Seminar

Abstract: A wide variety of partial differential equations that are of interest in industrial applications cannot be solved in closed form. Even those equations for which we do have a well-understood theory may not be solved over domains that aren’t nice enough. The finite element method is a powerful algorithm that provides solutions to both these issues. This talk will provide a very high-level overview of the theory FEM. How do we approximate solutions that we do not know a priori? How can we estimate our error?

Abstract: The spectrum of the Laplacian operator is an important object in the analysis of PDEs which depends on the domain and on the boundary conditions. The smallest ("principal") eigenvalue admits a useful variational characterization in terms of the Rayleigh quotient of the operator. We can adapt inverse iteration, an iterative technique for computing eigenvalues of symmetric PD matrices, to the infinite-dimensional setting.

Abstract: Machine learning is the study of how artificial intelligence mimics the human ability to learn. This is a gentle and interactive introduction to the types of questions involved in machine learning and some of the algorithms used to address those questions.