Geometry and Analysis Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
20 November 2017
14:15
Ben Davison
Abstract

Associated to a finite graph without loops is the Kac-Moody Lie algebra for the Cartan matrix whose off diagonal entries are (minus) the adjacency matrix for the graph.  Two famous conjectures of Kac, proved by Hausel, Letellier and Villegas, hint that there may be some larger cohomologically graded algebra associated to the graph (even if there are loops), providing "higher" Kac moody Lie algebras, or at least their positive halves.  Using work with Sven Meinhardt, I will give a geometric construction of the (full) Kac-Moody algebra for a general finite graph, using cohomological DT theory.  Along the way we'll see a proof of the positivity conjecture for the modified Kac polynomials of Bozec, Schiffmann and Vasserot counting various types of representations of quivers.

 

  • Geometry and Analysis Seminar
4 December 2017
14:15
Abstract

A bold conjecture of Boyer-Gorden-Watson and others posit that for any irreducible rational homology 3-sphere M the following three conditions are equivalent: (1) the fundamental group of M is left-orderable, (2) M has non-minimal Heegaard Floer homology, and (3) M admits a co-orientable taut foliation. Very recently, this conjecture was established for all graph manifolds by the combined work of Boyer-Clay and Hanselman-Rasmussen-Rasmussen-Watson. I will discuss a computational survey of these properties involving half a million hyperbolic 3-manifolds, including new or at least improved techniques for computing each of these properties.
 

  • Geometry and Analysis Seminar
Add to My Calendar