bio  website  nd.edu/~lnicolae 

location  University of Notre Dame  
age  50  
visits  member for  3 years, 3 months 
seen  6 hours ago  
stats  profile views  6,248 
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.
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Projective family of probability spaces
@Exterior I do not understand your comment. The arrows do matter. Think of the ring of $2$adics $\mathbb{Z}_{(2)}$ vs. the ring of $3$adics $\mathbb{Z}_{(3)}$. They're defined by identical diagrams, but the meaning of arrows is different. The result is nonisomorphic local rings. 
10h

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Projective family of probability spaces
How about the category of probability spaces $(\Omega, \mathscr{O}, P)$ where morphisms are measurable maps $(\Omega_0,\mathscr{O}_0,P_0)\to (\Omega_1,\mathscr{O}_1,P_1)$ such that $f_*P_0=P_1$. 
13h

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Integration currents VS Poincaré Dual
@user69938 I think you need to define things precisely. I think that you use a different notion of Poincare duality. I believe you will find the answer in section 7.3 of the notes www3.nd.edu/~lnicolae/Lectures.pdf 
13h

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A PoincareType Inequality and its generalization
@Hacino Missed that. 
13h

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A PoincareType Inequality and its generalization
The answer is no in both cases. (The first case is a special case of the 2nd question.) In the first case take $f(\theta)=\cos(2\theta)$ and $\phi(\theta)=1$. 
14h

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Generalize GaussBonnet Formula to nonsimple closed curves
What do you mean my nonsimple closed curve? Do you mean an immersed closed curve? 
14h

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Integration currents VS Poincaré Dual
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14h

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Integration currents VS Poincaré Dual
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14h

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Integration currents VS Poincaré Dual
The last equality that you wrote is the definition of the current $T_S$. Also do not confuse $H^{2r}(M)$ with $\Omega^{2r}(M)$. They are different spaces. 
15h

answered  Integration currents VS Poincaré Dual 
16h

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Integration currents VS Poincaré Dual
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2d

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Average probability that a random cosine polynomial with bernoulli coefficients is small
Have you tried using the CLT. The variance of $P_n(t)$ is $s(t)^2=\sum_{k=0}^n \cos^2kt$. Then, for fixed $t$, $\frac{1}{s(t)}P_n(t)$ converges weakly to $N(0,1)$ 
Mar 29 
awarded  dg.differentialgeometry 
Mar 27 
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Why not develop a Hamiltonianbased Morse theory?
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Mar 27 
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Why not develop a Hamiltonianbased Morse theory?
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Mar 27 
revised 
Why not develop a Hamiltonianbased Morse theory?
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Mar 27 
answered  Why not develop a Hamiltonianbased Morse theory? 
Mar 12 
revised 
Reasons for the Arnold conjecture
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Mar 12 
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Estimates of eigenvalues of elliptic operators on compact manifolds
The passage from scalar to vector bundle Laplacians is not difficult. The pseudodifferentia case has a few peculiarities. Hormander's results are the sharpest. They are discussed in Theorems 2.1, 2.3 of paper arxiv.org/pdf/1406.0934v1.pdf (They are proved in the appendix of the paper.) The references in the paper are also useful. 
Mar 11 
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More recently published comprehensive reference on inequalities in the spirit of HardyLittlewoodPólya
Another useful reference is Mitrinovic's monograph Analytic inequalities. books.google.com/… 