Dr. Marwa Banna
Dr. Tobias Mai
Seminar on Gaussian Hilbert Spaces
(Summer Semester 2020)News
- From now on, the seminar starts at 10:00 am (sharp).
Time and Place
Wednesday, 10:00 - 11:30 (online, via the platform Zoom)Content
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Gaussian Hilbert spaces are Hilbert spaces consisting of centered Gaussian random variables. Accordingly, Gaussian Hilbert spaces are located at the intersection of probability and Hilbert space theory and turn out to have a rich and powerful structure with various applications. Gaussian Hilbert spaces and related concepts appear, for instance, in stochastic analysis and in quantum field theory and have applications even outside probability theory like in Banach space geometry and in the area of partial differential equations.
In this seminar, we want to give an introduction to the theory of Gaussian Hilbert spaces following the identically named book by Svante Janson. We will discuss the main pillars of that subject, including the Wiener chaos decomposition, Wick products, the Fock space and the hypercontractivity phenomenon, as well as some of the beautiful applications in stochastic integration, Malliavin calculus, U-Statistics and operator theory. |
Seminar announcement
For further information, please contact Marwa Banna or Tobias Mai.
Talks
- Wednesday, May 13 - M. Banna: Gaussian spaces
- Wednesday, May 20 - T. Mai: Wiener chaos
- Wednesday, May 27 - S.-J. Meyer: Wick products I
- Wednesday, June 3 - S.-J. Meyer: Wick products II
- Wednesday, June 10 - M. Schu: Tensor products and Fock space I
- Wednesday, June 17 - M. Schu: Tensor products and Fock space II
- Wednesday, June 24 - S.-J. Meyer: Hypercontractivity
- Wednesday, July 1 - T. Mai: Variables with finite chaos decomposition and Stochastic Integration I
- Wednesday, July 8 - T. Mai: Stochastic Integration II
- Wednesday, July 15 - M. Banna: Limit theorems for generalized U-statistics
References
- Svante Janson, Gaussian Hilbert Spaces, Cambridge University Press, 1997
updated: 6 July 2020 Tobias Mai
