Geometry and Topology Seminar: The global shape of universal covers

Abstract: Given a compact geodesic space $X$, it is well understood how the geometry of its universal cover $\tilde{X}$ influences the qualitative algebraic behavior of the fundamental group $\pi_1(X)$.

When $\tilde{X}$ is compact (or equivalently, $\pi_1(X)$ is finite), it is also possible to obtain, under natural geometric assumptions, quantitative information about $\pi_1(X)$ such as Cayley diameter or Kazhdan constant with respect to suitable geometrically chosen generators.

I will talk about how this can be done, and the problem of understanding the shape of $\tilde{X}$.

Host: Jesus Sanchez