1,532 reputation
519
bio website
location Berlin, Germany
age 26
visits member for 3 years, 8 months
seen yesterday

I got my Master degree in Pure Mathematics in Rome, and now I'm a PhD-student in Berlin.

My main research interest is Arithmetic Geometry, but I'm here mainly because I like to keep an open eye towards a variety of fields in Mathematics!


Dec
16
awarded  Caucus
Dec
10
accepted Is the on-diagonal heat kernel “local” with respect to the metric?
Dec
8
comment How to (dis)prove the following about harmonic functions
And two functions $u$ and $v$ are harmonic conjugate if $u + iv $ is holomorphic. en.wikipedia.org/wiki/Harmonic_conjugate The article also answer your question.
Dec
2
comment Is the on-diagonal heat kernel “local” with respect to the metric?
Indeed I was obviously ignoring the fact that the $\sup$ can also be achieved for $t>0$ and $z \in \partial B$; which invalidates the argument.
Dec
2
comment Is the on-diagonal heat kernel “local” with respect to the metric?
Thank you for your interest Phillip! I agree that Dirichlet condition would provide uniqueness, and also that they wouldn't be relevant for the problem. I was now thinking to the strong maximum principle; if $B$ is a closed ball of small radius contained in $U$, then the maximum of $h$ for any time on $B$ is obtained for $t=0$; and the minimum as well. This forces $h\equiv 0$ for any time and any $z\in B$. It looks a bit too easy to be true though, and I want to check if there's a flaw in the argument.
Dec
1
asked Is the on-diagonal heat kernel “local” with respect to the metric?
Nov
2
awarded  Nice Question
Sep
30
awarded  Explainer
Sep
24
awarded  Autobiographer
Sep
1
comment Natural surjection from complex upper half plane into modular curve
Approach $1)$ unfortunately doesn't work, what you want to prove is that $\pi^{-1} (\pi (U))$ is open for anu $U$ open, and not the other way around. And $2)$ is using too much structure, you actually don't need to consider the complex structure on $Y(\Gamma)$. For the answer you could check this previous question: math.stackexchange.com/questions/61173/… .
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
13
awarded  Popular Question
Jun
11
accepted Example of a meromorphic function with no analytic continuation outside the unit disc
Jun
11
comment Example of a meromorphic function with no analytic continuation outside the unit disc
Thanks, this does exactly what I was looking for! I'm going to do the exercise then!
Jun
11
comment Example of a meromorphic function with no analytic continuation outside the unit disc
Thank you very much! I actually did miss it...
Jun
11
comment Are the two statements about continuous functions equivalent?
I think that the implication arrow in your first statement has to be reversed to get the definition of continuity.
Jun
11
asked Example of a meromorphic function with no analytic continuation outside the unit disc
Apr
20
awarded  Yearling
Jan
9
comment How important are automorphic representations among admissible ones?
Thanks for the answer!