817 reputation
517
bio website physik.uni-leipzig.de/~diez
location Leipzig, Germany
age 25
visits member for 3 years, 3 months
seen 4 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.


Nov
24
answered What's the geometric statement of this fibrewise integration on a symplectic manifold with Lagrangian fibration?
Nov
18
comment Smooth curves in a Frechet space
No problem! It is common here on mathoverflow to mark responses as answers if they satisfy your needs (in order to declare such questions as answered). On the other hand, if you still have open questions, I'm more than happy to expand my answer.
Nov
13
revised Smooth curves in a Frechet space
deleted 3 characters in body
Nov
13
answered Smooth curves in a Frechet space
Oct
28
revised Examples of topologies compatible with a given dual pair
deleted 1 character in body
Oct
28
asked Examples of topologies compatible with a given dual pair
Oct
12
accepted Inverse of partial differential operator as a smooth tame map
Sep
24
awarded  Tumbleweed
Sep
17
asked Localization on orbit type submanifolds (generalization of Atiyah-Bott-Berline-Vergne)
Sep
17
asked Inverse of partial differential operator as a smooth tame map
Sep
3
awarded  Critic
Aug
29
revised Invariant definition of the space of symbols on a vector bundle (pseudo-differential operators)
added 55 characters in body; edited title
Aug
28
comment Invariant definition of the space of symbols on a vector bundle (pseudo-differential operators)
Thanks Vít Tuček for your comment. Maybe I should have made this clear in the question: I'm not interested in the symbol of a differential operator but of a pseudo-differential operator. These symbols are more generally defined via the above symbol estimates. Furthermore, pseudo-differential operators does not have such a nice interpretation in terms of jet bundles, see for example mathoverflow.net/questions/75976/symbol-of-pseudodiff-operator
Aug
27
asked Invariant definition of the space of symbols on a vector bundle (pseudo-differential operators)
Aug
24
comment Separating duality for TVS?
Another notion often used (in particular, in the study of duals of locally convex spaces) is the following: a family $\alpha_x$ of linear, (continuous) functionals on $E$ "separates points of $E$" if for all non-zero $e \in E$ there exists $x$ such that $\alpha_x(e) \neq 0$. So I think "duality separating points" should work also.
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