Seminario Dottorato 2024/25 - Ishan JAZTAR SINGH (21.11.2024)

Enumerative geometry explores the use of combinatorial and intersection theory techniques to solve counting problems in algebraic geometry. Integrable hierarchies, in contrast, consist of infinite sequences of partial differential equations with symmetries that have significance in mathematical physics. Both fields have seen substantial developments over the past half-century. 

This talk will focus on the infamous Witten-Kontsevich theorem, which establishes a deep connection between topological invariants of the moduli space of curves and the Korteweg–de Vries hierarchy. I will attempt to offer intuitive motivation and a formal statement of the theorem, and, time permitting, discuss its generalizations and the role of quantum hierarchies in this context.