2022 Winter School in Mathematical Physics

Contribution List

1. Vito Pellizani (UNIBE) - Conformal algebra automorphism: from theory to experiment

12/01/2022, 09:00

Short talks

Conformal field theories (CFTs) are usually strongly coupled, which means that standard quantum field theory techniques fail. At the same time, conformal symmetry is such a strong constraint that any observable can derived from a set of simple building blocks, the so-called CFT data. On top of that, the conformal algebra has an automorphism which identifies the Hamiltonian on R x S^{d-1} with...

2. Sid Maibach (Bonn) - Real Valued 1D Genus 0 Modular Functors for the Weyl anomaly

12/01/2022, 09:25

Short talks

I will introduce the real determinant line bundle which characterizes the Weyl anomaly as a real-valued one-dimensional modular functor over the genus 0 moduli space of Riemann surfaces with analytically parametrized boundaries.
A universal property of such modular functors is obtained by studying the corresponding central extensions of the group of analytical circle diffeomorphisms. In...

3. Baptiste Cerclé (Paris-Saclay)- Towards integrability of Toda conformal field theories.

12/01/2022, 09:50

Short talks

Toda conformal field theories are a family of two-dimensional conformal field theories indexed by semi-simple and complex Lie algebras. One of their features is that, in addition to conformal symmetry, they enjoy an extended level of symmetry encoded by W-algebras. Besides, they can be defined via a path integral similar to the one of Liouville theory for which they provide a natural...

4. Weronika Czerniawska (UNIGE) - Selective Integration on Adelic Spaces and the Riemann-Roch theorem

12/01/2022, 10:15

Short talks

One cannot directly integrate over 2-dimensional geometric adeles associated to arithmetic and geometric surfaces, since they are are not locally compact spaces. Nevertheless it is still possible to conduct selective integration by choosing locally compact subquotient spaces. This leads to new integral representations of various geometric and arithmetic invariants and to new proofs of the...

5. Hadi Nahari (Lyon) - Morita equivalence of singular Riemannian foliations and I-Poisson geometry

12/01/2022, 10:40

Short talks

We define the notion of Morita equivalence for singular Riemannian foliations (SRFs) such that the underlying singular foliations are Hausdorff-Morita equivalent as recently introduced by Garmendia and Zambon. Then we introduce the category of I-Poisson manifolds where its objects are just Poisson manifolds together with appropriate ideals of smooth functions, but its morphisms are an...