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Hamiltonian systems, symplectic flows, classical integrable systems

9 votes

Lagrangian Submanifolds in Deformation Quantization

One has to choose an identification of a tubular neighborhood $U$ of $L$ in $M$ with a tubular neighborhood $V$ of the zero section of the normal bundle $NL$. Once one has done this, it means that w …
DamienC's user avatar
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8 votes

Theory of $n$-truncated $A_\infty$ categories/functors?

$A_n$-spaces are already discussed in the original paper of Stasheff, Homotopy associativity of H-spaces, I and II. In the linear setting, $A_n$-algebras are discussed e.g. in A∞-algebras, spectral se …
DamienC's user avatar
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5 votes

Quantization of conjugacy classes in a Lie group

Joseph Donin and Andrei Mudrov have worked a lot on this question... the quantization of conjugacy classes seems to be related to dynamical r-matrices and and the so-called reflection equation. See e. …
DamienC's user avatar
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5 votes

What is the current status of derived differential geometry?

I would recommend that you read the introduction of Pelle Steffens's foundational preprint on Derived $C^\infty$ geometry. The preprint is 205 pages long, but the introduction is "only" 35 pages :-) I …
DamienC's user avatar
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2 votes

What's the relation between the heat kernel proof of the index theorem and deformation quant...

I think you should have a look at the various papers of Louis Boutet de Monvel. But there is actually a construction of star-products on a symplectic manifold which makes use of the index theorem, due …
DamienC's user avatar
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2 votes
Accepted

About the geometry of completely integrable systems

preliminary remark I assume that being independant for functions here means that their differentials at any point are linearly indenpendant (and not at almost any point, like it is sometimes assumed. …
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