491 reputation
29
bio website
location Salerno, Italy
age 36
visits member for 3 years
seen Apr 1 at 7:45

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.


Mar
23
comment What is the “type” of a contact vector field?
I never doubted that type depended only on the conformal class of $\theta$. I wasn't sure it is invariant under the group of contact transformations. However, it is nice that you have such an "universal" sourcebook, and I'm going to have a look at it (I never read it from the beginning to the end, but I know it really contains a lot, so maybe I should do it!)
Mar
23
revised What is the “type” of a contact vector field?
Explained that the type is a function of $p\in M$
Mar
23
comment What is the “type” of a contact vector field?
@DanieleZuddas: yes, $X^k(\theta)$ is the $k^\textrm{th}$ derivative, and yes the type is in fact a function of the point $p\in M$.
Mar
23
revised What is the “type” of a contact vector field?
Added explanation of $X^k(\theta)$
Mar
23
asked What is the “type” of a contact vector field?
Mar
4
awarded  Yearling
Oct
23
revised Extending derivations to the superposition closure
added 787 characters in body
Oct
7
revised Extending derivations to the superposition closure
added 3 characters in body
Oct
7
asked Extending derivations to the superposition closure
Oct
4
accepted How to “lift” a transitive group action on a manifold?
Sep
30
comment How to “lift” a transitive group action on a manifold?
@BenMcKay: incidentally, can you always realise $\frak{g}$, the Lie algebra of $G$, as an algebra of vector fields on $M$, i.e., can you embed it into the (infinite-dimensional) Lie algebra of vector fields on $M$?
Sep
30
comment How to “lift” a transitive group action on a manifold?
@VítTuček: yes, actually in the cases I'm interested in, $\widetilde{M}$ is compact.
Sep
29
comment How to “lift” a transitive group action on a manifold?
Indeed. This is more or less what I suggested in my last lines. I'm aware of Lie-Palais theorem, though you need to require some extra topological conditions from $\widetilde{M}$. Still, I'd like to see some universal property characterising $\widetilde{G}$, like, e.g., "it is the unique group admitting $G$ as a factor by covering transformations", or something like that, and/or some algebraic way to construct it out of the available data!
Sep
29
asked How to “lift” a transitive group action on a manifold?
Sep
29
comment What is the most useful non-existing object of your field?
As a general rule, you appoint a name to something if that thing has been around for a while: even if its existence is disproved later, the name will stick to it. It's a nice phenomenon. Think about the aether: for decades people believed it surrounded us, now we know it cannot exists, but its name persists in SF and fantasy tales! I guess that before Galois the name "general solution for quintic equations" was often used, both by those who believed it existed and it was yet to be found, by those who erroneously believed they found it, and by those who were trying to prove it cannot exists!
Sep
24
awarded  Autobiographer
Sep
9
accepted Can the finiteness of a Burnside group with two generators be checked algorithmically by using Fuchsian von Dyck groups?
Sep
8
comment Can the finiteness of a Burnside group with two generators be checked algorithmically by using Fuchsian von Dyck groups?
Your almost cleared out all my doubts - yet I need time to fully digest your answer. Now, let us focus on your last sentence: "I certainly don't see any particular obstruction to attempting the computation in the case of $B(2,5)$". Believe me, I've been trying for years to find out what is the state-of-the-art concerning the finiteness of $B(2,5)$, but in vain. Can you point out somebody to whom I may ask? Why there are a lot of computers employed to discover the 'last' digit of $\pi$, or the 'biggest' prime, but none cares about finiteness of $B(2,5)$? Is there at least the algorithm written?
Sep
5
revised Can the finiteness of a Burnside group with two generators be checked algorithmically by using Fuchsian von Dyck groups?
Previous question, titled "Coverings of the free Burnside groups", was never answered. So, I reformulate it adding new details I discovered meanwhile.
Aug
6
accepted Is there a “unique” homogeneous contact structure on odd-dimensional spheres?