bio | website | nd.edu/~lnicolae |
---|---|---|
location | University of Notre Dame | |
age | 50 | |
visits | member for | 3 years, 7 months |
seen | 18 hours ago | |
stats | profile views | 6,656 |
I do mostly geometry and topology, with an analytic bias. For the past few years Morse theory has popped up in my research, but not in a conventional way.
Jul 16 |
awarded | Nice Answer |
Jul 8 |
comment |
Inverse problem of Chern Classes
The proof is simple.Any complex line is the pullback of the tautological line bundle over $\mathbb{CP}^\infty$. Next you observe that $\mathbb{CP}^\infty$ is a $K(\mathbb{Z},2)$. |
Jun 25 |
comment |
Complex structure on $S^6$ gets published in Journ. Math. Phys
The question raised is a valid one, though it could be slightly edited to sound less confrontational. Closing this discussion, would do a great disservice to the math community and smacks of censorship. |
Jun 20 |
answered | Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height |
Jun 10 |
awarded | Nice Answer |
Jun 3 |
comment |
Is this differential identity known?
The Fourier transforms of the distributions $(1+x^2)^\lambda$, $\lambda\in\mathbb{C}$, are studied in vol.1 of Gelfand and Shilov's book Generalized Functions, Chap.II, Sec. 2.6. The identity you discovered behaves nicely with respect to the Fourier transform and maybe it follows from the mountain of formulas in the above book. |
Jun 3 |
comment |
Sobolev spaces on compact manifolds
It would work once you show that $P :H^2(M)\to L^2(M)$ is onto. It is not clear to me why, when $M$ is noncompact, the operator $P$, viewed as an unbounded operator $L^2(M)\to L^2(M)$ with domain $H^2(M)$, is self-adjoint. |
Jun 2 |
awarded | Informed |
May 31 |
comment |
Is this a rational function?
By decomposing a rational unction into simple ractions you can get the answer to your question(s). |
May 28 |
comment |
Perturbation of a Fredholm sections which preserves compactness of 0-set
@MadsR.Bisgaard In concrete examples compactness is typically achieved by first obtaining a priori estimates (this is the tricky part) and then invoking some compact embedding results. In the case of symplectic Floer theory or contact homology the compactness is the major headache. |
May 27 |
awarded | Nice Answer |
May 27 |
comment |
Perturbation of a Fredholm sections which preserves compactness of 0-set
The tricky part is the compactness of the zero set. This requires some additional conditions on the original section and the nature of perturbation. The transversality is a consequence of Sard's theorem. |
May 27 |
comment |
Perturbation of a Fredholm sections which preserves compactness of 0-set
You need not feel uncomfortable. In the stated generality the result is not obvious. To obtain such a result you need to have some additional information about the Banach spaces involved, and some additional information on the original section $s$ so that you can get a bit of compactness. |
May 27 |
revised |
$A \wedge A \wedge A$ in Chern-Simons
added 5 characters in body |
May 27 |
answered | $A \wedge A \wedge A$ in Chern-Simons |
May 26 |
comment |
What is the probability that a Gaussian random variable is the largest of three Gaussian random variables?
I have added the word independent in the statement of your question. |
May 26 |
revised |
What is the probability that a Gaussian random variable is the largest of three Gaussian random variables?
added 14 characters in body |
May 26 |
comment |
What is the probability that a Gaussian random variable is the largest of three Gaussian random variables?
Are the variables independent? |
May 21 |
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About supersolvable Lie algebras
@YCor For simplicity, but I believe it should be true for arbitrary fields of characteristic $0$. |
May 21 |
revised |
About supersolvable Lie algebras
added 635 characters in body |