**Continued fraction and integrable systems**

**课程专家：**Andrew N W Hone（University of Kent, UK）

**课程地点及时间：**

西南中心401 2024年4月25日（星期四）上午9:00点-11:30点

西南中心401 2024年4月27日（星期六）上午9:00点-11:30点

西南中心401 2024年4月28日（星期天）上午9:00点-11:30点

西南中心501 2024年4月30日（星期二）上午9:00点-11:30点

**课程介绍：**

Lecture 1. Classical continued fractions I (Definition. Euclidean algorithm. Lagrange's theorem on periodicity.)

Lecture 2. Classical continued fractions II (Roth's theorem. Khinchin's constant. Engel series.)

Lecture 3. Continued fractions in function fields (J-fractions. Stieltjes transformation & Hankel determinants. Example: Chebyshev polynomials.)

Lecture 4. Continued fractions on hyperelliptic curves (3-term recursion. Orthogonal polynomials. Integrable dynamics & Somos sequences.)

**专家简介：**Andrew Hone is a Professor of Mathematics, holding the Established Chair in Applied Mathematics at the University of Kent. He studied in Oxford and Edinburgh, and did postdoctoral research in Rome and Adelaide, before starting as a Lecturer at Kent in 2000. The rest of his career has been spent in Kent, apart from a sabbatical in Sydney as a Visiting Professorial Fellow at the University of New South Wales (2017-19). Although a large part of his work has focussed on integrable systems. he has very broad research interests, ranging from mathematical biology to computer science, and his most recent projects concern connections between mathematical physics and contemporary problems in algebra and number theory. He is passionate about inspiring the next generation of mathematicians, and does outreach with the general public and local schools, encouraging them to be co-creators of new mathematical research.

**邀请人：**李世豪