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### The Story of Symplectic Duality: Where Algebra, Geometry and Mathematical Physics Meet

**Colloquium**

Speaker: | Alexander Braverman, University of Toronto |

Location: | 1147 MSB |

Start time: | Tue, Mar 6 2018, 4:10PM |

One of the most intriguing directions in modern algebra and representation theory is the study of the so called symplectic singularities and their quantizations. By symplectic singularity people usually mean an affine algebraic variety X whose smooth part is endowed with a symplectic structure satisfying some nice conditions at the boundary (to be explained in the talk). A typical example of a symplectic singularity is a Kleinian surface given by equation xy=z^n. The algebra of polynomial functions on a symplectic singularity comes with a certain family of non-commutative deformations (quantizations). Examples of these quantizations include universal enveloping algebras of semi-simple Lie algebras, so studying their representation theory can be thought of as a generalization of the representation theory of semi-simple Lie algebras.

Refreshment to follow the talk.