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

[Igor Khavkine]

Dear All,

The video recording of the talk by Elizaveta Vishnyakova from last week 
is now available on YouTube at

   https://youtu.be/SsY5xR4dd_E

The slides are available from

   https://users.math.cas.cz/~hvle/PHK/Vishnyakovacovering2026.pdf

Both links have also been recorded at the ResearchSeminars announcement

   https://researchseminars.org/talk/PHK-cohomology-seminar/152/

Best,

Igor

On 3/30/26 12:00 PM, sender of seminar announcement via phk_seminar wrote:
> 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 <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) 
> <https://www.math.cas.cz/index.php/events/event/4143>
> 
> at 14.00 (30 minutes later than usual).
> 
> 
> 
> 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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