As part of the Trimester Program “Probabilistic Methods in Quantum Field Theory”, this seminar series aims to provide a dynamic space for participants to share their research and foster discussions. The focus will be on quantum field theory as well as related topics, encouraging a broad exchange of ideas.
The seminars will take place on Wednesdays, alternating weeks (except during the summer school and workshop weeks), starting on June 4th.
Please see the precise dates below. Sessions will be held at 3 pm in the lecture hall of the HIM Institute (Poppelsdorfer Allee 45) and will be followed by a coffee break, allowing ample time for informal discussions.
- June 4: Thierry Levy (Sorbonne) – A combinatorial formula for Wilson loop expectations in 2d Yang-Mills theory
The 2d Yang—Mills holonomy process is a collection of random unitary matrices indexed by loops on a compact surface. Wilson loop expectations are expectations of products of traces of some of these random matrices. They play the role of n-point functions, and are the fundamental observables of this theory. They can be expressed as integrals over products of finitely many copies of the unitary group, and therefore be analysed with the tools of non-commutative Fourier analysis. This yields combinatorial expressions, which can be regarded as defining a model of random partitions over the surface, and from which one can nicely derive some of the properties of the Wilson loop expectations, including the Makeenko—Migdal loop equations, in the regime where the size of the unitary matrices tends to infinity.
- June 18: TBA
- July 9: Vivian Healey (Texas State University) – Title & abstract TBA
- July 23: TBA
- August 13: TBA
Organizers:
*In case of questions concerning services and administration at the HIM institute, please contact the coordinators of the HIM Trimester Programs, Emma Seggewiss or Kanami Ueda.