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Nonlinear analysis and differential topology in infinite dimensional Banach spaces


Until now, I have worked mainly on smoothness and geometrical properties of Banish spaces and their interplay with infinite-dimensional differential topology. For instance, I have shown inky thesis that every smooth sphere (note that we say the whole sphere and not the sphere minus a point) in any infinite-dimensional Banish space is diffeomorphic to a hyper plane, thus providing a full generalization of a celebrated result of Message’s. We have also established Avery strong approximate form of the Morse-Surd theorem, which holds in every differentiable manifold modelled on an infinite-dimensional Hubert space. The two main objectives of the project are
1) to continue research in the topic explained above, which is also one of the areas of speciality of Professor Gilles Godefory; and
2) to tyro expand my research into new directions such as the study of linear operators, invariant subspace problems and hyper cyclic operators, which are all among the fields of expertise of Professors Gilles Gaudery and Gilles Pismire, both working at the Institute de Mathématiques departs 6. I think that I could learn a lot of things from them and from their research teams, which would be extremely useful for me to develop my research in these directions. On the other hand, the Institute de Mathématiques de Paris 6 is one of the best centres of Mathematics in Europe, and the opportunity of interacting and working with its members would have a very positive impact on my postdoctoral training as a mathematician and would contribute to launch out my research activities into the new fields that I would like to explore.

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