Abstract: Discrete symplectic mappings are not called discrete Hamiltonian systems by the cognoscenti for a variety of reasons, and my aim with this project was to explore the problems involved. In this talk I first show how conservation laws for high order Lagrangian systems transfer to their equivalent Hamiltonian systems with a strikingly beautiful formula. This formula transfers mutatis mutandis to the discrete case. However, analogues of other results do not transfer. I present a series of examples that illustrate the various difficulties, and end with some conjectures and possible ways forward that could involve specialist analytic techniques. The talk assumes no specialist knowledge of the topic.

Abstract: Pascal's matrices are constructed from Pascal's triangle and they are encountered frequently in probability theory. In this talk we will discuss some of their striking properties and their application to polynomials.

(Note: lecture will start at 5:15)