<!DOCTYPE html>
<html>
<head>
<title>Cohomology in algebra, geometry, physics and statistics</title>
</head>
<body>
<p>
Wednesday, 8 April 2026 - 14:00 to 15:00 <br />
Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, ZOOM meeting
</p>
<p>
Speaker: Ruben Louis, University of Illinos Urbana-Champaign Urbana<br />
Title: On construction of differential Z-graded varieties (Joint work with A. Hancharuk)
</p>
<p class="ql-ed">
Abstract <br />
<p>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.</p><p>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.</p><p>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.</p><p>These constructions also yield applications to singular foliation theory, extending results of C. Laurent-Gengoux, S. Lavau, and T. Strobl. Explicit examples are provided.</p><p><a href="https://arxiv.org/abs/2512.23148" rel="noopener noreferrer" target="_blank">https://arxiv.org/abs/2512.23148</a></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">----------------------------------------------------</span></p><p><br></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">This lecture starts </span><strong class="ql-font-monospace" style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">30 minutes later</strong><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace"> </span><strong class="ql-font-monospace" style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">at 14:00.</strong></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">We shall open ZOOM meeting at 13.45 for (virtual) coffee and close ZOOM at 15.30</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Join Zoom Meeting</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><a href="https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09" rel="noopener noreferrer" target="_blank" style="color: rgb(17, 85, 204); background-color: rgb(255, 255, 255);">https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09</a></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Meeting ID:99598413922</span></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Passcode:Galois</span></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">-----------------------------------------------------------------------</span></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">On Wednesday April 15 </span>Alexei Kotov shall give a talk on <span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);"> </span><a href="https://www.math.cas.cz/index.php/events/event/4132" rel="noopener noreferrer" target="_blank"> Geometry through the Lens of dg Manifolds </a></p><p><br></p>
</p>
<p>
For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/16
</p>
<p>
Cohomology in algebra, geometry, physics and statistics mailing list <br />
phk_seminar@math.cas.cz <br />
https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
</p>
</body>
</html>