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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Stochastic partial differential equations arise naturally in several models of random phoenomena, in such fields as biology, physics and engineering. In particular, while deterministic models represent an efficient tool to describe time-evolution of real-world systems, they fail in rendering the presence of possible microscopic uncertainty of the model. Such randomness components may be related to several factors and are usually tracked through the introduction of a stochastic source of randomness in the equations involved. One of the most challenging goal of the mathematics of stochastic partial differential equations is the understanding of quantitative and qualitative properties of solutions and their dependence on the coefficients. The aim of the workshop is to bring together leading experts, as well as a number of talented young researchers and to share fresh information on new results and future perspectives. The stay at the Institute will promote informal interaction progress in collaborations.

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

The study of return-times and hitting-times of small sets ("rare events") in ergodic dynamical systems has undergone some intense research in the past 20 years. It is part of the wider field of probabilistic properties of (deterministic) dynamical systems. One general motivation from the sciences is that the times at which various extreme events (possibly modeling catastrophes in real-world systems) occur, often cannot be predicted over a reasonably long period. It is therefore important to at least understand the statistical laws governing these occurrences. Accordingly, there are well-developed stochastic models describing such rare events and enabling further theoretical analysis. These stochastic descriptions, however, necessarily start from simplifying assumptions and sometimes disregard additional detailed knowledge about the mechanisms driving the system. In contrast, there is a branch of ergodic theory which aims at analysing dynamical system models which incorporate this extra information, and rigorously derives statistical properties from the underlying deterministic dynamics. The central theme of this workshop is the aspiration for finding and proving probabilistic limit theorems which clarify patterns of occurrences of extreme events in nonlinear dynamics.

Systems theory, Control and Automation,    Complex Systems, Chaos and Self-Organisation

Our workshop covers a broad range of topics, such as complex longitudinal and survival data analysis, high-dimensional data analysis, precision medicine, and artificial intelligence/machine learning methods, among others. Our workshop will have 2 plenary sessions, 24 invited sessions, and a poster session.

Institute of Mathematical Statistics