Symmetries and correspondences in number theory, geometry, algebra, physics: intra-disciplinary trends

Organizers:

Ivan Fesenko (Nottingham), Yakov Kremnitzer (Oxford),
Sir 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 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.

Schedule of talks

July 5 - July 8, 2014

Venue: Lecture Theatre L2
Mathematical Institute
Radcliffe Observatory Quarter
Woodstock Road
Oxford OX2 6GG