Due to the rather broad spectrum of topics within the IMPRS, the curriculum consists of a core curriculum to be attended by all students and a variety of more specialized lectures and courses. The heart of our teaching program certainly is the Ringvorlesung. Each semester the Ringvorlesung focuses on one field and is usually delivered by scientific members of the IMPRS who introduce different approaches and visions within this field.
- Lecturer: IMPRS Faculty, Daniela Cadamuro, Angkana Rüland, Matteo Smerlak
- Date: Friday 09.15-11.00 (Rüland) 09.30-11.00 (Cadamuro) tbc (Smerlak)
- Room: MPI MiS G3 10
- Audience: IMPRS students, Phd students, postdocs
- Keywords: Scattering theory, Calder'on Problem, Evolutionary dynamics
Schedule and Abstracts
Part A by Angkana Rüland (25.10., 01.11., 08.11.,15.11.): The Calder'on Problem -- A Prototypical Inverse Problem
Exercise classes only on 25.10. and 08.11.
Part B by Daniela Cadamuro (22.11., 29.11., 13.12. 20.12.): Scattering Theory
This course offers an introduction to the mathematical and foundational aspects of scattering theory in quantum mechanics. We consider the one-dimensional Schrödinger operator on the line with a multiplicative potential, and present some facts about both the forward and inverse scattering problems. In the first case one studies the properties of the scattering matrix (and of the Møller operators) depending on those of the potential, while in the second case one determines the potential from scattering data, such as the reflection coefficient. As an application, we consider the stability of "quantum inequalities" under scattering, which is relevant in physics, for example for the phenomenon of "quantum backflow".
IMPRS student lecture (06.12., 10.30 o'clock): Sharwin Rezagholi: Symbolic dynamics and cellular automata:
Symbolic dynamics is a subfield of dynamical systems and theoretical computer science where elementary parts of topology, algebra, and discrete mathematics meet in a beautiful way. This minicourse will cover the central definitions and results, such as shifts, subshifts, shifts of finite type, cellular automata, and entropy/word complexity. There are no prerequisites.
IMPRS student lecture (10.01. , 09.30) Felix Gaisbauer: A brief introduction to opinion dynamics and a model of opinion expression
I will give a very short introduction to opinion dynamics, including the Ising model and the voter model. I will then turn to a model our group is currently developing, which does not investigate opinion change, but public opinion expression. I will present a game-theoretic as well as a dynamical systems approach to opinion expression. There are no prerequesites.
Part C by Matteo Smerlak (17.01., 24.01., 31.01., 07.02., 9.15 ): Evolutionary dynamics