Recent content by Therodre

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    What is the Tangent Space to the Unitary Group?

    I don't know if that's whay you meant by But the exponential map is not in general surjective form the Lie algebra of the group to the identity component of the group.
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    Are Real Numbers R a Subset of Complex Numbers C?

    I had not seen disregardthat's answer. I have to disagree again, you say that a colimit is only unique up to unique isomorphism (uui in short) as a (co-)cone. Nut a colimit is a co-cone. And certainly not only the object to which the arrow point, it is the object together with the arrows. If L...
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    Are Real Numbers R a Subset of Complex Numbers C?

    Something can certainly be well defined and have many automorphism (and thus not be unique up to unique isomorphism) the field of complex number is typically such a thing. But such a thing will not satisfy a universal property in the corresponding category. An object that satisfies a universal...
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    Are Real Numbers R a Subset of Complex Numbers C?

    Well you're exemple looks confusing to me because as an exemple of object that is unique up to isomorphism you take an object that is unique up to unique isomorphism. My point was that when objects are uniquely isomorphic then there's no harm in identifying them. Your example is a good...
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    Are Real Numbers R a Subset of Complex Numbers C?

    Hi, I fail to see why that would be confusing. C is naturally endowed with a real 2-dimensional Vector space structure, ans also with a field structure (thus a complex 1-dimensional vector space structure). Although i would not say that two isomorphic structure are as close as it gets to being...
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    2D slice of a 6D Calabi-Yau manifold , and other?

    Actually no, to be projective you need at least to be Kähler, and some compact complex surfaces are not even Kähler, like Hopf surface. There are cohomological obstructions to being projective, for instance, all your H^p for p odd must be of even rank, this is not the case for Hopf surfaces...
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    Langlands Programs: Learn What They Are & Why You're Curious

    Hi, It is a vast and deep generalisation of class field theory. But answering to such a broad question would require a long and possibly technical message. Have you tried wiki? Can you narrow your questions about the langlands program a tad? Here is the gist of the Langlands Program (well...
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    Number Theory: Why always elementary proofs?

    Au contraire! I'd say that, generally speaking, number theorist as well as algebraic geometer (and... come to think of it, almost all mathematicians) prefer conceptual proofs, that give a good understanding of the situation, rather than a clever trick, which can be nice of course, but sometimes...
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    What is so special about elliptic curves?

    Well, that certainly is a pickle. Algebraic geometry is one of the broadest and most important field in mathematics. It has deep connections with almost every area of mathematics, and even theoretical physics (through complex geometry). Number theory, complex geometry, algebraic topology...
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    The nature of the dirac delta function

    Your equation has no meaning at x=0. You have equality of your two sides for all x non zero. There's not much more that can be said.
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    The nature of the dirac delta function

    Well, 0/x is just the zero function over ℝ-{0}, so... your equation is tantamount to 1/x=1/x over ℝ-{0}, which is of course correct.
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    The nature of the dirac delta function

    The dirac delta function is not a function. It is often presented as the function satisfying f(x)=0 for x non zero, f(0)=∞, and such that ∫f=1. Of course no such function exists, and its actual definition is more sophisticated. It is not really a bad way to picture that "function" in your...
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    The nature of the dirac delta function

    Hi, This won't work, because your definition of the dirac delta "function" is heuristical, and if you "rigorize" it, your equation won't work (if you actually to try to make it rigorous, you'll face another problem, namely that 1/x is not locally integrable, and you'll have to look at what is...
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    What is so special about elliptic curves?

    Hi, I'm not sure the best way to get why Elliptic Curves are important, is to understand the relationship between then and Fermat's Theroem. To be honnest, the relationship seems rather fortuitous, and to this day, we do not have a very deep understanding of the nature of this link, if it is...
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