Fall semester:
February 18th: Minhua Cheng
Title: Introduction to Translation surfaces
February 23rd: Devanshi Merchant
Title: Mostow's Rigidity Theorem
Abstract: For surfaces, Gauss-Bonnet tells us that area is a topological invariant, but we can put many different metrics on it.
In higher dimensions, for a closed hyperbolic manifold, Mostow Rigidity tells us that, not only is the volume invariant, but there is only one metric up to isometry. In this talk, I will give you Gromov's proof of Mostow Rigidity for dimension 3.
March 2nd: Neelam
Title: Roller-Duality theorem for CAT(0) cube complexes
Abstract: The "Virtual Haken Conjecture" proven by Ian Agol in 2012, was a massive milestone in 3-manifold topology. It states that every compact, irreducible 3 manifold with infinite fundamental group is virtually Haken (it has a finite cover that contains an incompressible surface). CAT(0) cube complexes were the "missing link" that turned this topological problem into a combinatorial and geometric one. The construction by Micah Sageev allows us to construct a cube complex using "walls". In this talk, we will see this construction of a cube complex using a pocset (set of walls).
April 1st: Alice Ponte
Title: Nielsen-Thurston Classification