Integrable Systems Symposium on 30 January 2023

Programme:

10:00 Sonja Hohloch (Antwerp)

11:00 Tamás Görbe (Groningen)

12:00-13:00 Lunch break

13:00 Nikolay Martynchuk (Groningen)

14:00 Bohuan Lin (Groningen)

15:00-15:30 Coffee break

15:30 Alexey Bolsinov (Loughborough)

Location: room 105 Bernoulliborg

Titles and Abstracts:

Sonja Hohloch Creating and classifying hyperbolic-regular singularities in the presence of an $S^1$-action

This talk is based on a joint recent preprint and ongoing joint research with Yannick Gullentops around creating and classifying hyperbolic-regular singular fibers in 2 degree of freedom integrable Hamiltonian systems where one of the integrals has a periodic flow.

Tamás Görbe Compactified Ruijsenaars-Schneider Models

The compactified Ruijsenaars-Schneider (RS) models are integrable n-body systems obtained from the standard RS (aka relativistic Calogero-Sutherland) systems by Wick rotation. Models with trigonometric potentials describe particles moving along a circle with a pairwise interaction that depends on the chord distance. Moreover, the compactified Hamiltonians are periodic not only in the position variables, but also in the momenta! A surprising fact is that there are two dramatically different types of dynamics, distinguished by the value of the coupling parameter. For certain couplings (which we call type 1), particle distances have lower (and upper) bounds, while other (type 2) couplings allow particle collisions to happen resulting in a more complicated dynamics.

I will present the global phase space and quantization of models with type 1 couplings and describe the open problem of solving systems with type 2 couplings. Based on joint work with László Fehér and Martin Hallnäs.

Nikolay Martynchuk: Scattering invariants and singularities of integrable Hamiltonian systems

In this talk, we will discuss topological scattering theory for integrable Hamiltonian systems. We shall review the so-called scattering monodromy invariant and show how it can be generalised to singularities and the `molecule' theory of two degree of freedom integrable systems.

Bohuan Lin Interplay betweeen Dynamics and Geometry in Integrable Systems and Engineering Problems

In this talk I will report on my PhD thesis.

Alexey Bolsinov: Nijenhuis Geometry and integrability

The talk will be focused on new developments in Nijenhuis Geometry. Similar to Riemannian, Poisson and symplectic geometry, the Nijenhuis geometric structure is defined by means of a tensor of order 2 (i.e., by a matrix) but, in contrast to the above examples, this tensor is not a bilinear form but linear operator. The additional geometric condition imposed on this operator is that its Nijenhuis torsion identically vanishes. I will try to explain how Nijenhuis structure is related to various aspects of integrability in geometry and mathematical physics.