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2012 Symposium abstract: "Symmetry in Mathematics and Quantum Physics"

Symmetry is one of the central concepts in mathematics. In geometry, it corresponds to transformations preserving various objects. In number theory, to symmetries of numbers and equations, etc. Elementary particles and quantum fields can also be symmetrical, and the more we know about their symmetries the better we understand the interactions between them. A unifying theory of mathematical symmetries, the Langlands Program, has been gradually built over the last 45 years. Recently, in the work of Edward Witten and others, an unexpected link to Quantum Physics was discovered: the Langlands Program was connected to the electromagnetic duality and its generalizations. In this talk I will give an overview of these topics for non-specialists.