16,805 reputation
23668
bio website nd.edu/~lnicolae
location University of Notre Dame
age 50
visits member for 3 years, 8 months
seen 2 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.

2d
revised Finding combinatorial models / statistics
edited title
Aug
27
comment Asymptotic $\int_M \mathrm{exp}[\mathbf{e}\left(n -\frac{t}{2\pi i}\right)] \left( 1 + \frac{5}{6} \mathbf{e}^2 \right)^{1/2} $ on quintic Calabi-Yau
What is the meaning of $(1+\frac{5}{6}\mathbf{e}^2)^{1/2}$?
Aug
27
comment Asymptotic $\int_M \mathrm{exp}[\mathbf{e}\left(n -\frac{t}{2\pi i}\right)] \left( 1 + \frac{5}{6} \mathbf{e}^2 \right)^{1/2} $ on quintic Calabi-Yau
I fixed a TeX typo. The math content is unchanged.
Aug
27
revised Asymptotic $\int_M \mathrm{exp}[\mathbf{e}\left(n -\frac{t}{2\pi i}\right)] \left( 1 + \frac{5}{6} \mathbf{e}^2 \right)^{1/2} $ on quintic Calabi-Yau
added 1 character in body
Aug
25
comment Square of the distance function on a Riemannian manifold
@Raziel Yes, you're right.
Aug
25
revised Square of the distance function on a Riemannian manifold
added 66 characters in body
Aug
25
answered Square of the distance function on a Riemannian manifold
Aug
24
comment Fredholm subvector spaces of $B(\mathcal{H})$
No vector subspace of $B(H)$ can consist only of Fredholm operators since $0$ is not a Fredholm operator.
Aug
19
revised Almost-converses to the AM-GM inequality
added 149 characters in body
Aug
19
comment Stone-Cech compactification of $\mathbb{R}^n$ and smooth functions
The existence of a "small'' subspace $U$ of continuous functions separating the points of your space $X$ imposes restrictions on $X$ For example, if $\dim U=n$, then you can continuously embed $X$ in $\mathbb{R}^n$.
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.