853 reputation
411
bio website
location Salerno, Italy
age 36
visits member for 3 years, 5 months
seen 10 hours ago

Reasonably expert in Differential Geometry, I work mostly with jet bundles and their natural structures trying to exploit them in the areas of nonlinear PDEs and Calculus of Variations.


Jul
31
comment What does it mean that the Hessian is proportional to the metric?
Very illuminating - thanks! The statement "The level sets of your function formed by manifolds with constant normal curvature" is the most interesting one for me: do you have a reference for it?
Jul
31
accepted What does it mean that the Hessian is proportional to the metric?
Jul
31
asked What does it mean that the Hessian is proportional to the metric?
Jul
30
comment Is there a well-known tautological bundle over $\mathbb{P}(\Lambda^nV)$?
Ok, let me try. If $[\omega]\in \mathrm{G}(n,V)$, then $\omega=v_1\wedge\cdots\wedge v_n$, and $\pi^{-1}([\omega])=\langle v_1,\ldots,v_n\rangle$, which is the easy implication. Conversely, knowing that $\dim \pi^{-1}([\omega])=n$, you choose a basis of $V$ such that $\{v_1,\ldots,v_n\}$ generates $\pi^{-1}([\omega])$: now you suggest to write down $\omega$ as a linear combination of $v_1\wedge\cdots\wedge v_n$ and other terms, and show that the coefficients in front of the latter must necessarily be zero. Yes, it should work, thanks! Do you have any clue about question #2?
Jul
30
revised Is there a well-known tautological bundle over $\mathbb{P}(\Lambda^nV)$?
Removed unnecessary "$\times V$" from the title
Jul
29
revised Is there a well-known tautological bundle over $\mathbb{P}(\Lambda^nV)$?
I have completely rewritten the question "Is the tautological bundle over the Grassmannian inherited from a bundle over the Plucker embedding space?" since from the users' feedback I realised it was lousily laid down. The content however is unaltered.
Jul
25
comment Triangles in rigid Riemann surfaces
Now I understand. You are absolutely right.
Jul
25
comment Triangles in rigid Riemann surfaces
Help me to understand your reasoning. First, by transitivity, you reduce the problem to the case when the two triangles have a vertex in common, say $x_0$: then you are basically asking whether the isotropy subgroup $G_{x_0}$ is 2-transitive (any triangle with one vertex $x_0$ is uniquely determined by two other points). And you say "NO" by using finiteness of $G_{x_0}$: is this enough? What if the surface is the hyperbolic plane: does this finiteness argument works?
Jul
21
answered Transformations that leave the Plucker embedding of G(2,4) invariant
Jul
14
revised Is there a well-known tautological bundle over $\mathbb{P}(\Lambda^nV)$?
Changed "inherited by" in "inherited from"
Jul
13
asked Is there a well-known tautological bundle over $\mathbb{P}(\Lambda^nV)$?
Jul
7
comment Stability of the Solar System
It also depends on the notion of "Solar System": if it comprises "parabolic" objects like comets (and I believe it should), then it is not stable at all. From my point of view, "stable" and "periodic" are interchangeable terms. Besides, how can you predict when/why/where a distant iceberg will decide to dive into the sun?
Jul
7
revised Differential operators between modules, $\mathcal{D}_A(M, M)$ necessarily a filtered, almost commutative ring?
added 145 characters in body
Jul
7
revised Equivalence of “Weyl Algebra” and “Crystalline” definitions of rings of differential operators between modules?
I forgot to add a comment on the kind of modules my reasoning works with
Jul
7
answered Differential operators between modules, $\mathcal{D}_A(M, M)$ necessarily a filtered, almost commutative ring?
Jul
7
answered Equivalence of “Weyl Algebra” and “Crystalline” definitions of rings of differential operators between modules?
Jun
17
awarded  Good Question
Jun
17
revised Why there is a relation among the second-order minors of a symmetric $4\times 4$ matrix?
Added a comment to Allen Knutson answer
Jun
16
awarded  Self-Learner
Jun
16
awarded  Yearling