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Talks by Urs Frauenfelder and Nikita Nikolaev

Jun 30, 2020 from 05:00 PM to 06:00 PM (Europe/Madrid / UTC200)
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The informal talks organized by the b-lab have now external guests! We are happy to welcome Urs Frauenfelder and Nikita Nikolaev, who will offer the following short lectures:

Delayed Potentials and Weber's Electrodynamics

Speaker: Urs Frauenfelder

When: Tuesday 30th of June, at 17:00 - 18:00.

Abstract: This is joint work with Joa Weber.

We first discuss work of Carl Neumann from 1868 about a delayed Coulomb potential and its relation to the electrodynamic potential of Wilhelm Weber. Then we explain how Weber's Electrodynamics can be interpreted as a Hamiltonian system and how it is related to Riemannian and Lorenzian geometry. Finally we quantize the system.

Abelianisation of Meromorphic Connections and Spectral Coordinates on their Moduli Spaces

Speaker: Nikita Nikolaev

When: Friday 3rd of July, at 17:00 - 18:00.

Abstract: Recently, I began developing a mathematical theory of abelianisation for meromorphic connections [arXiv:1902.03384] (so far, only for the case of SL(2)-connections with at most log-singularities). This technique recently emerged in the physics of supersymmetric gauge theories (with distinct echoes of the WKB method from the early days of quantum mechanics). The vision is that it provides a generalisation of the abelianisation of Higgs bundles (aka the spectral correspondence, a key step in the analysis of Hitchin integrable systems) to flat bundles: thus, flat bundles of rank $n$ on a complex curve are put in correspondence with flat line bundles over an $n$-fold cover (the spectral curve). One important proposed consequence of this correspondence is a construction of a cluster atlas of Darboux coordinate charts on character varieties and de Rham moduli spaces. I will present some of my recent progress towards this vision.


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