Lecturer: PATRICK MIMPHIS TCHEPMO DJOMEGNI

Abstract

Most real-world problems and the fundamental laws of physics are formulated in terms of differential (often nonlinear) or difference equations (DEs). Despite significant advances in analytical techniques, the majority of nonlinear DEs do not admit explicit solutions. This course is devoted to the analysis of continuous-time dynamical systems, with an emphasis on qualitative rather than quantitative methods. In particular, the module examines system stability and sensitivity to small perturbations.

The CRM opens an annual call for CRM Intensive Research Programmes (IRP) approximately two years in advance. The CRM started organising IRPs in 2003 and has held two to three per year since then. Each programme consists of a number of resident researchers, from junior to senior, and at least two scientific events (workshops, advanced courses, and conferences).

The CRM opens an annual call for CRM Intensive Research Programmes (IRP) approximately two years in advance. The CRM started organising IRPs in 2003 and has held two to three per year since then. Each programme consists of a number of resident researchers, from junior to senior, and at least two scientific events (workshops, advanced courses, and conferences).

The CRM opens an annual call for CRM Intensive Research Programmes (IRP) approximately two years in advance. The CRM started organising IRPs in 2003 and has held two to three per year since then. Each programme consists of a number of resident researchers, from junior to senior, and at least two scientific events (workshops, advanced courses, and conferences).

The CRM opens an annual call for CRM Intensive Research Programmes (IRP) approximately two years in advance. The CRM started organising IRPs in 2003 and has held two to three per year since then. Each programme consists of a number of resident researchers, from junior to senior, and at least two scientific events (workshops, advanced courses, and conferences).

This Thematic Month aims to cover topics related to singularity theory of algebraic or analytic spaces, algebraic study of differential equations, and their applications to questions of transcendence.

The interface of mathematics with computer science form a large, diverse and rich landscape. Of course, many classical mathematical tools and concepts turn out to be very useful to answer questions arising from computer science. Besides, the core objects of computer science (typically discrete) that were once considered non-classical in mathematics have now a well-established and growing theory. In addition, the main ideas of computer science (the very notions of computation and algorithmic complexity) yield new points of views and new questions on many mathematical objects.

Scientific Machine Learning (SciML) is a relatively new research field based on both machine learning (ML) and scientific computing tools. Its aim is the development of new methods to solve several kinds of problems, which can be forward multidimensional partial differential equations, identification of parameters, or inverse problems. The methods we seek must be robust, reliable and interpretable. The new SciML tools allow the natural inclusion of data in the numerical simulation in order to generate new results.

The thematic month “Arithmetic and Information Theory” focuses on arithmetic geometry, information theory and their interplay.