# Mathematics Colloquia and Seminars

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### Localization on compact spaces, q-W algebras and modularity

**Mathematical Physics & Probability**

Speaker: | Fabrizo Nieri, Uppsala University |

Location: | 2112 MSB |

Start time: | Wed, Mar 14 2018, 3:10PM |

The BPS/CFT correspondence allows a wide class of supersymmetric gauge theories to be studied through 2d CFT-like methods. In particular, vortex

and instanton partition functions of unitary quiver gauge theories have been

identified with chiral correlators or conformal blocks of infinite dimensional

symmetry algebras. In this talk, I will discuss three and five dimensional

backgrounds, in which cases the relevant algebras are the so-called q-W

algebras. When the supersymmetric gauge theories are defined on compact spaces such as the three or five spheres, localization yields partition functions in

the form of matrix models exhiniting peculiar modular properties. I will show

that these structures can be nicely encoded into the existence of q-W algebras

with multiple chiral sectors which are non-trivially fused together through SL

(2,Z) or SL(3,Z) elements. As an application, I will explain how these

algebraic constructions can be used to confirm or predict new results relating

three and five dimensional partiton functions.