Pure Maths Seminar: Simon Malham
Wednesday 15 June 2022, 3:00pm to 4:00pm
Venue
PSC - PSC A54 - View MapOpen to
Postgraduates, Staff, UndergraduatesRegistration
Registration not required - just turn upEvent Details
Integrable nonlinear PDEs and their combinatorial algebra structure.
One interpretation of integrability for nonlinear PDEs is that they are linearisable. By this we mean that solutions can be found by solving the linearised form of the PDE and a linear Fredholm integral equation. The latter characterises the nonlinear PDE hierarchies that can be linearised. We will show this procedure, to determine such hierarchies, can be abstracted to a combinatorial algebra equipped with a quasi-Leibniz product (for Hankel operators). Integrability boils down to establishing polynomial expansions in the combinatorial algebra which in turn boils down to a system of linear algebraic equations for the polynomial coefficients. There are many open associated problems which we will discuss. For example, the nonlinear Schrodinger hierarchy requires a combinatorial triple system, and all such flows are examples of Fredholm Grassmannian flows.
Speaker
Simon Malham
Contact Details
Name | Dirk Zeindler |
Telephone number |
+44 1524 593644 |