“Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control and more” Jesús María Sanz-Serna, Universidad Carlos III de Madrid, Spain
November 17, 2017
11:20 am- 12:20 pm
Armitage 123

Symplectic Runge-Kutta (RK) schemes were introduced in the 1980’s to integrate numerically Hamiltonian systems of differential equations. As it turns out, unbeknownst to the user, symplectic RK schemes implicitly appear in a number of applications, including automatic differentiation, optimal control, etc. The talk explains in very general terms the links between symplectic integration and those application areas.

“The Ins and Outs of the Diffusion Approximation”
Charles Epstein, Department of Mathematics at UPENN
October 17, 2017
12:45 pm- 1:45 pm
Science Building Lecture Hall

Population Genetics is the study of how the distribution of different types of individuals evolves in a reproducing population. The standard models incorporate effects of random mating, mutation, selection, and migration. In their simplest form these models are discrete Markov chains that model a finite population. These discrete models are very difficult to analyze and compute with, and so methods were developed to replace the discrete models with continuum models allowing for the usage of calculus. We describe both the discrete and continuous models and how they are related, as well as recent work on the analysis and numerics of the continuous models.

“Notes on the Minkowski Measure, the Minkowski Symmetral, and the Banach-Mazur Distance”
Xing Huang, Ph.D. student from China
September 29, 2017
11:20 am- 12:20 pm
Armitage 123

In this talk we derive some basic inequalities connecting the Minkowski measure of symmetry, the Minkowski symmetral and the Banach-Mazur distance. We then explore the geometric contents of these inequalities and shed light on the structure of the quotient of the space of convex bodies modulo affine transformations.