报告题目:Continued fractions and hyperelliptic curve

报告人：Andy Hone 教授（University of Kent）

报告时间：2024.04.22 14:00-15:00

报告地点：广B208

摘要：We consider continued fraction expansions of certain functions on hyperelliptic curves, starting with a family of J-fractions constructed by van der Poorten, and explaining how it relates to orthogonal polynomials and discrete integrable systems. In particular, we show how this leads to a direct method to derive Hankel determinant formulae for Somos-4 sequences and generalisations to genus g>1. We also briefly describe an analogous construction with S-fractions, leading to another family of discrete integrable systems associated with the Volterra lattice. This turns out to be related to the J-fractions via contraction: it seems that the Miura transformation between the  Volterra and Toda lattices was first written down by Stieltjes!

报告人简介：Andy believes in inspiring the next generation of mathematicians, and is involved with School Outreach activities with local schools and the general public, encouraging them to be co-creators of new mathematical research. Until late 2014 he was Head of the Mathematics group but then took up an EPSRC Established Career Fellowship, working on the project Cluster algebras with periodicity and discrete dynamics over finite fields, which applies ideas from mathematical physics to contemporary problems in algebra and number theory.

邀请人：沈守枫