MAGIC Launch Lecture 2022

MAGIC Launch Lecture 2022

Sep
28
Wed 2022

15:00 - 16:00

Organised by Sam Blackburn.

Hosted by University of Newcastle.

Title: Coproducts, knots and quantum groups
Speaker: Martina Balagovic (Newcastle University)

Quantum groups are certain quasitriangular bialgebras defined in the 1980s as deformations of enveloping algebras of Lie algebras, with motivation coming from quantum physics.

I will explain what that means, and explain two ideas which lead to one of their applications:

  1. 1. How reversing arrows in a definition of an algebra (a structure with a product and a unit) produces a coalgebra (a structure with a coproduct and a counit), and how a compatible algebra and coagebra structure provides a setting in which it is possible to pose a certain "universal" version of the Yang Baxter equation, which describes scattering in statistical mechanics.
  2. 2. How quantum groups provide a "universal" solution to the Yang Baxter equation, and how such solutions can be used to generate invariants of knots.

Despite some long words from physics and topology, this will be a talk about algebra and representation theory, and assume only a good knowledge of linear algebra (including some understanding of tensor products).

At the end, to provide a link with some recent developments in the field, I will briefly discuss how adding the boundary on the physics side of this story changes the algebra and the topology. 

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