Title: An Elementary Introduction to Fredholm Determinants
Speaker: Fudong Wang
Date: Thursday, June 11
Time: 2:00 pm
Abstract: At the beginning of the 20th century, Fredholm introduced a way to solve a class of linear integral equations which are now called them Fredholm integral equations. In his 1903’s paper, Fredholm introduced a determinant of a functional, which now is called Fredholm determinant. In this lecture, we will begin with the definition of determinant in the finite-dimensional spaces and review some properties of the determinants. After that, we will focus on the determinant of form $det(I+F)$ where $F$ is “small”. Following Fredholm’s 1903 paper, we will discuss Fredholm determinant $D_f$ and explore some properties of the determinant and how it connects to the finite determinants. Lastly, we will discuss how to construct the famous “soliton” solution to the equation of Koreteweg-de Vries by the so-called Fredholm determinant method introduced by Pöppe(1983).
Video: google drive