bio | website | physik.uni-leipzig.de/~diez |
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location | Leipzig, Germany | |
age | 25 | |
visits | member for | 3 years, 2 months |
seen | yesterday | |
stats | profile views | 580 |
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 |