Fall, 2007

• Speaker Benjamin Doyon, Durham University
  • Title Conformal field theory and Schramm-Loewner evolution
  • Time/place Friday, 9/7/2007, 1:00 pm in Hill 705
  • Abstract The scaling limit of two-dimensional statistical models at criticality can be described by two theoretical frameworks: conformal field theory (that is, vertex operator algebras, their modules and representations), and Schramm-Loewner evolution (SLE). The first one has a long history, starting more than 20 years ago with works by both mathematicians and physicists, whereas the second one encompasses recent advances, starting in 2000 with a paper of Schramm until generalisations still under construction. The two frameworks seem quite unrelated in their formulation as well as in their applications. But it is nowadays believed by many that understanding the relation between them will allow us to make important steps in the understanding, both physical and mathematical, of critical regimes of statistical models. I will review the frameworks, advances made in relating them, and the many open problems. This talk will be accessible to non-specialists.

• Speaker Liang Kong, Max Planck Institute, Bonn
  • Title An introduction to open-closed conformal field theory
  • Time/place Friday, 9/14/2007, 1:00 pm in Hill 705
  • Abstract Open-closed conformal field theory describes the perturbative open-closed string theory and some critical phenomena in condensed matter physics. It provides a powerful tool to study the still mysterious object called "D-brane", which is important to Kontsevich's homological mirror symmetry program. In this talk, I will outline a mathematical study of open-closed conformal field theory based on the theory of vertex operator algebra. In particular, I will give a tensor-categorical formulation of rational open-closed conformal field theory. I will also briefly discuss what D-branes are in our framework. This talk will be accessible to graduate students who know the definition of category.