Summer school: PDE and probability

Contribution List

7. Anomalous diffusion and Euler flows

Prof. Jan Burczak (Universität Leipzig)

Scalar anomalous dissipation is a phenomenon in fluid dynamics in which a quantity advected by a fluid (e.g. the density of pollutant particles advected by a water current) is dissipated even 'without the final assistance of viscosity'. This behaviour has strong links to turbulence: in particular to Kolmogorov's 'zeroth law', to Onsager's theory, and to Richardson's hypothesis of turbulent...

6. Large-scale behaviour of random motions with long memory

Balint Toth (Bristol & Budapest)

The course will discuss at least two of the following three topics.

1.
Random walks and diffusions in divergence-free random drift fields.
Motivation, examples, main questions.
Diffusive limit (CLT) and homogenisation under H_{-1} and ellipticity. (In probability and quenched, w.r.t. the environment)
Relaxing the ellipticity condition. Motivation (why care?). Diffusive limit and...

3. Quantum diffusion and random matrix theory

Felipe Hernandez (Penn State University)

The random Schrodinger equation and its discrete analogue, the tight-binding model, have been studied as models of electron transport in disordered systems. It is conjectured that the long-time behavior is either localized or diffusive. In the localized regime, solutions remain trapped near their initial position. This phase has been established rigorously near the spectral edges, and is...

4. Rigorous justification of wave kinetic theory

Zaher Hani (University of Michigan)

Wave kinetic theory, also known as wave turbulence theory, is the kinetic description of systems with an asymptotically large number of weakly interacting waves. It is the wave analog of Boltzmann’s kinetic theory for particle systems, and plays a fundamental role in various fields of science. Over the last five years, in collaboration with Yu Deng (Chicago), we have developed a robust...

2. Rigorous results for timelike Liouville field theory

Prof. Sourav Chatterjee (Stanford University)

Liouville field theory has long been a cornerstone of two-dimensional quantum field theory and quantum gravity, which has attracted much recent attention in the mathematics literature. Timelike (or imaginary) Liouville field theory is a version of Liouville field theory where the coupling constant is made imaginary. I will talk about recent work that gives a rigorous construction of timelike...

1. TBA

Prof. Martin Hairer (EPFL)