PDE and Applied Mathematics Seminar[ Edit ]
Moderator: Yehuda Pinchover
In this talk we will focus on non linear partial differential equation arising on junctions, satisfying non linear and non dynamic Neuman boundary condition at the junction point. We give results on existence and uniqueness of regular solutions, and sketch the proof which differs from the classical approach with fixed point argument. Thereafter, we will focus on the stochastic control theory, where we introduce a new stochastic game, where the state of control is the probability of moving to another edge. We conclude by giving Feynman Kac's representation of solutions, making the link between the stochastic and the PDE theory.
After summarizing 1D periodic Jacobi matrices, I will define periodic Jacobi matrices on infinite trees. I'll discuss the few known results and some interesting examples and then discuss lots and lots of interesting conjectures. This is joint work mainly with Nir Avni and Jonathan Breuer but also with Jacob Christensen, Gil Kilai and Maxim Zinchenko.
It is on the spectral theory of a class of operators on trees, for which there has been literature on the random case even in the theoretical physics literature but I am not aware of any application to anything close to real physics so this is probably better as a math talk but I leave it to you to sort it out if you are interested. I don’t care at all which it is called or even if it is jointly sponsored.