|November 20, 2014
|Gluing tetrahedra and 3-manifold — Saima Anis|
|We tried to construct in a natural way a 3-dimensional manifold together with actions of the group PSL(2, F7) on 4-tuples with entries from PL(F7), where F7 is the finite field with 7 elements.|
|December 4, 2014
|Critical points of distance functions — Wouter van Limbeek|
Let M be a Riemannian manifold. Then the distance to a fixed basepoint gives a nice function on M that encodes a lot of the geometry of M (e.g. near the basepoint the gradient trajectories are geodesic segments). Inspired by this fact, Grove and Shiohama developed the beginnings of a Morse theory of these functions (even though they are usually not differentiable!). The theory is still in an early state, but there are already nice applications to due to Grove-Shiohama, Grove-Petersen and Gromov. I will discuss some of the theory and these applications.