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<title>Cohomology in algebra, geometry, physics and statistics</title>
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Wednesday, 1 April 2026 - 13:00 to 14:00 <br />
Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, ZOOM meeting
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Speaker: Elizaveta Vishnyakova, Department of Math. UFMG, Belo Horizonte, Brazil<br />
Title: About Graded coverings of supermanifolds and their applications
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Abstract <br />
<p>In geometry, the concept of a covering space is classical and well established. A familiar example is the universal covering \( p: \mathbb{R} \to S^1 \), given by \( t \mapsto \exp(it) \). Analogous constructions appear in algebra as well—for instance, in the theory of modules over rings, where one encounters flat or torsion-free coverings. Although they arise in different contexts, these notions share a common underlying idea: an object from a given category is covered by an object belonging to a smaller (or different) category in such a way that certain universal properties are satisfied.</p><p><br></p><p>In their paper "Super Atiyah classes and obstructions to splitting of supermoduli space," Donagi and Witten introduced a construction of the first obstruction class to the splitting of a supermanifold. Later, we observed that the infinite prolongation of their construction satisfies universal properties analogous to those found in other covering theories. In other words, this construction yields a covering of a supermanifold in the category of graded manifolds associated with the nontrivial homomorphism \( \mathbb{Z} \to \mathbb{Z}_2 \). Moreover, the space of infinite jets can also be viewed as a covering of a (super)manifold in the category of graded manifolds corresponding to the homomorphism \( \mathbb{Z} \times \mathbb{Z}_2 \to \mathbb{Z}_2 \), given by \( (m, \bar{n}) \mapsto \bar{n} \). (For ordinary manifolds, this homomorphism reduces to the trivial map \( \mathbb{Z} \to 0 \).)</p><p><br></p><p>Our talk is devoted to the current state of the theory of graded coverings, including the general framework, key examples, and a presentation of our recent results.</p><p>----------------------------------------------</p><p class="ql-align-justify">The seminar starts <strong>30 minutes earlier than usual</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 12.45 for virtual coffee and close ZOOM at 14.30</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="background-color: rgb(255, 255, 255); color: rgb(17, 85, 204);">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"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">------------------------------------------------------------------------------</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">On Wednesday April 8 </span><strong>Ruben Louis </strong>shall give a talk<strong> </strong><strong style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);"> </strong><a href="https://www.math.cas.cz/index.php/events/event/4143" rel="noopener noreferrer" target="_blank" style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);"><strong>On construction of differential Z-graded varieties</strong> (Joint work with A. Hancharuk)</a></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);"> at 14.00 (30 minutes later than usual).</span></p><p><br></p><p><br></p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/16
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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
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