Our CAMP seminars provide you with a wide array of topics covering the mathematical sciences. This seminar series, which has been running since 2012, is organized by the CRM research groups, inviting experts and collaborators to deliver a talk on a specific topic related to the research carried out at the center. The CAMP seminar series is the perfect meeting point for the PhD students currently working on their thesis projects and other young researchers interested on the opportunities offered at the CRM.
past session || July Friday 16th, 2021 – 12:00 (CET)
How to model complex systems? Complex is what we perceive as spatially, temporally and dynamically rich and esthetically beautiful. This richness is declined in the shapes of turbulent vortices, the rage of a storm, the exponentially fast diffusion of a virus or an economic crisis. I will present a physically informed machine learning approach, which combine the point of view of statistical physics and dynamical systems theory to devise statistical tools that act as magnifying glasses for complex systems. The first specific question I have tackled is to determine how many variables, equations or data we need to describe a specific event, whether this turns out or not to be extreme for the system we examine. One of the outcomes of this investigation is the possibility of studying some of the most complex systems we can figure out, namely an ensemble of turbulent vortices in a confined geometry with just three simple dynamical equations. These equations do not only describe the mean state of the system but they allow for short term predictability of its motion. Another counterintuitive result is that extreme events of the atmospheric circulation correspond to specific bricks of the underlying and unknown mathematical geometry of those systems, namely the unstable fixed points of the dynamics. Equipped with these statistical tools, we can search the footprint of unstable fixed points in natural phenomena and discover their correspondence with extreme events encountered in the everyday life: so far – and I give an overview of these research in this manuscript – we have discovered that they appear either as extreme turbulent vortices in the atmosphere, or as storms, hurricanes, earthquakes or even as specific states of the brain.