SPRING 2024 SAMUEL EILENBERG LECTURES
Title: Moduli spaces of high dimensional manifolds
Abstract: Following influential work of John Harer in the 1980s, Ulrike Tillmann in the 1990s, and Ib Madsen and Michael Weiss in the 2000s, we learned a new approach to the moduli space of Riemann surfaces, and to the diffeomorphism groups and mapping class groups of oriented 2-manifolds. A lesson learned by their work is that patterns emerge in the large-genus limit, another is that these patterns are well expressed in homotopy theoretic terms.
Inspired by these developments in (real) dimension 2, Oscar Randal-Williams and I set out to study moduli spaces of higher-dimensional manifolds in a similar spirit. The goal of this semester’s Eilenberg Lectures will be to present some of our joint work, as well as some background, context, and some very recent developments in high-dimensional manifold theory building on our work.
First lecture: January 22, 2024 at 4:10pm
Room 520 Mathematics
SPECIAL LECTURE SERIES
Speaker: Professor Nikita Nekrasov (Simons Center for Geometry and Physics)
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, February 2, 2024
Room 520, Mathematics Hall
Flyer | Notes | Lecture notes: Not split per lecture will be updated as course continues
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