MODUS Seminar Program

Weekly talks in the MODUS Seminar in the summer semester 2024:
Wednesday, 12:15-13:45, Room S102, FAN-B
Individual talks may be held via zoom or at different times, see the information, below.
The list of talks is still incomplete and further talks will be added.

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24.04.2024, 12:15h
Julia Slipantschuk
Dynamical Systems and Data, Universität Bayreuth
Transfer operators and applications

Abstract: A fruitful approach for providing effective statistical descriptions of chaotic dynamical systems is to lift the dynamics to linear evolution operators on infinite dimensional Banach spaces. Spectral data of these operators, known as Koopman or transfer operators, yield insight into the long-term behaviour of the underlying system. In this talk I will give a short introduction into the spectral theory of transfer operators associated to (mostly) low-dimensional discrete chaotic dynamical systems, and present a complete description of eigenvalues of these operators for a certain special class of non-linear maps. In general, such explicit descriptions of eigendata are rarely available, and in various applications algorithms or numerical schemes to approximate these are required. I will present strong spectral convergence and consistency results for a popular numerical approximation scheme -- extended dynamic mode decomposition (EDMD) -- applied to examples of chaotic systems given by one-dimensional expanding maps.

Monday, 6.05.2024, 10:30h, S102
Talk in the lecture series Scientific Computing, Coffee and Tea at 10:00h
Luca Bonaventura
Dipartimento di Matematica, Politecnico di Milano, Italy
A deeper look at shallow water models

Abstract: The derivation of the classical hydrostatic, vertically averaged shallow water equations will be presented and revisited to highlight typical conceptual errors. The choice of time scales determined implicitly by the identification of standard flow regimes will be discussed. Examples of non-hydrostatic shallow water models will be presented and the prospects for their rigorous derivation will be discussed.

8.05.2024, 12:15h
Jirka Vomlel
Institute of Information Theory and Automation (ÚTIA), Academy of Sciences of the Czech Republic
Uncovering Relationships: Using Bayesian Networks to Analyze Open-Minded Thinking and Conspiracy Beliefs in Czech University Candidates

Abstract: I will begin with a brief introduction to one of the glass-box models of artificial intelligence called Bayesian Networks (BNs), a model named after the English statistician Rev. Thomas Bayes. BNs represent a probabilistic model that can help visualize relationships between variables. I will illustrate the use of Bayesian networks on data from a Czech university entrance exam. This data included a test of open-minded thinking designed by Jonathan Baron and also examined students' attitudes towards various conspiracies. Using BNs, we can identify conspiracy clusters and their relationships with open-minded thinking.

15.05.2024, 12:15h
April Herwig
AG Numerik komplexer Systeme, TU München
An introduction to pseudospectra and application to validated computational dynamics