We will run a FADA seminar focusing around braids, 
broadly interpreted, and aiming at fostering discussions between 
algebraists, topologists and geometers.

FADA Seminar Schedule: 

• 9:00am   Jack Brand (ANU)
  Overtwisted disks in contact 3-manifolds using Morse diagrams
  One of the most important questions to ask about a contact structure is whether it is overtwisted or tight. In 1989, Eliashberg proved his famous result that the classification of overtwisted contact structures is equivalent to the classification of homotopy classes of 2-plane fields, and therefore it is the tight contact structures that are geometrically more interesting. More recently, efforts have been made (originally by Goodman, Honda-Kazez-Matic) to detect whether a contact structure compatible with an open book decomposition is overtwisted or tight by studying the monodromy of the open book decomposition. In this talk, we provide a new criterion for the overtwistedness of a contact structure using the Morse diagrams compatible with an open book decomposition.

• 10:30am   Morning tea (provided)

• 11:00am   Anand Deopurkar (ANU)
  Stability conditions, metrics, and compactifications
  A stability condition on a triangulated category turns the category into a geometric object. We can then import powerful techniques from geometry to the study of triangulated categories and stability manifolds. I will elaborate on this theme. Specifically, I will describe how a stability condition defines a metric on the category. I will describe how this metric can be used to construct a compactification of the stability manifold, using ideas inspired by the study of metrics on Riemann surfaces, namely Teichmuller theory. I will then discuss potential applications, examples, and unexplored areas.