## Symmetries and Correspondences in Number Theory, Geometry, Algebra and Quantum Computing

**Date:**
5 - 8 July 2014

**Location: ** University of Oxford

**Event type:**
Workshop

**Organisers: ** Ivan Fesenko (Nottingham), Yakov Kremnitzer (Oxford), Martin Taylor (Oxford), Boris Zilber (Oxford)

Symmetries and correspondences play the most central role in modern number theory. Class field theory and Langlands type correspondences are complemented by other powerful theories such as arithmetic noncommutative class field theories, a variety of higher class field theories, insights from 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 equivariant Riemann–Roch theorems, higher commutative summation formulas, as well as related work in representation theory, algebraic analysis, geometry, K-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.

Talks will be given by leaders in their areas. They will often be of less technical and more general, overview and programme nature, describing new trends and perspectives and sketching potential for developments and interaction with other areas of mathematics.

CMI Enhancement and Partnership Program