added pointer to:

- Alan Weinstein,
*Deformation quantization*, Séminaire Bourbaki volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Talk no. 789 [numdam:SB_1993-1994__36__389_0]

I have brushed-up the two original bibitems (which had been both incomplete and broken):

François Bayen, Moshé Flato, Christian Fronsdal, , André Lichnerowicz, Daniel Sternheimer,

*Deformation theory and quantization. I. Deformations of symplectic structures.*, Annals of Physics**111**1 (1978) 61-110 [doi:10.1016/0003-4916(78)90224-5]François Bayen, Moshé Flato, Christian Fronsdal, André Lichnerowicz, Daniel Sternheimer,

*Deformation theory and quantization. II. Physical applications*, Annals of Physics**111**1 (1978) 111-151 [doi:10.1016/0003-4916(78)90225-7]

renaming this entry from “deformation quantization” to “formal deformation quantization” so that *deformation quantization* can serve as a disambiguation page with *strict deformation quantization*

there is an old MO discussion wondering about this

]]>added to the section *Motivic Galois group action on the space of quantizations* a pointer to the proof by Dolgushev that $\pi_0$ of the space of formal deformation quantizations of an $\mathbb{R}^n$ 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)

]]>Added the following quote from section 1.4

- Sergei Gukov, Edward Witten,
*Branes and Quantization*, Adv. Theor. Math. Phys. 13 (2009) 1–73, (arXiv:0809.0305, euclid)

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.

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.

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.

]]>Thanks!

I have added a few more links.

]]>Done, also added a page for John Jones.

]]>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).

]]>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. (?))

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? )

]]>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.

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