Tuesday, 28-May-2024
Abstract
The enumerative geometry of the moduli spaces of curves, which began in the 1980s with a famous paper of Mumford, is now an extremely developed field, with perhaps thousands of papers dedicated to it. Some highlights: MMM (Morita-Miller-Mumford) classes, Mumford's conjecture (Madsen-Weiss theorem), Witten's conjecture (Kontsevich's theorem), Gromov-Witten invariants. After reviewing this "one-dimensional" case, I will explain some "higher-dimensional" generalizations: KSBA spaces of stable surfaces and higher-dimensional varieties, kappa classes on them, "higher" Gromov-Witen invariants, etc.
Speaker
Valery Alexeev
Research area
Pure Mathematics
Affilation
University of Georgia
Date
Tuesday 28 May 2024, 12:05 pm
Location
Room 4082, Anita B. Lawrence