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SUMMARY:Hovhannes Khudaverdian
DTSTART:20200615T120000Z
DTEND:20200615T140000Z
DTSTAMP:20260423T023055Z
UID:GDEq/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/8/">Non
 -linear homomorphisms and thick morphisms</a>\nby Hovhannes Khudaverdian a
 s part of Geometry of differential equations seminar\n\n\nAbstract\nIn 201
 4\, Voronov introduced the notion of thick morphisms of (super)manifolds a
 s a tool for constructing $L_{\\infty}$-morphisms of homotopy Poisson alge
 bras. Thick morphisms generalise ordinary smooth maps\, but are not maps t
 hemselves. Nevertheless\, they induce pull-backs on $C^{\\infty}$ function
 s.  These pull-backs are in general non-linear maps between the algebras o
 f functions which are so-called "non-linear homomorphisms". By definition\
 , this means that their differentials are algebra homomorphisms in the usu
 al sense. The following conjecture was formulated: an arbitrary non-linear
  homomorphism of algebras of smooth functions is generated by some thick m
 orphism. We prove here this conjecture in the class of formal functionals.
  In this way\, we extend the well-known result for smooth maps of manifold
 s and algebra homomorphisms of $C^{\\infty}$ functions and\, more generall
 y\, provide an analog of classical "functional-algebraic duality" in the n
 on-linear setting.\n
LOCATION:https://researchseminars.org/talk/GDEq/8/
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