2017-12-13  18:43 hrs.

### The Berezinskii-Kosterlitz-Thouless Phase Transition

#### David BrydgesMathematics Department University of British Columbia

The 2016 Nobel Prize in Physics was awarded half to Thouless and half to Haldane and Kosterlitz “for theoretical discoveries of topological phase transitions and topological phases of matter”. I shall review a part of this development that may be attractive for a general mathematical audience. In particular

•  The context in statistical mechanics: the rotator model on $Z^2$.

•  The role of cohomology of complexes in this model.

•  How cohomology brings in the electrostatics of charged point particles.

•  How electrostatics in two dimensions causes the discontinuous change in charge-density correlations called the KT phase transition.

•  Theorems (old and new) on the existence and nature of the KT transition.

#### Palapa Guillermo Torres -- Lunes 21 de agosto de 2017, 12:00 horas

Unidad Cuernavaca del Instituto de Matemáticas UNAM