In this CRC colloquium, organized by N.N., we're happy to welcome:
Is dispersion a stabilizing or destabilizing mechanism? Landau-damping induced by fast background flows
Abstract. In this talk I will present a uni_ed approach for the e_ect of fast rotation and dispersion as an averag-ing mechanism for regularizing and stabilizing certain evolution equations, such as the Navier-Stokes and Burgers equations. On the other hand, I will also present some results in which large disper-sion acts as a destabilizing mechanism for the long-time dynamics of certain dissipative evolution equations, such as the Kuramoto-Sivashinsky equation. In addition, I will present some results concerning two- and three-dimensional turbulent ows with high Reynolds numbers in periodic domains, which exhibit \Landau-damping" mechanism due to large spatial average in the initial data
- Rishabh Gvalani
Perfection and ergodicity for conservative SPDEs
Abstract: We analyse the dynamics of the solutions to a class of conservative SPDEs from two perspectives: firstly, we provide a purely probabilistic construction of a random dynamical system (RDS). Secondly, we establish existence and uniqueness of invariant measures. To our knowledge, the construction of the RDS is the first result of its kind for SPDEs with conservative multiplicative noise and relies importantly on a pathwise $L^1$ stability estimate. Our results apply to regularised versions of the Dean—Kawasaki equation. This is joint work with Benjamin Fehrman (Oxford) and Benjamin Gess (MPI-MiS/Bielefeld).
- Claude LeBris
Technologies for quantum computing: a mathematical perspective
Abstract: The course addresses a selection of mathematical issues related to the building of physical devices that are likely candidates to become the elementary bricks of a potential quantum computer.
The issues raised concern mathematical control theory, stabilization techniques, but also mathematical analysis of models for closed and open quantum systems, and the numerical approaches for (classically) simulating those systems.
After a presentation of the basis of the internal functioning of a classical computer, and a quick introduction to key concepts of computer science, the course will detail the similarities and differences introduced in the current technologies of quantum computing. Some models for quantum gates will then be introduced and studied. A particular emphasis will be put on the notion of decoherence and how it is solved using a combination of suitable engineering techniques and mathematical theories.
The course is targeted to a non expert audience, that may have some familiarity with some of the topics approached but not with the entirety of them, and want to be exposed to a mathematical assessment of the state of the art, along with some mathematical endeavours related to the current technological challenges