报告主题：Asymptotics and Heun Equations
时间：2023年11月17日13:00-13:45
地点：上川路校区二教105/腾讯会议 会议号：984 1292 8754 密码：6666
报告人：占龙俊
报告内容简介：
Heun equation is the most general ordinary linear Fuchsian equation of second order having four regular singular points. We studied a system of second order different equation, the coefficients are rational functions, satisfied by orthogonal polynomial P_n(z) associated with the Jacobi type weights、Laguerre type weights and weights with gap. We consider n, the dimension of the Hankel matrix tends to infinity (infinite dimension). The second order differential equations satisfied by P_n(z), after asymptotic, are Heun equations. That means the orthogonal polynomial is the solution of the Heun equation. Heun equation may write as Hamiltonian structure, then from the Hamiltonian structure deduce the Painleve equation, namely, After asymptotic the coefficients of second differential equation may write as Heun equation and Painleve equations.
主讲人简介：
占龙俊，2019年博士毕业于澳门大学，2019-2021年在复旦大学做博士后。主要研究方向：随机矩阵理论、渐近分析、Rieman-Hilbert方法等，在JMP等杂志上发表多篇论文。