[PHK_seminar] [Cohomology]Wednesday 1 Apr, Elizaveta Vishnyakova

[Petr Somberg]

 This is just a gentle reminder of our seminar!

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> Cohomology in algebra, geometry, physics and statistics
> Wednesday, 1 April 2026 - 13:00 to 14:00
> Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1,   ZOOM meeting
>
>
> Speaker: Elizaveta Vishnyakova, Department of Math. UFMG, Belo Horizonte,
> Brazil
> Title: About Graded coverings of supermanifolds and their applications
> Abstract
>
>
> 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.
>
>
>
>
> 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 \( \mathbb{Z} \to 0 \).)
>
>
>
>
> 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.
>
> ----------------------------------------------
> The  seminar  starts  30 minutes  earlier than usual.
> We shall open ZOOM meeting at 12.45 for  virtual coffee and close ZOOM at
> 14.30
>
>
>
> Join Zoom Meeting
>
>
>
> https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09
>
>
>
> Meeting ID:99598413922
> Passcode:Galois
>
>
>
> -------------------------------------------------------------------------
> -----
>
>
> On Wednesday April 8 Ruben Louis  shall give a talk    On construction of
> differential Z-graded varieties (Joint work with A. Hancharuk) at 14.00
> (30 minutes later  than usual).
>
>
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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
> https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
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