KolloquiumGRK Multisymplectic observables and higher Courant algebroids |  |
Speaker:Antonio Miti, Università Cattolica del Sacro Cuore
Organizer:Mathematisches Institut
Details:
Multisimplectic manifolds are a straightforward generalization of symplectic manifolds where one considers closed non-degenerate k-forms in place of 2-forms.
Recent works by Rogers and Zambon showed how one could associate such a geometric structure with two higher algebraic structures: an L∞-algebra of observables and an L∞- algebra of sections of the higher Courant algebroid twisted by the multisymplectic form ω.
The scope of this talk is to report on joint work with Marco Zambon (arXiv:2209.05836).
Our main result is proving the existence of an L∞-embedding between the above two L∞-algebras generalizing a construction already found by Rogers around 2012 for multisymplectic 3-forms only. Moreover, we display explicit formulae for the sought morphism involving the Bernoulli numbers.
Although this construction is essentially algebraic, it also admits a geometric interpretation when declined to the particular case of pre-quantizable symplectic forms. Moreover, the latter case provides some evidence that this construction may be related to the higher analog of geometric quantization for integral multisymplectic forms.
Recent works by Rogers and Zambon showed how one could associate such a geometric structure with two higher algebraic structures: an L∞-algebra of observables and an L∞- algebra of sections of the higher Courant algebroid twisted by the multisymplectic form ω.
The scope of this talk is to report on joint work with Marco Zambon (arXiv:2209.05836).
Our main result is proving the existence of an L∞-embedding between the above two L∞-algebras generalizing a construction already found by Rogers around 2012 for multisymplectic 3-forms only. Moreover, we display explicit formulae for the sought morphism involving the Bernoulli numbers.
Although this construction is essentially algebraic, it also admits a geometric interpretation when declined to the particular case of pre-quantizable symplectic forms. Moreover, the latter case provides some evidence that this construction may be related to the higher analog of geometric quantization for integral multisymplectic forms.
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Type:Colloquium
Language:English
Category:Research
External link:https://uni-goettingen.zoom.us/j/91336854872
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Direct link to event:https://events.goettingen-campus.de/event?eventId=844690
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