APIOS Talk 26 August 2021

Speaker Dr. Nobutaka Nakazono Tokyo University of Agriculture and Technology, Japan Title Special solutions to the multiplicative type Hirota’s dKdV equation Abstract In 1977, Hirota found a discrete analogue of the KdV (dKdV) equation. Then, in 1991 Capel, Nijhoff and Papageorgiou found its deautonomized vesrion. The solutions of both versions have been well investigated. In […]

APIOS Talk 9 Sep 2021

Speaker Prof. Xiaochuan Liu Xi’an Jiaotong University, China Title The study of integrable hierarchies in terms of Liouville Correspondences Abstract In this talk, we survey recent results on the Liouville correspondences of integrable hierarchies of Camassa-Holm type. The Liouville transformation between the isospectral problems of the two integrable hierarchies is shown to establish the Liouville […]

APIOS talk 15 July 2021

Speaker Dr. Peter van der Kamp La Trobe University, Australia Title Integrable maps: from reduction of lattice equations and as generalised Manin transformations. Abstract This talk consists of two parts. Integrable maps can be obtained as reductions of integrable lattice equations, and they can be understood as compositions of generalised Manin involutions. I will discuss […]

APIOS talk 6 May 2021

Speaker Dr. Cheng Zhang Shanghai University, China Title On the inverse scattering transform for integrable PDEs on the half-line Abstract In this talk, we provide an inverse scattering transform for integrable PDEs on the half-line. The method is based on the notions of integrable boundary conditions as well as the Sklyanin-type double-row monodromy matrix. Taking […]

APIOS talk 22 April 2021

Speaker Prof. Jan de Gier The University of Melbourne, Australia Title Transition probabilities and asymptotics for integrable two-species stochastic processes Abstract I will discuss exact, multiple integral formulas for the transition probability (Green’s function) of two different integrable two-species stochastic particle models: the Arndt-Heinzel-Rittenberg (AHR) model and the 2-TASEP whose generator is the $q\rightarrow 0$ […]

APIOS Talk 6 April 2021

Speaker Dr. Shi-Hao Li Sichuan University, China Title Condensation algorithm of Pfaffians and discrete integrable system Abstract Dodgson’s condensation algorithm of determinants is an efficient way to compute the value of determinant. In recent years, it was realised that the Dodgson’s condensation algorithm is actually a full discrete Toda lattice in 3-dimension with proper initial […]

APIOS Talk 25 March 2021

Speaker Prof. Di Yang USTC Title On tau-functions for the KdV hierarchy Abstract For an arbitrary solution to the KdV hierarchy, we give an expression of the generating series of logarithmic derivatives of the tau-function of the solution explicitly in terms of the so-called basic matrix resolvent. Based on this we develop two new formulae […]

APIOS Talk 09 March 2021

Speaker Dr. D. Croydon Kyoto University Title Invariant measures for KdV and Toda-type discrete integrable systems Abstract I will describe how to construct infinite versions of four well-studied discrete integrable models (namely the ultra-discrete KdV equation, the discrete KdV equation, the ultra-discrete Toda equation, and the discrete Toda equation), and discuss some arguments that are […]

APIOS Talk 25 February 2021

Speaker Dr. Gleb A. Kotousov DESY, Theory Group Title Density of states for an integrable spin chain Abstract The focus of the talk is a certain critical 1D quantum spin chain that lies within the integrability class of a staggered six-vertex model. In the scaling limit the spin chain exhibits a continuous spectrum of conformal […]

APIOS 2021 Announcement

Dear readers, the edition of APIOS 2020 is coming to an end. We would like to thank all the attendees and all the speakers of APIOS of this year. APIOS will be go on pause and resume in mid-February 2021. If you’re interested to give a talk or you would like to suggest a speaker, […]