16,605 reputation
23667
bio website nd.edu/~lnicolae
location University of Notre Dame
age 50
visits member for 3 years, 6 months
seen 19 hours ago
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.

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
4
comment Reference for Convergence/Collapse of Riemannian manifolds
I am sure that Petersen gives several references. Those are the best place to start.
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
comment 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
May
21
comment About supersolvable Lie algebras
Thanks for your clarifications. I am adding a refined question following your suggestions.