782 reputation
517
bio website physik.uni-leipzig.de/~diez
location Leipzig, Germany
age 25
visits member for 3 years, 2 months
seen yesterday

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.


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
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