Course by Thierry Lévy and Ambar Sengupta - Four chapters on low-dimensional gauge theories  21 - 23 April 2015

10:00 - 12:00

Organisers

Thierry Lévy, Université Pierre et Marie Curie

Ambar Sengupta, Louisiana State University

Lecturers

  • Thierry Lévy (UPMC)
  • Ambar Sengupta (Louisiana State University)


Description

1. Historical introduction : from classical electromagnetism to gauge theories


Tuesday 21 April, time: 10:00-12:00

Gauge theories govern the interaction between the fundamental constituents of matter. Electromagnetism is the most familiar such theory. In this lecture we look back at Maxwell's equations for the electromagnetic field and explore how these relate to the Yang-Mills equations for gauge theories.

2. A case study : two-dimensional Yang-Mills theory
Wednesday 22 April, time: 10:00-12:00

In this lecture we explore the  Yang-Mills measure in two dimensions. This measure arises from the study of a quantum theory for the Yang-Mills gauge field. Geometry and probability interweave in the construction and study of this measure.

3. A connection with random matrix theory : the master field


Thursday 23 April, time: 10:00-12:00
Every gauge theory has associated to it a group of symmetries, typically a subgroup of U(N), the  group of NxN unitary matrices. A rich structure emerges when considers the behavior of this theory as N goes to infinity. This lecture will explore results and questions in this area, which lies at the juncture of random matrix theory and stochastic geometry.

4. The scale of dimensions : Yang-Mills and Chern-Simons


Thursday 23 April, time: 15:00-17:00
Chern-Simons theory is a gauge theory in three dimensions that has an elegant mathematical structure with a topological flavor. In this theory we explore aspects of Yang-Mills and Chern-Simons functional integrals from a geometric viewpoint.

Name University Dates of visit
Thierry Lévy Université Pierre et Marie Curie 21/04/2015 - 23/04/2015
Ambar Sengupta Louisiana State University 21/04/2015 - 23/04/2015
Total Guests : 2
Name University Dates of visit
Total Guests : 0