This summer (2016) will feature two mini-courses: Mini-course # 1 Title: An introduction to geometric analysis Professor: Reza Seyydali Will meet: June 20-July 1 Abstract: The main goal of this course is to provide an introduction into the area of geometric analysis. Geometric analysis is largely to study partial differential equations on manifolds. The first part of the course is to study general theory of linear elliptic differential operators on compact manifolds. In the second part, we go over some techniques of nonlinear PDEs. Mini-course # 2 Title: Topics in Grassmannians and Stiefel manifolds Professor: Jason Cantarella weeks of July 18th and 25th Abstract: The Grassmann and Stiefel manifolds are the manifolds of k-dimensional linear subspaces of a vector space and of orthonormal k-frames on a vector space. They appear over and over again throughout modern mathematics, and serve as canonical examples in various different fields. This minicourse will explore the theory of these manifolds from the geometric, topological, probabilistic, and numerical point of view, with as much as I can figure out about the connections to representation theory and algebraic geometry.