[PHK_seminar] [Cohomology]Wednesday 9 Oct, Maxim Grigoriev

[Petr Somberg]

 This is just a remainder of our seminar for today!

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> Cohomology in algebra, geometry, physics and statistics
> Wednesday 9 October 2024 - 13:30 to 14:30
> Place: ZOOM metting
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> Speaker: Maxim Grigoriev, Mons University
> Title: Graded geometry of local gauge theories
> Abstract
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> Gauge PDEs generalize AKSZ sigma models to the case of general local
> gauge theories. Despite being very flexible and invariant these
> geometrical objects are usually infinite-dimensional and are difficult to
> define explicitly, just like standard infinitely-prolonged PDEs. We
> propose a notion of a weak gauge PDE where the nilpotency of the BRST
> differential is relaxed in a controllable way. In this approach a
> nontopological local gauge theory can be described in terms of a
> finite-dimensional geometrical object. Moreover, among such objects one
> can find a minimal one which is unique in a certain sense. In the case of
> a Lagrangian system, the respective weak gauge PDE naturally arises from
> the presymplectic structure. We prove that any weak gauge PDE determines
> the standard jet-bundle BV formulation of the underlying gauge theory,
> giving an unambiguous field-theoretical interpretation of these objects.
> The relation to the covariant phase space and the multisymplectic
> approaches is also discussed. The formalism is illustrated by a variety
> of models including (super) gravity, (chiral) Yang-Mills, and a
> non-Lagrangian self-dual Yang-Mills theory.
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> We shall open ZOOM at 13.15 for  veritual coffee and close the room at
> 15:00
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> Join Zoom Meeting
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> https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRU9
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> MeetingID:99598413922
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> Passcode:Galois
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> For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/16
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