Seminar 4.10.2018: Miroslav Kramar

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 4.10.2018: Miroslav Kramar

Postby quittner » Wed Sep 19, 2018 10:18 am

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Thursday 4.10.2018 at 14:00 Lecture room M-223

Miroslav Kramár (INRIA Saclay):
Towards understanding complex spatio-temporal systems

Abstract:
Nonlinear dynamical systems play an important role in modelling of
various processes in fields ranging from physics, chemistry and biology
to many other natural and social sciences. Despite the importance of
nonlinear models and intense efforts of many researchers, the global
dynamics of many of these systems is still far from being properly
understood. Our comprehension of the dynamics becomes even more
tentative if the governing equations are not known. In this case the
study of the system is based on data collected from experiments. In this
talk I will introduce rigorous mathematical methods for analysing the
dynamics of a system from time series and demonstrate these methods on a
variety of different problems which exhibit an intricate pattern
formation. In the first part I will explain how to describe these
patterns using persistent homology. Persistent homology allows us to
transform experimental or numerical data into a point cloud in the space
of persistence diagrams. There are a variety of metrics that can be
imposed on the space of persistence diagrams. By choosing different
metrics one can interrogate the pattern locally or globally, which
provides deeper insight into the dynamics of the process of pattern
formation. In the second part of this talk I will discuss topological
methods for identifying robust dynamical structures that act as
organising block of the dynamics.
quittner
 
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