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Jan
23
awarded  Custodian
Jan
23
reviewed Approve Is there an analytic function such that
Jan
23
comment Why $M \times S^1 $ becomes a manifold with G_2 structure, when $M$ is CY?
As suggested by Igor Belegradek, this is essentially obvious if one uses the correct definition of $G_2$. To give a useful answer one should know which definition of $G_2$ you are starting with.
Dec
30
comment Why should affine lie algebras and quantum groups have equivalent representation theories?
Related: mathoverflow.net/questions/178113/… The "natural" relation indeed involves $k$ positive integer and integrable representations but the proof uses the theorem of Kazhdan-Lusztig via a relation between level $k-h$ and $-k-h$ due to Finkelberg (-k<0 so one can applies Kazhdan-Lusztig).
Dec
28
comment Number theory and physics
From a mathematical point of view this story is related to the non-commutative tori and so to the various ways to "go at infinity" in the moduli space of elliptic curves.
Dec
28
comment Number theory and physics
from a circle of ideas which are only partly mathematically well founded, which have been developed by physicists and which have evolved continuously from a "real" physics problem along an often complicated history.
Dec
28
comment Number theory and physics
This question seems to partly relies on the difference between "real" and "unreal" physics. I don't think that a mathematician should care about what is "real" in physics. When someone says "the motivation comes from physics", he probably means theoretical physics and it is maybe what "unrealistic physics" is. But the fact that the part of theoretical physics in question is "real" or not, which probably means "directly related to the experience", is irrelevant from the mathematician point of view. In general, "come from physics" does not mean "come from a precise experimental fact" but come...
Dec
17
answered Derived categories of arithmetic schemes?
Dec
11
comment Does quantum mechanics ever really quantize classical mechanics?
... the space of classical states (which is not a vector space)
Dec
11
comment Does quantum mechanics ever really quantize classical mechanics?
It seems to me that there is a confusion between states and observables in this question. The analogue of the classical $\frac{d}{dt}\rho = \{H,\rho\}$, where $\rho$ is a function on the phase space, so a classical observable, is $\frac{d}{dt}A=[H,A]$ where $A$ is an operator acting on the space of states, i.e. a quantum observable. The algebra of quantum observables is indeed a deformation of the algebra of classical observables but I don't know what "relevant representations" means. The algebra of quantum algebra acts on the space of quantum states but the classical algebra does not act on..
Nov
4
awarded  Nice Question
Sep
20
comment When is the tangent bundle of a manifold naturally a complex manifold?
In the mirror symmetry story, this kind of argument appears when $M$ as a extra structure: the structure of an affine manifold. Then it is true that the tangent bundle $TM$ of an affine manifold $M$ is naturally a complex manifold (where "naturally" means preserved by diffeomorphisms coming from diffeomorphisms of $M$ preserving the affine structure) (and of course not from any diffeomorphism of $M$ as indicated in Robert Bryant answer).
Sep
14
revised What is the Hochschild cohomology of the Fukaya-Seidel category?
edited body
Sep
13
revised What is the Hochschild cohomology of the Fukaya-Seidel category?
added 8 characters in body
Sep
13
asked What is the Hochschild cohomology of the Fukaya-Seidel category?
Sep
4
awarded  Nice Question
Sep
4
asked Del Pezzo surfaces and homotopy groups of spheres
Sep
4
comment Intrinsic definition of the weight filtration
I could be interested by a description in terms of algebraic cycles, so probably I would like to know what Chow-weight truncations are.
Aug
30
asked Intrinsic definition of the weight filtration
Aug
19
awarded  Enlightened