Special Lecture Series
Speaker: Professor Nikita Nekrasov (Simons Center for Geometry and Physics and Columbia)
The Count of Instantons
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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