On Toda lattice
Toda lattice, as an important integrable system, has been widely studied in the recent 50 years. It was introduced by Toda by considering the lattice with exponential interaction and later many applications of the Toda lattice have been studied. Its interplay with orthogonal polynomials, matrix models and 2d gravity have attracted many scholars' attention. Besides, Toda lattice relates to many branches of mathematical theories such as integrable geometry, integrable combinatorics, integrable probability and so on. In this talk, I will firstly discuss some properties of the original Toda lattice and its connections with other subjects, and then focus on a brief introduction to my related works, mainly on the discoveries about the other types of Toda lattices as well as their physical and mathematical properties.
Dr Shi-Hao Li, The University of Melbourne