BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Henrik Winther
DTSTART:20230301T162000Z
DTEND:20230301T180000Z
DTSTAMP:20260423T023049Z
UID:GDEq/82
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/82/">Je
 t functors in noncommutative geometry</a>\nby Henrik Winther as part of Ge
 ometry of differential equations seminar\n\n\nAbstract\nWe construct an in
 finite family of endofunctors $J_d^n$ on the category of left $A$-modules\
 , where $A$ is a unital associative algebra over a commutative ring $k$\, 
 equipped with an exterior algebra $\\Omega^\\bullet_d$. We prove that thes
 e functors generalize the corresponding classical notion of jet functors. 
 The functor $J_d^n$ comes equipped with a natural transformation from the 
 identity functor to itself\, which plays the rôle of the classical prolon
 gation map. This allows us to define the notion of linear differential ope
 rator with respect to $\\Omega^{\\bullet}_d$. These retain most classical 
 properties of differential operators\, and operators such as partial deriv
 atives and connections belong to this class. Moreover\, we construct a fun
 ctor of quantum symmetric forms $S^n_d$ associated to $\\Omega^\\bullet_d$
 \, and proceed to introduce the corresponding noncommutative analogue of t
 he Spencer $\\delta$-complex. We give necessary and sufficient conditions 
 under which the jet functor $J_d^n$ satisfies the jet exact sequence\, $0\
 \rightarrow S^n_d \\rightarrow J_d^n \\rightarrow J_d^{n-1} \\rightarrow 0
 $. This involves imposing mild homological conditions on the exterior alge
 bra\, in particular on the Spencer cohomology $H^{\\bullet\,2}$.\n\nThis i
 s a joint work with K. Flood and M. Mantegazza.\n
LOCATION:https://researchseminars.org/talk/GDEq/82/
END:VEVENT
END:VCALENDAR