Geometric Singular Perturbation Theory
Supervisors Dr. Frits Veerman (veerman@math.uni-heidelberg.de) Prof. Dr. Anna Marciniak-Czochra (anna.marciniak@iwr.uni-heidelberg.de) |
Time: Tuesdays, 14:00h (sharp), room 2/414 Mathematikon |
Participants: Master's students Mathematics/ Physics. Ph.D students are also encouraged to join. |
Abstract: The aim of this seminar is to introduce a number of modern analytical techniques collectively known as Geometric Singular Perturbation Theory (GSPT). Combines aspects of classical asymptotic analysis with notions from dynamical systems and geometry to provide a rigorous and insightful framework for analysing so-called singularly perturbed dynamical systems, which are characterised by the occurence of multiple time- and spatial scales. Complex, high-dimensional systems can be divided into components that are easier to understand, which allows deeper understanding of the structure of the full dynamical system. GSPT can often be used to provide a rigorous basis for heuristic model reduction procedures, and is therefore frequently applied to biological, physical and chemical models. The seminar starts with a small number of lectures introducing necessary concepts from dynamical systems theory, and subsequently presenting the main ideas of GSPT. After that, seminar participants are invited to present (parts from) research papers that put these techniques into practice, thereby giving a wide overview of the applicability of GSPT in mathematical, biological and physical research. Seminar participants are expected to be familiar with ordinary differential equations, and in particular mathematical techniques such as phase plane analysis. Familiarity with partial differential equations is useful, but not necessary. |
Materials: A list of topics with literature references can be found here. The seminar schedule can be found here. |