundamental structures and stunning perspectives. Several of the new structures are higher structures in the sense of their level of complexity and their relation with higher structures in geometry, topology and category theory.

## Speakers:

- Fedor Bogomolov (Courant Institute, New York/Univ. Nottingham)
- Kevin Buzzard (ICL, London)
- Ted Chinburg (Univ. Pennsylvania Philadelphia)
- Christopher Deninger (Univ. Münster)
- Edward Frenkel (Univ. California Berkeley)
- Denis Gaitsgory (Harvard Univ.)
- Dominic Joyce (Univ. Oxford)
- Mikhail Kapranov (Kavli IMPU, Tokyo)
- Minhyong Kim (Univ. Oxford)
- Robert Langlands (IAS, Princeton)
- François Loeser (Univ. Paris 6-7)
- Ralf Meyer (Univ. Göttingen)
- Matthew Morrow (Univ. Bonn)
- Sergey Oblezin (Univ. Nottingham)
- Christophe Soulé (IHES, Bures-sur-Yvette)
- Urs Schreiber (Nijmegen)
- Masatoshi Suzuki (TIT, Tokyo)
- Constantin Teleman (Berkeley/Oxford)
- Yuri Tschinkel (Courant Institute, New York)

Venue: Lecture Theatres L2 and L1

Mathematical Institute

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford OX2 6GG

Supported by

- Clay Mathematics Institute
- School of Mathematical Sciences University of Nottingham
- QMAC
- Bogomolov Laboratory

These four days of the Oxford conference is an organic part of the six days of activities starting with the Nottingham workshop on *Symmetries and Correspondences: Higher structures in number theory, July 3-4, 2014*

## Schedule of talks

## Registered Participants