Program

Program Booklet (download)

Introductory lectures for graduate students

14:00-15:00 Cristian Rios (University of Calgary)
- Title: Weak derivatives and their applications
- Abstract: This lecture intends to introduce the concept of weak derivative and the ensuing definition of Sobolev spaces in Lebesgue spaces. Some density and embedding concepts will be discussed, as well as some applications and generalizations. This lecture is directed to graduate students and only assumes a background of Lebesgue integration theory.
15:00-16:00 Irina Mitrea (Temple University)
- Title: On the Dirichlet Problem for the Laplacian
- Abstract: In this lecture we will discuss a number of classical results in Harmonic Analysis and Partial Differential Equations that play a role in establishing well-posedness for the Dirichlet Problem for the Laplacian with Lp datum in a couple of simple geometric contexts. The goal of the lecture is to introduce graduate students to a first blueprint/benchmark of what can be achieved in the theory of elliptic boundary value problems for second order elliptic systems. The presentation is self-contained and assumes only a minimal background in analysis.

- Title: Behavior of solutions near singularities for perturbed Kepler problems
- Abstract: This is a classic topic in celestial mechanics. Estimates by Sundman (1913) and Sperling (1970) are well-known to the community, but their proofs are somewhat complicated. In this talk we will share a simpler approach based on some ODE techniques.