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<title>Cohomology in algebra, geometry, physics and statistics</title>
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Wednesday 9 October 2024 - 13:30 to 14:30 <br />
Place: ZOOM metting
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Speaker: Maxim Grigoriev, Mons University<br />
Title: Graded geometry of local gauge theories
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Abstract <br />
<p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">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.</span></p><p><br></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">______________________________________________________________________________________</span></p><p><br></p><p><span style="background-color: rgb(246, 246, 246); color: rgb(0, 0, 255);">We shall open ZOOM at 13.15 for veritual coffee and close the room at 15:00</span></p><p><br></p><p><span style="color: rgb(0, 0, 255); background-color: rgb(246, 246, 246);">Join Zoom Meeting</span></p><p><br></p><p><a href="https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09" rel="noopener noreferrer" target="_blank" style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 204);">https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRU</a>9</p><p><br></p><p><span style="color: rgb(0, 0, 255); background-color: rgb(246, 246, 246);">MeetingID:99598413922</span></p><p><br></p><p><span style="color: rgb(0, 0, 255); background-color: rgb(246, 246, 246);">Passcode:Galois</span></p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/16
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Cohomology in algebra, geometry, physics and statistics mailing list <br />
phk_seminar@math.cas.cz <br />
https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
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