ERC FluCo

I am the principal investigator of the ERC Consolidator Grant “FluCo” (Fluctuations in continuum and conservative stochastic partial differential equations) funded by the European Research Council starting November 2023.

ERC Consolidator Grant “FluCo”

Fluctuations are ubiquitous in real world contexts and in key technological challenges, ranging from thermal fluctuations in physical systems, to algorithmic stochasticity in machine learning, to fluctuations caused by small-scale weather patterns in climate dynamics. At the same time, such complex systems are subject to an abundance of influences, and depend on a large variety of parameters and interactions. A systematic understanding of the interplay of stochasticity and complex dynamical behavior aims at unveiling universal properties, irrespectively of the many details of the concrete systems at hand. In the context of “FluCo” we aim to derive and analyse universal concepts the scaling limits of such complex systems, capturing not only their average behavior, but also their fluctuations.

We propose to analyze the class of conservative stochastic partial differential equations (SPDE)

as such a universal fluctuating continuum model, and unveil its mathematical analysis as a fruitful field for the discovery of new mathematical structures and methods. We aim to approach this challenges by a novel combination of methods from strongly nonlinear, conservative SPDEs and singular SPDEs.

The analysis of conservative SPDEs conjoins several contemporary fields of analysis and probability: Singular SPDEs, nonlinear PDEs, kinetic theory, supercriticality, and stochastic dynamical systems. We are, therefore, confronted with an interplay of stochasticity, irregularity, and nonlinearity, posing new challenges and going beyond established methods.