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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 12th 2012

    I have expanded the Idea-section at deformation quantization a little, and moved parts of the previous material there to the Properties-section.

    • CommentRowNumber2.
    • CommentAuthoradeelkh
    • CommentTimeJan 8th 2013
    • (edited Jan 8th 2013)

    I just added some rough notes from a lecture John Jones gave this morning (http://www.newton.ac.uk/programmes/GDO/gdow01). I didn't manage to get all the TeX right the first time, and the nLab seems down now so I will have to fix it later.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 8th 2013

    Thanks!! That’s great.

    I’ll maybe go through it in a few minutes to fix the instiki-syntax errors (I guess you were copy-and pasting? )

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 9th 2013

    Ah, I see you are editing right now. I was just about to look into it.

    (It’s strange that the link to HKR theorem does not work. (?))

    • CommentRowNumber5.
    • CommentAuthoradeelkh
    • CommentTimeJan 9th 2013

    I am just not used to the instiki TeX so I usually have to do my best and then keep editing the page until I have fixed everything. For the HKR theorem, I fixed it by making "Theorem" lowercase.

    I will add some remarks on the Deligne conjecture that Jones also made (which I was too tired to type yesterday).

    • CommentRowNumber6.
    • CommentAuthoradeelkh
    • CommentTimeJan 9th 2013

    Done, also added a page for John Jones.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJan 9th 2013

    Thanks!

    I have added a few more links.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 25th 2013

    I am beginning to expand deformation quantization to include the discussion of deformation quantization of field theories by Costello-Gwilliam. So far I began to restructure the Definition-section accordingly. Will now fill in material, as time permits.

    But meanwhile: in the course of this I slightly rearranged the material whose addition was announced in #5, #6 above. For instance the definition of Poisson manifolds and their deformation I moved out of the Properties-section into the Definition-section. This now makes Kontsevich’s theorem sit a bit lonely in a single subsection in the Properties-section. But I guess eventually we should expand there on its proof, which will justify a dedicated subsection after all.

    I am thinking the relation discussed further below to Hochschild and cyclic cohomology deserves to be highlighted and expanded on much more, eventually. I’ll see what I can do. Will be forced offline in a short while, though.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeApr 23rd 2013
    • (edited Apr 23rd 2013)

    I slightly re-arranged the references at deformation quantization. Igor Khavkine rightly amplified to me that Fedosov’s deformation quantization already applies also to (regular) Poisson manifolds, which was not well-reflected in the entry. So I moved that to the top of the list, where it seems to belong, so that Kontsevich’s result is now a little bit below.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2013
    • (edited Jun 12th 2013)

    Added the following quote from section 1.4

    to the Idea-section at deformation quantization (with a tad of commentary):

    Generally speaking, physics is based on [[ strict ]] quantization, rather than [[ formal ]] deformation quantization, although conventional quantization sometimes leads to problems that can be treated by deformation quantization.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeAug 19th 2013
    • (edited Aug 19th 2013)

    added to the section Motivic Galois group action on the space of quantizations a pointer to the proof by Dolgushev that π 0\pi_0 of the space of formal deformation quantizations of an n\mathbb{R}^n is indeed (a torsor over) the Grothendieck-Teichmüller group.

    (Just heard a talk about this at GAP XI. Therefore just a brief pointer, don’t have much time)

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeAug 20th 2013

    there is an old MO discussion wondering about this

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