700 reputation
515
bio website physik.uni-leipzig.de/~diez
location Leipzig, Germany
age 25
visits member for 3 years
seen 6 hours ago

I am currently pursuing my PhD degree under the joint supervision of Prof. Rudolph (Leipzig, Germany) and Prof. Huebschmann (Lille, France).

My research is motivated by conceptual and mathematical problems of classical field theory, which I try to attack with infinite-dimensional differential geometry. In particular, I am interested in the action of Fréchet Lie groups on Fréchet manifolds to investigate the moduli spaces occurring as configuration spaces of gauge theory and general relativity.


Aug
9
awarded  Yearling
Jul
25
comment Topology on the dual of a Frechet space
It's a long time since I looked at Prof. Wurzbachers work, so take the following with a grain of salt: I wasn't to convince that his definition of a cotangent bundle does not run in the same kind of complications, i.e. it is not locally trivial in a smooth manner (since the above result of Neeb yields a counter example for every vector space topology on the dual). If I remember it correctly, Wurzbacher just says "this bundle is obviously locally trivial" and don't comment on possible issues. Kaveh, do you think his work is rigorous?
Jul
25
comment Topology on the dual of a Frechet space
You can still form the exterior bundle (and in particular the cotangent bundle) in the set-theoretic sense. So the differential $df$ still belongs to the cotangent bundle, however you don't have a smooth structure on it and thus you cannot say that the map $m \mapsto (df)_m$ is smooth in the usual way.
Jul
24
answered Topology on the dual of a Frechet space
Jul
2
awarded  Curious
Jul
1
asked Universal bundles: construction of the map associated to a group homomorphism
May
5
awarded  Autobiographer
Apr
19
awarded  Nice Question
Apr
6
comment Reference Request: Elliptic differential operators in the Fréchet setting
Thank you for this reference, looks indeed like a good start. In addition, the work "The inverse function theorem of Nash and Moser" of Hamilton also treatises differential operators and even a big part of the elliptic theory (discusses for example greens functions). More literature recommendations are still highly welcomed.
Apr
6
asked Reference Request: Elliptic differential operators in the Fréchet setting
Feb
19
answered Exponential mapping versus flow
Feb
9
awarded  Popular Question
Jan
17
revised Curvature as infinitesimal holonomy
deleted 14 characters in body
Jan
17
comment Curvature as infinitesimal holonomy
Thanks abx for the reference to the Ambrose-Singer theorem. I see the close relationship between my question and this theorem, but I think the derivative of the holonomy is even a stronger result. I updated my question to better clarify my idea and the intuition one gets from the abelian case. @ Liviu: Thank you for the link! This goes in the direction I had in mind. Do you know why one can restrict ones attention to a small parallelogram and does not consider arbitrary small loops?
Jan
17
revised Curvature as infinitesimal holonomy
added 627 characters in body
Jan
17
asked Curvature as infinitesimal holonomy
Dec
30
comment Design slides for presentation (conference talk)
Why is this question off-topic? What is more relevant to a researcher than to present their own work in a good and comprehensible way? (Also mathoverflow.net/questions/29866/… is a comparable question, just that my current question is more about the slides and not the whole talk)
Dec
29
asked Design slides for presentation (conference talk)
Dec
10
comment Parametrised Hilbert spaces; can we put a norm on the following space of Hilbert spaces?
In your problem, do you have an explicit dependence of $\Omega_s$ from $s$ which allows you to define a continuous map from $H(s)$ to $H(s')$ for every $s < s'$ or $s > s'$? In that case you might want to have a look at the inverse and direct limit construction of topological vector spaces. In this way you don't have a topology on $H$ but have nonetheless a limit space $\lim H(s)$.
Dec
7
comment Parameter dependent differential equation in a Lie group
I think you refer to Theorem B3, which however only handles the case of a scalar parameter $\epsilon \in \mathbb{R}$. Thanks nonetheless!