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 […]