Earth's atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing reliable computational models for weather forecasting and climate simulation.

Lecture I The fundamental tools of similarity theory and formal single scale asymptotics will allow us to systematize the large zoo of scale-dependent model equations that one finds in modern textbooks of theoretical meteorology.

Lecture II The meteorological analogue of the incompressible flow equations are the ”anelastic” and ”pseudo-incompressible” models. Here we will learn how the presence of internal gravity waves in the atmosphere implies an asymptotic three-scale problem that renders the formal derivation and justification of these models much more intricate than the classical low Mach number derivation of the incompressible flow equations.

Lecture III The mechanisms by which tropical storms develop into hurricanes and typhoons are still under intense debate despite decades of research. A recent theory for the dynamics of strongly tilted atmospheric vortices will show how asymptotic methods help structuring this scientific debate, and how they offer new angles of scientific attack on the problem.

Lecture * If time permits, I will also summarize some ramifications of the scaling regimes and scaling theories considered in Lectures I-III on the construction of reliable computational methods.[-]

Earth's atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing reliable computational models for weather forecasting and climate simulation.

Lecture I The fundamental tools of similarity theory and formal single scale asymptotics will allow us to systematize the large zoo of scale-dependent model equations that one finds in modern textbooks of theoretical meteorology.

Lecture II The meteorological analogue of the incompressible flow equations are the ”anelastic” and ”pseudo-incompressible” models. Here we will learn how the presence of internal gravity waves in the atmosphere implies an asymptotic three-scale problem that renders the formal derivation and justification of these models much more intricate than the classical low Mach number derivation of the incompressible flow equations.

Lecture III The mechanisms by which tropical storms develop into hurricanes and typhoons are still under intense debate despite decades of research. A recent theory for the dynamics of strongly tilted atmospheric vortices will show how asymptotic methods help structuring this scientific debate, and how they offer new angles of scientific attack on the problem.

Lecture * If time permits, I will also summarize some ramifications of the scaling regimes and scaling theories considered in Lectures I-III on the construction of reliable computational methods.[-]

Earth's atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing reliable computational models for weather forecasting and climate simulation.

Lecture I The fundamental tools of similarity theory and formal single scale asymptotics will allow us to systematize the large zoo of scale-dependent model equations that one finds in modern textbooks of theoretical meteorology.

Lecture II The meteorological analogue of the incompressible flow equations are the ”anelastic” and ”pseudo-incompressible” models. Here we will learn how the presence of internal gravity waves in the atmosphere implies an asymptotic three-scale problem that renders the formal derivation and justification of these models much more intricate than the classical low Mach number derivation of the incompressible flow equations.

Lecture III The mechanisms by which tropical storms develop into hurricanes and typhoons are still under intense debate despite decades of research. A recent theory for the dynamics of strongly tilted atmospheric vortices will show how asymptotic methods help structuring this scientific debate, and how they offer new angles of scientific attack on the problem.

Lecture * If time permits, I will also summarize some ramifications of the scaling regimes and scaling theories considered in Lectures I-III on the construction of reliable computational methods.[-]

Originally arisen to understand characterizing properties connected with dispersive phenomena, in the last decades the method of multipliers has been recognized as a useful tool in Spectral Theory, in particular in connection with proof of absence of point spectrum for both self-adjoint and non self-adjoint operators. In this seminar we will see the developments of the method reviewing some recent results concerning self-adjoint and non self-adjoint Schrödinger operators in different settings, specifically both when the configuration space is the whole Euclidean space \R^d and when we restrict to domains with boundaries. We will show how this technique allows to detect physically natural repulsive and smallness conditions on the potentials which guarantee total absence of eigenvalues. Some very recent results concerning Pauli and Dirac operators will be also presented.
The talk is based on joint works with L. Fanelli and D. Krejcirik.[-]

The viewpoint proposed in this lecture is that uncertainty quantification for kinetic equations does not always represent the viewpoint of the experimentalists. Instead they want to determine the uncertain coefficient in a PDE by measuring the solution at the parts of the boundary, given data on other parts of the boundary. In other words experimentalists are interested in solving the inverse problem in a Baysian setting.
We shall give examples and results to this end. In particular we shall consider a model from mathematical biology, namely the motion of cells, as described by the kinetic chemotaxis equations. The corresponding macroscopic Keller-Segel type model will be a diffusion equation. Our aim is to study the inverse problems for these two settings. We shall analytically study the convergence of the inverse problem of the kinetic equation to the inverse problem of the corresponding diffusion equation.
This is joint work with Kathrin Hellmuth, Qin Li and Min Tang[-]