Tue, 26 Oct 2021
16:30
L5

String-like amplitudes for surfaces beyond the disk

Hugh Thomas
(UQÀM)
Abstract
In 1969, Koba and Nielsen found some equations (now known as u-equations or non-crossing equations) whose solutions can be described as cross-ratios of n points on a line. The tree string amplitude, or generalized Veneziano amplitude,  can be defined as an integral over the non-negative solutions to the u-equations. This is a function of the Mandelstam variables and has interesting properties: it does not diverge as the Mandelstam variables get large, and it exhibits factorization when one of the variables approaches zero. One should think of these functions as being associated to the disk with marked points on the boundary. I will report on ongoing work with Nima Arkani-Hamed, Hadleigh Frost, Pierre-Guy Plamondon, and Giulio Salvatori, in which we replace the disk by other oriented surfaces. I will emphasize the part of our approach which is based on representations of gentle algebras, which arise from a triangulation of the surface.

 

Mon, 26 Apr 2010 13:00 -
Tue, 27 Apr 2010 14:00
SR1

Delzant and Potyagailo's hierarchical accessibility

Nicholas Touikan
(UQÀM)
Abstract

Take a group G and split it as the fundamental group of a graph of groups, then take the vertex groups and split them as fundamental groups of graphs of groups etc. If at some point you end up with a collection of unsplittable groups, then you have a hierarchy. Haken showed that for any 3-manifold M with an incompressible surface S, one can cut M along S and and then find other incompressible surfaces in M\S and cut again, and repeating this process one eventually obtains a collection of balls. Analogously, Delzant and Potyagailo showed that for any finitely presented group without 2-torsion and a certain sensible class E of subgroups of G, G admits a hierarchy where the edge groups of the splittings lie in E. I really like their proof and I will present it.

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