### Special Lecture Series

**Speaker**: Professor Nikita Nekrasov (Simons Center for Geometry and Physics and Columbia)

**The Count of Instatons**

**Abstract**: Graduate level introduction to modern mathematical physics with the emphasis on the geometry and physics of quantum gauge theory and its connections to string theory. We shall zoom in on a corner of the theory especially suitable for exploring non-perturbative aspects of gauge and string theory: the instanton contributions. Using a combination of methods from algebraic geometry, topology, representation theory and probability theory we shall derive a series of identities obeyed by generating functions of integrals over instanton moduli spaces, and discuss their symplectic, quantum, isomonodromic, and, more generally, representation-theoretic significance.

Quantum and classical integrable systems, both finite and infinite-dimensional ones, will be a recurring cast of characters, along with the other (qq-) characters.

**First lecture: Friday, September 15, 2023**

**Fridays at 1:30pm until 3pm **(except for the following dates: 10/6 , 10/20/, 11/3, 11/17, 11/24, 12/1-12/8 (TBD), and 12/15)

**Room 520, Mathematics Hall**

**2990 Broadway (117th Street)**

Lecture notes: Not split per lecture will be updated as course continues

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