Keynote speakers

• Evgeny Ferapontov
  Department of Mathematical Sciences, Loughborough University, UK
  Title of talk: Homogeneous third-order Hamiltonian operators
  Abstract: I will address the classification of homogeneous third-order Hamiltonian operators of differential-geometric type. Operators of this form appear in applications as Hamiltonian structures of the associativity equations, and possess a number of unexpected connections with projective differential geometry. Based on the correspondence with quadratic line complexes, a complete list of such operators with n≤5 components is obtained.
  [1] E.V. Ferapontov, M.V. Pavlov and R.F. Vitolo, Projective-geometric aspects of homogeneous third-order Hamiltonian operators, J. Geom. Phys. 85 (2014) 16-28; arXiv:1401.7235
  [2] E.V. Ferapontov, M.V. Pavlov and R.F. Vitolo, Towards the classification of homogeneous third-order Hamiltonian operators, IMRN (2016), doi:10.1093/imrn/rnv369; arXiv:1508.02752.


• Christian Klein
  Institut de Mathématiques de Bourgogne, Dijon, France
  Title of talk: Numerical study of 2+1 dimensional nonlinear dispersive PDEs
  Abstract: We present several numerical studies of solutions to PDEs from the family of nonlinear Schrödinger and Kortweg-de Vries equations. We study the formation of dispersive shocks and of potential blow-ups in the solutions. A universality conjecture for the break-up of the solutions is presented.
  


• Boris Konopelchenko
  Physics Department, Università del Salento, Lecce, Italy
  Title of talk: Confluences, Jordan forms and regularizations of hydrodynamic type systems
  Abstract: Novel class of integrable hydrodynamic type systems which govern the dynamics of critical points of confluent Lauricella type functions defined on the finite dimensional Grassmannians Gr(2,n) is constructed. It is shown that in general such systems are given by non-diagonalizable quasi-linear systems with normal Jordan blocks. Connection of the systems corresponding to the deepest confluence with the problems of the change of type transitions for the quasilinear systems of mixed type and possible regularizations of the Burgers-Hopf equation is discussed.
  


• Franco Magri
  Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Milano, Italy
  Title of talk: Haantjes manifolds and WDVV equations
  Abstract: TBA
  


• Vladimir B. Matveev
  Université de Bourgogne, Dijon, France
  Title of talk: Rogue Waves in 1+1 and 2+1 integrable systems, related with AKNS and KP-I hierarchies
  Abstract: The discovery of multi-rogue wave (MRW) solutions of the focusing NLS equation, made in 2010 (Eur. Phys. J., Special topics 185 (2010) 247-258), drastically improved a vision of the links between rogue waves and the theory of integrable systems. The multiple rogue wave solutions of the NLS equation can be described by means of a Wronskian determinant representation with a very simple structure. This structure allows to relate them with multi-rogue waves solutions of the KP-I equation via a remarkable relation, which we call NLS-KP-I correspondence. We provide arguments showing that "extreme" rogue waves in 2+1 dimensional models occur as a result of the collision of a certain number of "simple" rogue waves.
  Moreover, we will show that it is possible to extend the basic formulas, which we used in the NLS case, to obtain the MRW rational or quasi-rational solutions of any rank, for all equations of the reduced AKNS (RAKNS) hierarchy.
  We also show that a (for the NLS equation) well known scaling invariance and Galilean invariance property of solutions can be extended, with appropriate modifications, to the whole AKNS hierarchy and its reduced and deformed versions.
  


• Antonio Moro
  Northumbria University, Newcastle, UK
  Title of talk: On the integrable structure and thermodynamics of “complex" networks
  Abstract: A large variety of real world systems can be naturally modelled by networks, i.e. graphs whose nodes represent the components of a system linked (interacting) according to specific statistical rules. A complex network is realised via a graph of nontrivial topology typically constituted by a large number of nodes/links. Fluid and magnetic models in Physics are just two among the many classical examples of systems which can be modelled by using simple or complex networks. In particular "extreme" conditions (thermodynamic regime), networks, just like fluid and magnetic models, exhibit a critical behaviour intended as a drastic change of state due to a continuous change of thermodynamic parameters. Using an approach to thermodynamics, recently introduced to describe a general class of van der Waals type models and magnetic systems in mean field approximation, we analyse the integrable structure of corresponding networks and use the theory of conservation laws to provide an analytical description of the system outside and inside the critical region.
  


• Maxim Pavlov
  Novosibirsk State University, Russia
  Title of talk: The Gibbons-Tsarev System and Isomonodromic Deformations
  Abstract: In this talk we consider the remarkable Gibbons-Tsarev system, which describes multi-component hydrodynamic reductions of integrable three-dimensional quasilinear equations of second order. We show that this system possesses infinitely many solutions, determined by isomonodromic deformations of integrable dispersive systems. Description of these solutions will be presented in this talk.
  


• Alexander Veselov
  Department of Mathematical Sciences, Loughborough University, UK
  Title of talk: Logarithmic Frobenius structures and theory of hyperplane arrangements
  Abstract: The logarithmic Frobenius structures correspond to a special class of solutions of the famous Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. There are examples related to Coxeter configurations and their restrictions, but the general classification is still an open problem. I will discuss some relations of this problem with the theory of hyperplane arrangements, including holonomy Lie algebras and logarithmic vector fields. The talk is based on a joint work with M. Feigin.