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

[Igor Khavkine]

Dear All,

The video recording of the talk by Ruben Louis from this week is now 
available on YouTube at

   https://youtu.be/kNaZLvK1E5U

The slides and the original paper are available from

   https://users.math.cas.cz/~hvle/PHK/RubendifferentialZgraded_2026.pdf
   https://arxiv.org/abs/2512.23148

The links have also been recorded at the ResearchSeminars announcement

   https://researchseminars.org/talk/PHK-cohomology-seminar/158/

Best,

Igor

On 4/6/26 1:00 PM, sender of seminar announcement via phk_seminar wrote:
> 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 <https://arxiv.org/abs/2512.23148>
> 
> ----------------------------------------------------
> 
> 
> 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 <https://cesnet.zoom.us/ 
> j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09>
> 
> 
> Meeting ID:99598413922
> 
> Passcode:Galois
> 
> -----------------------------------------------------------------------
> 
> On Wednesday April 15 Alexei Kotov shall give a talk on Geometry through 
> the Lens of dg Manifolds <https://www.math.cas.cz/index.php/events/ 
> event/4132>
> 
> 
> 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
> https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
> 
> 
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