Preliminary course catalogue - changes and additions are still possible.
Click on the course title for more information!
New (and partly not yet in den annotated course catalogue):
Please note the registration modalities for the individual seminars published in the comments to the course catalog: As a rule, places are allocated after pre-registration by e-mail at the preliminary meeting at the end of the lecture period of the summer semester. You must then register online for the exam; the registration period runs from August 1, 2025 to October 8, 2025.
Seminar: Computational PDEs – Gradient Flows and Descent Methods
Lecturer: Sören Bartels
Language: Talk/participation possible in German and English
Seminar: Mo, 14-16h, SR 226, Hermann-Herder-Str. 10
Preliminary Meeting 15.07., 12:30, Raum 209, Hermann-Herder-Str. 10
Preparation meetings for talks: Dates by arrangement
The seminar will be devoted to the development of reliable and efficient discretizations of time stepping methods for parabolic evolution problems. The considered model problems either result from minimization problems or dynamical systems and are typically constrained or nondifferentiable. Criteria that allow to adjust the step sizes and strategies that lead to an acceleration of the convergence to stationary configurations will be addressed in the seminar. Specific topics and literature will be assigned in the preliminary meeting.
Mathematical Seminar
Elective
Lecturer: Wolfgang Soergel
Language: Talk/participation possible in German and English
Seminar: Di, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Preregistration: In case of interest, please email to Wolfgang Soergel
Preliminary Meeting 17.07., 12:15
Structure of noncommutative rings with applications to representations of finite groups.
necessary: Linear Algebra I and II \
useful: Algebra and Number Theory
Mathematical Seminar
Elective
Seminar: Medical Data Science
Lecturer: Harald Binder
Language: Talk/participation possible in German and English
Seminar: Mi, 10:15-11:30h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preregistration:
Preliminary Meeting 23.07., 10:15, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
To answer complex biomedical questions from large amounts of data, a wide range of analysis tools is often necessary, e.g. deep learning or general machine learning techniques, which is often summarized under the term ``Medical Data Science''. Statistical approaches play an important rôle as the basis for this. A selection of approaches is to be presented in the seminar lectures that are based on recent original work. The exact thematic orientation is still to be determined.
Good knowledge of probability theory and mathematical statistics.
Mathematical Seminar
Elective
Seminar: Minimal Surfaces
Lecturer: Guofang Wang
Language: Talk/participation possible in German and English
Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting 30.07., SR 125, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Minimal surfaces are surfaces in space with a ‘minimal’ area and can be described using holomorphic functions. They appear, for example, in the investigation of soap skins and the construction of stable objects (e.g. in architecture). Elegant methods from various mathematical fields such as complex analysis, calculus of variations, differential geometry, and partial differential equations are used to analyse minimal surfaces.
Mathematical Seminar
Elective
Seminar: Random Walks
Lecturer: Angelika Rohde
Assistant: Johannes Brutsche
Language: Talk/participation possible in German and English
Seminar: Mo, 16-18h, SR 127, Ernst-Zermelo-Str. 1
Preliminary Meeting 22.07., Raum 232, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Preregistration: If your are interested in the seminar, please write an email to Johannes Brutsche listing your prerequisites in probability and note if you plan to attend the Probability Theory II.
Random walks are stochastic processes (in discrete time) formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. Many results that are part of this seminar also carry over to Brownian motion and related processes in continuous time. In particular, the theory for random walks contains many central and elegant proof ideas which can be extended to various other settings. We start the theory at the very beginning but quickly move on to proving local central limit theorems, study Green's function and recurrence properties, hitting times and the Gambler's ruin estimate. Further topics may include a dyadic coupling with Brownian motion, Dirichlet problems, random walks that are not indexed in \(\mathbb{N}\) but the lattice \(\mathbb{Z}^d\), and intersection probabilities for multidimensional random walks (which are processes \(X:\mathbb{N}\rightarrow\mathbb{R}^d\)). Here, we will see that in dimension \(d=1,2,3\) two paths hit each other with positive probability, while for \(d\geq 4\) they avoid each other almost surely.
Probability Theory I \
Some talks only require knowledge of Stochastics I, so if you are interested in the seminar and have not taken part in the probability theory I class, do not hesitate to reach out to us regarding a suitable topic.
Mathematical Seminar
Elective