Manchester Geometry Seminar - Theodore Voronov
| Dates: | 3 February 2025 |
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| Times: | 15:00 - 16:00 |
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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 (Manchester)
Title: On a complex arising from variation of integrals and on the superanalog of differential forms
Abstract: All known constructions of differentials in homological algebra fall into one or two types: the combinatorial (simplicial) differential, and the Koszul or de Rham type differential. In both cases, the identity d^2=0 comes about from canceling terms in alternating sums. It turns out that there is a differential of an entirely geometrical nature defined in terms of variation of integral ("action"), without any embedded alternation, for which the equality d^2=0 holds for geometrical reasons. Such a differential gives a "complex of Lagrangians" where cohomological degree is the number of independent variables (which increases under the action of differential). The de Rham complex can be presented as its subcomplex giving the de Rham differential a variational interpretation. For supermanifolds, this leads to the superanalog of de Rham theory that cannot be obtained by naive algebraic approach . It has connections with integral geometry in the sense of Gelfand-Gindikin-Graev and Gelfand's general hypergeometric equations. Another application is to the classical Helmholtz criterion in the inverse problem of calculus of variations.
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Frank Adams Room 1
Alan Turing Building
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