Equations of waves and flows are used extensively in physics and biology, to describe phenomena ranging from the flow past an airfoil, to the collective motion of cells and to the motion of water surface. A major issue is to explain how the propagation through space and the concentration to various scales can emerge from these mathematical models. Fundamental progress have been made since the beginning of the millenium around the role played by specific solutions that either propagate or shrink while keeping the same shape, such as solitary waves for example. These specific solutions are the key to understand the global dynamics. The goal of this project is to push forward the current knowledge on their stability, their emergence over time, and the dynamics they are responsible in several equations. The FloWAS project will study seemingly unrelated models, whose solutions in fact display remarkably close behaviours. First, we aim at describing how a thin layer of fluid can detach off a boundary and be ejected away in a stream. This is a key phenomenon to understand the drag exerted on moving objects. For this we will study singular solutions of the unsteady Prandtl system of fluid mechanics. Second, we will study concentration phenomena arising in the movement of bacteria. For that we will consider nonlinear structures appearing in the Keller-Segel system: how they can collapse, and how they can interact. Third, we will consider how, from initially disordered wave packets, order appears over time and traveling waves emerge. This study will be made on the critical wave equation. Applications to weak wave turbulence will be pursued. Describing all these phenomena lies at the frontier of current research, and we expect applications to a wide range of models.

The EUTOPIA Science and Innovation Fellowships program is an ambitious initiative to train young research leaders. This strategic program is launched by the EUTOPIA Alliance, a network of six universities that has recently been awarded an Erasmus+ ‘European Universities’ pilot project. It brings together Université Paris Seine, Universitat Pompeu Fabra, Vrije Universiteit Brussel, Goeteborgs Universitet, Univerza v Ljubljani and University of Warwick, who have joined forces to provide fellows with an innovation-driven world-class research eco-system. The program focuses on 5 interdisciplinary Key Research Areas: 1- Materials engineering; 2- Data & Intelligence; 3- Health; 4- Sustainability; 5- Welfare & Inclusion. The program offers 76 two-years post-doctoral fellowships over five years and aims to promote the research potential and career perspective of outstanding, innovative young researchers. Fellows are offered full freedom to pursue their research project whilst benefiting from expert academic supervision, state-of-the art research infrastructure and being part of an interdisciplinary research community. The program offers career mentoring; and promotes transferable skills, innovation and entrepreneurship awareness and secondment with partners. While letting fellows choose their hosting university, the program will create a transnational community of researchers through joint initiatives such as yearly symposia, a strong network, etc. International mobility, both among EUTOPIA members and towards international academic institutions will be encouraged. Université Paris Seine will manage the program on behalf of the EUTOPIA Alliance. The program will rest on a unified governance, a joint, high standard, selection procedure, and resource sharing. In addition, more than 45 companies, local authorities and non-profit organizations who are ready to train or host some researchers on secondments already support the program.

In the past years, quantum non-equilibrium emerged as a new principal research arena, promising to assist the current development of new quantum technologies and to shine a new light on disparate fields of theoretical and experimental physics, from black holes to condensed matter and statistical physics. As quantum dynamics represents a major challenge for modern computational methods, relevant developments have come from devising new generalised and extended forms of classical hydrodynamic theory to effectively describe its macroscopic features. This effort is nowadays constituting an essential part of contemporary theoretical physics, contributing to a deeper understanding of dynamical phenomena and providing new directions in different experimental areas. This proposal focuses on the interplay between classical non-linear dynamics and quantum evolution, promising to a) unveil a new deep comprehension of how the non-equilibrium dynamics in many-body quantum systems can dissipate or either recover quantum information and how effective non-linear classical behaviour emerges, b) release new efficient theoretical tools to access quantum many-body quantum systems which are strongly interacting and in non-equilibrium settings beyond linear response, far away from known regimes of low-energy, low-temperatures or weak interactions. The outcomes will provide new reliable and much needed theoretical methods as well as a new dictionary to catalogue and relate different non-equilibrium phenomena in quantum and classical physics and deepen our understanding of out-of-equilibrium matter.

The ergodic theory of parabolic dynamical systems is an area in smooth ergodic theory that is relevant for its connections to mathematical physics and to analytic number theory. A dynamical system is parabolic whenever its orbits diverge at an intermediate (often polynomial) rate between bounded/logarithmic (called elliptic) and exponential (called hyperbolic) rate. The proposal tackles several outstanding questions in the ergodic theory of parabolic flows with emphasis on quantitative aspects. The main goal is to go beyond renormalization techniques that have proved extremely powerful in several classes of examples: Interval Exchange Transformations and Flows on surfaces, horocycle flows, nilflows on quotients of step-two nilpotent groups and Gauss sums. Renormalization methods are not available in other equally fundamental examples of similar nature: billiards in non-rational polygons, higher step nilflows and non-horospherical unipotent flows in homogeneous dynamics. A unified approach to effective ergodicity is proposed that encompasses all of the above mentioned examples. Outstanding questions include ergodicity and existence of periodic orbits of non-rational billiards in polygons, effective ergodicity of higher step nilflows with optimal deviation exponents and applications to bounds on Weyl sums for higher degree polynomials and effective ergodicity of non-horospherical unipotent flows on semi-simple finite-volume quotients. The analytical foundations of the method lie in the study of invariant distributions for parabolic flows. In the examples considered the analysis can be carried out by methods of non-Abelian Fourier analysis (theory of unitary representations). In general, for non-homogeneous parabolic flows, all questions concerning invariant distributions and their relevance for smooth ergodic theory are wide open. Several problems to probe the question of existence of invariant distributions are proposed.

Do only foolish people drown and only compulsive gamblers suffer flood losses? Conventional wisdom is based on flawed underlying assumptions and the EU vision of a disaster- and climate-resilient society cannot be achieved by relying on “behaviour-blind” assessments and policy. Whilst the behaviour of individuals, businesses and public services before, during and after a crisis has a significant impact on damages, recovery and resilience, current assessments fail to include such critical factors because they are hardly understood. Floods and weather hazards are affecting 2bn people and exposure is expected to grow due to climate change. Despite trillions of public funds invested, current flood reduction and planning policies are failing to reduce risks and losses of lives. This is due to a mismatch between the rising application of risk, vulnerability and resilience assessments and the understanding of their empirical validity. The overreaching goal of this proposal is to move from “behaviour-blind” to “behaviour-aware” assessments, indicators and policies to save lives and public money. Lifting the current barriers to predicting and simulating risk perception and behaviour will create forefront knowledge and open new horizons. Social and technological changes have widened the gaps in our knowledge making new empirical research essential to refine or replace existing theories. This project will provide four demonstrators representative of the European and Mediterranean context, graded in size, wealth and exposure to reach general considerations: Paris, Barcelona, Bucharest and Algiers. It is aiming at cross-validation on floods and transferability to other emergencies (technological disasters, epidemics, terrorism, etc). It will launch a new line of research by providing “behaviour-aware” participatory assessments and indicators, spatially-explicit interactive short- and long-term simulation tools enabling decision-makers to refine their strategies and policies.