This is a the second talk of the series of two talks in which we give a sketch of the main ideas motivating the Langlands Program. These are designed to be pre-talks in preparation for Professor Michael Harris's Michalik Lecture on Sept 30 and his ACoG seminar talk on Sept 29.
Abstract
We develop a loosely coupled splitting method for coupled problems called the Robin-Robin splitting method based on Robin-type interface conditions. We apply this method to several coupled problems, most notably the fluid-structure interaction problem in both a time-semi-discrete framework and a fully discrete framework.
If you are considering your post-graduation options or are curious as to what opportunities Pitt can provide you to prepare for your future career, this talk is for you. Lauren will discuss how to connect with the Career Center and the services it offers. Note also that this talk comes ahead of the career fair, which will be held on September 28th-30th.
All students are welcome to attend and there will be pizza.
Topology changes occur naturally in geometric evolution equations like mean curvature flow. As classical solution concepts break down at such geometric singularities, the use of weak solution concepts becomes necessary in order to describe topological changes.
For two-phase mean curvature flow, the theory of viscosity solutions by Chen-Giga-Goto and Evans-Spruck provides a concept of weak solutions with basically optimal existence and uniqueness properties.
We introduce a spectral method to approximate PDEs involving the fractional Laplacian with zero exterior condition. Our approach is based on interpolation by tensor products of sinc-functions, which combine a simple representation in Fourier-space with fast enough decay to suitably approximate the bounded support of solutions to the Dirichlet problem. This yields a numerical complexity of O(NlogN) for the application of the operator to a discretization with N degrees of freedom.