Classical and Quantum Integrability

The non-commutative KdV equation and enumerative geometry

2 sept. 2019, 15:30

30m

Amphi Gevrey

Afternoon Session

Orateur

Paolo Rossi (Università degli Studi di Padova)

Description

In the past years, in a joint project with A. Buryak, we have developed a general framework to construct classical and quantum field systems (in one space and one time dimensions) from intersection theory of the moduli space of stable curves. Recently a particularly interesting example came under our attention, which actually produces a integrable system of Hamiltonian PDEs in two space and one time dimensions. Computations of quadratic double ramification integrals, an entirely natural problem in algebraic geometry, turn out to produce a interesting generalization of the KdV hierarchy to 2 non-commutative space dimensions (KdV on a noncommutative Moyal torus).