2020.06.11 Christophe Garban - A new point of view on topological phase transitions (Part 1)
Channel: One World Probability
Date: 2020-06-17

Topological phase transitions were discovered by Berezinskii-Kosterlitz-
Thouless in the 70's. They describe intriguing phase transitions for classical
spins systems such as the plane rotator model (or XY model).

Part 1 : General introduction on the topological phase transitions. Without
assuming any a priori background, we will discuss how this phase transition
arises in cases such as :
- the XY model (spins on Z^2 with values in the unit circle)
- the integer-valued Gaussian Free Field
- Abelian Yang-Mills on Z^4
We will also discuss some of the main contributions of Fröhlich and Spencer to
this theory.

Part 2 : A statistical reconstruction problem.
We will connect topological phase transitions to a statistical reconstruction
problem concerning the Gaussian Free Field and will show that the feasibility
of the reconstruction undergoes a KT transition.

The talks will be based mostly on the preprint:
https://arxiv.org/abs/2002.12284