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Special Lecture Series: The Count of Instatons

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)

Flyer

Notes

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

Lecture recording

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