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, […]

APIOS Talk 18 August 2020

Speaker A/Prof. Milena Radnovic University of Sydney, Australia Title Integrable billiards and extremal polynomials. Abstract In this talk, we will present a novel relationship between periodic trajectories of ellipsoidal billiards and the theory of generalised Chebyshev polynomials on systems of segments. Using that relationship, we prove fundamental properties of billiard dynamics, such as monotonicity of […]

APIOS Talk 04 Aug 2020

Speaker Dr. Ian Marquette University of Queensland, Australia Title Construction of polynomial algebras related to superintegrable systems Abstract Over the years, it has been discovered that symmetry algebras of superintegrable systems take the form of polynomial algebras. For examples, the integrals of 2D superintegrable models related to fourth and sixth PainlevĂ© transcendent lead to cubic […]

APIOS Talk 21 Jul 2020

Speaker Prof. Youjin Zhang Tsingua University, China Title Special Cubic Hodge Integrals and the Fractional Volterra Hierarchy Abstract We show that the generating function of cubic Hodge integrals satisfying the local Calabi-Yau condition is the tau function of a particular solution of an integrable hierarchy called the fractional Volterra hierarchy. This integrable hierarchy is a […]