[PHK_seminar] [Cohomology]Wednesday 8 Apr, Ruben Louis

[Petr Somberg]

 This is just a gentle reminder of our seminar starting soon!

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> Cohomology in algebra, geometry, physics and statistics
> Wednesday, 8 April 2026 - 14:00 to 15:00
> Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, ZOOM meeting
>
>
> Speaker: Ruben Louis, University  of Illinos Urbana-Champaign Urbana
> Title: On construction of differential Z-graded varieties  (Joint work
> with A. Hancharuk) Abstract
>
>
> Given a commutative unital algebra O, a proper ideal I⊂O, and a
> positively graded differential variety over O/I, we construct a Z-graded
> extension whose negative part is an arborescent Koszul–Tate resolution of
> O/I. This extension is obtained by means of an explicit algorithm that
> exploits the homotopy retract data of the arborescent Koszul–Tate
> resolution, thereby significantly reducing the number of homological
> computations required in the construction.
>
> When the positively graded differential variety is defined over O and
> preserves the ideal I, the extension admits a canonical and explicit
> description in terms of decorated trees together with the associated
> computed data.
>
> As a by-product, to every Lie–Rinehart algebra over the coordinate ring
> of an affine variety W, we associate an explicit differential Z-graded
> variety. Its negative component is the arborescent Koszul–Tate resolution
> of the coordinate ring​ of W, while its positive component is the
> universal dg-variety of the given Lie–Rinehart algebra.
>
> These constructions also yield applications to singular foliation theory,
> extending results of C. Laurent-Gengoux, S. Lavau, and T. Strobl.
> Explicit examples are provided.
>
>
> https://arxiv.org/abs/2512.23148
>
>
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> This lecture  starts   30 minutes  later  at  14:00.
> We shall open  ZOOM meeting at 13.45 for (virtual) coffee and close ZOOM
> at 15.30
>
>
> Join Zoom Meeting
>
>
>
> https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09
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>
>
> Meeting ID:99598413922
> Passcode:Galois
> -----------------------------------------------------------------------
> On Wednesday   April  15   Alexei Kotov  shall give a talk on   Geometry
> through the Lens of dg Manifolds
>
>
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>
>
> For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/16
>
>
> Cohomology in algebra, geometry, physics and statistics mailing list
> phk_seminar at math.cas.cz
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