Talks

The flow associated to a given smooth vector field $u(t,x)$ is well-defined, it is smooth, and it can be used to solve the classical linear PDEs associated to $u$, namely the transport and the continuity equations. The situation is substantially different when $u$ is not smooth (e.g. when $u$ is not Lipschitz continuous in the space variable, but only Sobolev or BV). Goal of the lecture is to provide an overview on classical and recent results about flow maps and PDEs associated to non-smooth vector fields.

In the recent resolution of the strong Onsager’s conjecture in L^3 framework, so-called wavelet-inspired Nash’s iteration has been developed. In this lecture, we will sketch this new method and provide the necessary background. The lecture will be based on our recent joint work with Matthew Novack.

* Introduction to resonant light matter interaction (coherent and incoherent scattering, Rabi oscillations, Mollow triplets) * Origin of antibunching in resonance fluorescence (L. Hanschke et al. Phys. Rev. Lett. 125, 170402 (2020)) * Doubly-dressed Mollow triplets (C. Gustin et al. Phys. Rev. Research 3, 013044 (2021) * Dynamic Mollow triplets from Janes-Cummins systems (K. Fischer et al. Nature Photonics 10, 163–166 (2016)) * Dynamic Mollow triplets from two-level systems (K. Boos et al. arXiv:2305.15827 (2023) – accepted at PRL)

Active materials such as bacteria, molecular motors and eukaryotic cells continuously transform chemical energy taken from their surroundings to mechanical work. Dense active nematics show mesoscale turbulence, the emergence of chaotic flow structures characterised by high vorticity and self-propelled topological defects. I shall describe the physics of active nematics and discuss examples where this is relevant to living matter.