We will introduce the notion of an operad, which generalize the properties coming from associative algebras or Lie algebras. While the definition of an operad to somewhat complex everything will be done through example so we can get familiar with operads and their vast array of applications. If time permits we will give some applications to deformation theory of associative algebras.
I shall discuss an entropy functional defined for convex bodies and its related analysis in the study of the large time asymptotics of the Gauss curvature flow. This is a joint work with Pengfei Guan at McGill.
We discuss the history of Baumgartner's result that all \aleph_1-dense sets of reals can be order-isomorphic, as well as related results of Shelah and Abraham. We'll outline a proof, due to Todorcevic, that is simpler than Baumgartner's original argument. Finally, we present some recent results of Justin Moore concerning the problem of making all \aleph_2-dense sets of reals isomorphic.