Organisers

M. Feigin , Glasgow

E. Ferapontov , Loughborough

V. Novikov , Loughborough
About:
This is the webage for the Integrable Days a twoday workshop to celebrate 65th birthday of Alexander Veselov.
Integrable Days are a part of the `Classical and Quantum Integrability’ collaborative workshop series, involving universities of Glasgow, Edinburgh, HeriotWatt, Leeds, Loughborough and Northumbria, and supported by the London Mathematical Society
This years meeting will be an occasion to celebrate the 65th birthday of our friend, colleague and teacher Alexander P. Veselov, who initiated Integrable Days at Loughborough University, which run annually in November since 1996.
Links to recordings can be found here.
This event was kindly funded by the London Mathematical Society.
Programme:
Speakers
Sophie MorierGenoud (Paris)  qanalogues of real numbers
In recent joint work with Valentin Ovsienko we defined qanalogues of real numbers. Our construction is based on a qdeformation of the Farey graph. I will explain the construction and give the main properties. In particular I will mention links with the combinatorics of posets, cluster algebras, Jones polynomials...
This talk was not recorded
Giovanni Felder (Zurich)  The integrable Boltzmann system
Ludwig Boltzmann, in his search for an example of a chaotic dynamical system, studied the planar motion of a particle subject to a central force bouncing elastically at a line. As recently noticed by Gallavotti and Jauslin, the system is actually integrable if the force has an inversesquare law. I will review the construction of the second integral of motion and present the results: the orbits of the Poincaré map are periodic or quasiperiodic and anisochronous, so that KAM perturbation theory (Moser's theorem) applies, implying that for small perturbations of the inversesquare law the system is still not chaotic. The proof relies on mapping the Poincaré map to a translation by an element of an elliptic curve. A corollary is the Poncelet property: if an orbit is periodic for given generic values of the integrals of motions then all orbits for these values are periodic.
Rod Halburd (UCL)  Variants of the Painlevé property and integrable subsystems
We use global results about functions that are meromorphic in regions of the plane to find individual solutions of differential, difference and delaydifferential equations whose only movable singularities are poles. We also allow for simple global branching. In this way we can find or describe subsets of solutions of equations that are in general nonintegrable.
Vsevolod Adler (Moscow)  Stationary solutions of nonautonomous symmetries of integrable equations
The talk is about some recent results on Painlevetype reductions for integrable equations. My first example is a reduction obtained as a stationary equation for mastersymmetry of KdV equation. It is equivalent to some fourth order ODE and numerical experiments show that some of its special solutions may be related to the GurevichPitaevskii problem on decay of initial discontinuity. The second example is about nonAbelian Volterra lattices. Here we study several loworder reductions and demonstrate their relation with nonAbelian analogues of discrete and continuous Painleve equations.
Anna Felikson (Durham)  Mutations of noninteger quivers: finite mutation type
Given a skewsymmetric noninteger (real) matrix, one can construct a quiver with noninteger weights of arrows. Such a quiver can be mutated according to usual rules of quiver mutation introduced within the theory of cluster algebras by Fomin and Zelevinsky. We classify noninteger quivers of finite mutation type and prove that all of them admit some geometric interpretation (either related to orbifolds or to reflection groups). In particular, the reflection group construction gives rise to the notion of noninteger quivers of finite and affine types. We also study exchange graphs of quivers of finite and affine types in rank 3. The talk is based on joint works with Pavel Tumarkin and Philipp Lampe.
Oleg Chalykh (Leeds)  Twisted Ruijsenaars model
The quantum Ruijsenaars model is a qanalogue of the Calogero—Moser model, described by n commuting partial difference operators (quantum hamiltonians) h_1, …, h_n. As it turns out, for each natural number l>1 there exists another integrable system whose quantum hamiltonians have the same leading terms as the lth powers of h_1, …, h_n. I will discuss several ways of arriving at this generalisation.