614 reputation
414
bio website poisson.dm.unipi.it/~monge
location Pisa (Italy)
age 33
visits member for 4 years, 9 months
seen Oct 23 at 2:53

Sep
8
comment Help with my research topic
By the way, don't feel afraid to change advisor (either formally, either "de facto"). If after two years you are not being helped in any way to get in touch with current research problems don't make the mistake (that I did) to think that your best opportunity is trying to make your current setup work at all costs. Getting in touch with the state of the art in a research field is hard, you should have someone you can question about it.
Aug
22
asked Extension of the product formula for valuations to a simultaneous completion
Jul
2
awarded  Curious
Feb
25
comment Is a left topological group which is a manifold a topological group?
That the idea does not work "as is" with $H=K$, where I was looking for a non-continuous $H\rightarrow{}K$ that could then be composed with the canonical $K\rightarrow{}Inn(K)$. But actually I just realized that this can work very easily with $S^1$ and $SO(2)$, considering an isomorphical embedding $S^1\rightarrow{}SO(2)$ and a non-continuous homomorphism $S^1\rightarrow{}S^1$ (which exists). In this way we easily have a non-continuous homomorphism $S^1\rightarrow{}Aut(SO(2))$, and a similar example (that is also compact).
Feb
24
comment Is a left topological group which is a manifold a topological group?
It is interesting to point out that the same example cannot work with compact semisimple Lie groups (replacing $xe^{f(y)}$ with the conjugacy $yxy^{-1}$, that sends as well $G\rightarrow{}Inn(G)\subseteq{}Aut(G)$), because in this case any automorphism is automatically continuous, as pointed out in mathoverflow.net/a/40700/3680
Feb
24
revised Is a left topological group which is a manifold a topological group?
added 111 characters in body
Feb
24
comment Is a left topological group which is a manifold a topological group?
Nice example, thanks!
Feb
24
accepted Is a left topological group which is a manifold a topological group?
Feb
23
comment Is a left topological group which is a manifold a topological group?
yes, let's also assume $G$ paracompact, with countable atlas as topological manifold. @GeraldEdgar nice theorem, even if I don't see an immediate application to the present case, what is a reference for it?
Feb
22
awarded  Nice Question
Feb
22
revised Is a left topological group which is a manifold a topological group?
added 195 characters in body
Feb
22
comment Is a left topological group which is a manifold a topological group?
I see... thanks, if you write it as an answer I will accept it. In any case, I was not thinking about this kind of examples, I think I should add that $G$ is supposed to be connected.
Feb
22
comment Is a left topological group which is a manifold a topological group?
If you make the coset of a a one-parameter subgroup open (and hence also closed), how can the group still be a topological manifold?
Feb
21
asked Is a left topological group which is a manifold a topological group?
Jan
27
answered Ergodicity of composition with a rotation
Oct
29
awarded  Nice Answer
Oct
11
comment A Differential Equation with Nested Functions
can you provide some background?
May
12
awarded  Popular Question
Jan
31
awarded  Yearling
May
16
comment about the local ring of $\mathbb{Z}_p[T]/(pT^2+T+1)$ at the prime p
Another way to see immediately that the equation has a solution is via Newton's polygon: it is formed by two sides with slopes 0 and 1, and each corresponds to a non-trivial factor, having degree 1.