Theodore Voronov - Thick morphisms and spinor representation
| Dates: | 3 October 2019 |
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| Times: | 14:30 - 15:30 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Theodore Voronov |
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Theodore Voronov joins us for the Geometry, Topology and Mathematicals Physics Seminar.
Abstract:
Thick morphisms (also called microformal morphisms) between manifolds or supermanifolds are a generalization of smooth maps --- and which are not usual maps, but rather relation between the corresponding cotangents, equipped with some extra data. They were discovered for the purpose of constructing L-infinity morphisms of higher (homotopy) brackets, when manifolds in question have an S-infinity ("homotopy Schouten") or P-infinity ("homotopy Poisson") structure. The key feature of thick morphisms is that they induce NONLINEAR, in general, pullbacks on functions. (This nonlinearity is exactly the feature making them useful for homotopy brackets purposes.) It was also found that there is a "quantum version" of thick morphisms in the form of integral operators of special type. Such "quantum pullbacks" can be seen as a generalization of spinor representation, as it became clear recently. I will try to explain all that.
(Based on a joint work with H. Khudaverdian, see https://arxiv.org/abs/1909.00290.)
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Frank Adams Room 1
Alan Turing Building
Manchester
