bio  website  nd.edu/~lnicolae 

location  University of Notre Dame  
age  50  
visits  member for  3 years, 8 months 
seen  2 hours ago  
stats  profile views  6,732 
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 CalabiYau
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 CalabiYau
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 CalabiYau
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 
Almostconverses to the AMGM inequality
added 149 characters in body 
Aug
19 
comment 
StoneCech 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 selfadjoint. 
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 0set
@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. 