[PHK_seminar] [Cohomology]Wednesday 6 Nov, Zoran Skoda

[Petr Somberg]

 The seminar for today is going to start soon!


> Cohomology in algebra, geometry, physics and statistics
> Wednesday, 6 November 2024 - 13:30 to 14:30
> Place: ZOOM meeting
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> Speaker: Zoran Skoda, University of Zadar
> Title: Braiding phenomena in cyclic homology
> Abstract
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> Unlike the case of Hochschild (co)homology and most other cohomology
> theories, the original constructions of cyclic (co)homology in 1980s did
> not have coefficients. In a variant, Hopf cyclic homology, the
> coefficients were discovered around 2000 as stable anti-Yetter--Drinfeld
> modules, reminding of Yetter--Drinfeld (YD) modules familiar from the
> center construction. Bressler observed that cyclic nerve of a groupoid is
> determined by the ordinary nerve of its inertia groupoid. Thus I
> conjectured in late 2002 that passing to the appropriate monoidal
> category of sheaves one could replace the (sheaves over) inertia by
> taking the monoidal center of the (sheaves over) original groupoid. This
> has been proved in 2004 in two variants, well known by Hinich on orbifold
> case and another by me. As monoidal center involves braiding, it pointed
> that requiring or adding braidings can provide examples of cyclic
> homology with coefficients; I constructed some toy examples using
> standard resolutions and Bohm, Stefan and others independently much more
> realistic examples using distributive laws. It fits also with work of
> Kaledin who introduced new kind of traces to treat coefficients. Kowalzig
> has recently also explained anti- for YD modules in the case of centers
> of certain bimodule categories. This talk is to outline motivations and
> my present picture of these braiding (or Yang--Baxter) phenomena in
> cyclic homology.
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> We shall open ZOOM at 13.15 for virtual coffee and close the room at
> 15:00
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> Join Zoom Meeting
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> https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRU9
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> MeetingID:99598413922
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> Passcode:Galois
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> For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/16
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> Cohomology in algebra, geometry, physics and statistics mailing list
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