Some TOP topology (Tam Nguyen Phan) | Lecture 1

The main theme of this lecture series is to show how to construct homeomorphisms between two spaces via the method of Bing shrinking. Topics covered include the generalized Schoenflies conjecture, the Bing involution, manifolds factors (which are spaces that may not be manifolds by whose products with some manifold are manifolds) and a touch on the double suspension theorem. Assumed knowledge is basic point-set topology (mainly metric-space topology).

Billiards (Lucas Dahinden) | Lecture 2

We study the dynamics of billiards on tables with smooth boundary, with a bias towards finding periodic orbits. We first follow a classical introduction on euclidean Billiards. Then we expand the discussion to settings of current research, like Riemannian manifolds and homogeneous Finsler billiards, which are studied with a diverse set of tools.