After a short introduction on the symplectic packing problem, we will explain how recent results of B‐H. Li, T.‐J. Li, A. K. Liu, and Gao on symplectic cones lead to a concrete understanding of symplectic packings for rational ruled surfaces. If time permits, we will also explain how this relates to recent work of M. Hutchings on embedded contact homology.

This is joint work with O. Buse.

If you travel $m$ miles in $t$ hours, then you have averaged $m/t$ miles per hour. But did you ever travel at that speed for an instant? What about for an hour? In this talk we look at three problems that arise from continous motion, including a physical interpretation of the intermediate value theorem and some counter intuitive results about average speeds. With inspiration from Siyavus Acar and Ralph Boas.

In this series of lectures our goal is to prove a version of Schur-Horn-Kostant theorem for Lebesgue measure spaces. As an applicaiton we will see that Bloch-Flaschka-Ratiu's convexity theorem can be extended to all compact toric symplectic manifolds.

I shall describe how to use the wreath product construction to obtain simple proofs of some classical subgroups theorems (Nielsen-Schreier, Kurosh) and also for some new ones. The talk will be completely accessible and I will develop the concepts from the beginning.

I will survey what is known about pro-$p$ groups that contain a subgroup of finite cohomological dimension, including results of Serre, Scheiderer, and aiming at a description of the structure of pro-$p$ groups that are virtually free pro-$p$.