Seminar talk, 4 January 2017: Difference between revisions
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| speaker = Theodore Voronov | | speaker = Theodore Voronov | ||
| title = Microformal geometry and its applications | | title = Microformal geometry and its applications | ||
| abstract = The talk will discuss a new notion of microformal" (or "thick") morphisms of smooth (super)manifolds that generalizes ordinary smooth maps. These new morphisms act on smooth maps via pullback that however is a nonlinear transformation. (More precisely, a formal nonlinear differential operator). There appears a formal category, which is a "thickening" of the usual category of (super)manifolds. The construction appeared in relation to homotopic analogs of Poisson structures, for which it gives | | abstract = The talk will discuss a new notion of microformal" (or "thick") morphisms of smooth (super)manifolds that generalizes ordinary smooth maps. These new morphisms act on smooth maps via pullback that however is a nonlinear transformation. (More precisely, a formal nonlinear differential operator). There appears a formal category, which is a "thickening" of the usual category of (super)manifolds. The construction appeared in relation to homotopic analogs of Poisson structures, for which it gives <math>L_\infty</math> morphisms. Another application is an "adjoint operator" for a nonlinear map of vector bundles. One can define also "quantum microformal morphisms", for which the above is the classical limit. | ||
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| slides = | | slides = | ||
Revision as of 00:48, 21 December 2016
Speaker: Theodore Voronov
Title: Microformal geometry and its applications
Abstract:
The talk will discuss a new notion of microformal" (or "thick") morphisms of smooth (super)manifolds that generalizes ordinary smooth maps. These new morphisms act on smooth maps via pullback that however is a nonlinear transformation. (More precisely, a formal nonlinear differential operator). There appears a formal category, which is a "thickening" of the usual category of (super)manifolds. The construction appeared in relation to homotopic analogs of Poisson structures, for which it gives morphisms. Another application is an "adjoint operator" for a nonlinear map of vector bundles. One can define also "quantum microformal morphisms", for which the above is the classical limit.
References:
arXiv:1409.6475, arXiv:1411.6720, arXiv:1506.02417, arXiv:1512.04163
