Fwd: Fwd: Seminar announcement TODAY 4pm

[ICTP Math Section]

Begin forwarded message:

> *From: *Barbara Fantechi <fantechi at sissa.it>
> *Date: *Jul 7, 2025 at 10:11
> *To: *math-users <math-users at lists.sissa.it>
> *Subject: Seminar announcement TODAY 4pm*
>
>
> Dear everyone, sorry for last-minute announcement
>
> Today at 4pm in room 136
>
> Dr Tim Henke (Porto)
>
> Title: Topological CS/WZNW duality: equivalence of the Hitchin and KZ 
> connections
>
> Abstract: The Pauly Isomorphism identifies the geometric quantisation 
> of the moduli space of parabolic bundles over a marked Riemann surface 
> with the space of conformal blocks associated to the same marked 
> surface. This isomorphism is the mathematical formalisation of the 
> physical duality between Chern–Simons gauge theory and WZNW conformal 
> field theory. Both vector spaces depend crucially on the complex 
> structure of the surface, but the physical duality is understood to be 
> purely topological. This implies that the Pauly Isomorphism should be 
> projectively flat with respect to variations of the complex structure. 
> These are given by the Hitchin connection for the moduli space and the 
> Knizhnik–Zamolodchikov connection on the sheaf of conformal blocks. 
> For higher genera the equivalence follows from the non-parabolic case. 
> We treat the genus 0 case that is crucial for developing topological 
> invariants from the moduli theory.
> I will explain the construction of the different spaces, define the 
> bundles on both sides of the isomorphism and sketch the ideas that go 
> into the proof.
>
========================================
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

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