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 Talk 26 November 2020

Speaker Prof. Changzheng Qu Ningbo University Title Integrable Systems and Invariant Geometric Flows in affine-related Geometries Abstract Invariant geometric flows in certain geometries have been studied extensively from different points of view. In this talk, we are mainly concerned with invariant geometric flows in centro-affine, centro-equiaffine and affine geometries etc. First, we show that the […]

APIOS Talk 10 November 2020

Speaker Prof. Artur Sergyeyev Silesian University in Opava Title Integrable (3+1)-dimensional systems from contact geometry Abstract We present a large new class of (3+1)-dimensional integrable systems using a novel kind of Lax pairs related to contact geometry, thus showing inter alia that there is significantly more of such systems than it appeared before. In particular, […]

APIOS Talk 29 October 2020

Speaker Dr. Vera Roshchina University of New South Wales Title Faces of convex sets: dimensions and regularity Abstract The facial structure of convex sets can be surprisingly complex, and unexpected irregularities of the arrangements of faces give rise to badly behaved sets. I will focus on specific properties of facial structure that capture irregularities (dimensions […]

APIOS Talk 01 October 2020

Speaker Prof. B. Xue Zhengzhou University Title Integrable Dynamic Systems with N-peakons Abstract Since the discovery of Camassa-Holm equation, because of the special properties that peakon gets, it has received considerable attention in modern Mathematics and Physics. Many new integrable dynamic systems with N-peakon have been obtained, for instance, the DP equation, the Novikov equation, […]

APIOS Talk 13 October 2020

Speaker Prof. X. Chang Chinese Academy of Sciences Title On Frobenius-Stickelberger-Thiele polynomials and modified Camassa-Holm peakon lattice Abstract In this talk, we will introduce some basic properties of the so-called Frobenius-Stickelberger-Thiele (FST) polynomials and highlight its roles in solving the multipeakons of the modified Camassa-Holm equation by use of inverse spectral method. The talk is […]

APIOS Talk 15 September 2020

Speaker Prof. Yuma Mizuno, Tokyo Institute of Technology Title Difference equations arising from cluster algebras Abstract The theory of cluster algebras gives powerful tools for systematic studies of discrete dynamical systems. Given a sequence of quiver mutations that preserves the quiver, we obtain a finite set of algebraic relations, yielding a discrete dynamical system. Such […]

APIOS Talk 03 September 2020

Speaker Prof. Atsuo Kuniba The University of Tokyo Title Generalized hydrodynamics for randomized box-ball system Abstract Box-ball system (BBS) is a prominent example of soliton cellular automaton in one dimension. By now its integrability has been well understood from the viewpoint of quantum groups, Bethe ansatz, ultradiscretization and tropical geometry. In the last few years, […]