Webrelaunch 2020

Stochastic Geometry (Summer Semester 2020)

This course is offered every year in the summer term. This term it is offered in English.

The registration for the Ilias workspace is now open.

Schedule
Lecture: Monday 14:00-15:30 SR 2.067
Thursday 11:30-13:00 SR 3.069
Problem class: Friday 14:00-15:30 SR 2.058
Lecturers
Lecturer PD Dr. Steffen Winter
Office hours: Please contact me by email.
Room 2.049 Kollegiengebäude Mathematik (20.30)
Email: steffen.winter@kit.edu
Problem classes Steffen Betsch M.Sc.
Office hours: by appointment.
Room 2.009 Kollegiengebäude Mathematik (20.30)
Email: steffen.betsch@kit.edu

Description of the course

How can we estimate the amount of wood in a hectare of woodland, or the surface area of a catalytic converter? How can we estimate the volume of air in construction foam to guarantee its load capacity? Complex structures like foams, cell tissues, soil or fiber structure of paper often show a macroscopic homogenity but strong local variations in its fine details. It is therefore natural to ask, whether one can use probabilistic models to describe and analyse such structures?

The mathematical field of stochastic geometry develops and evaluates models for such random geometric structures. The mathematical background for this theory is formed, on the one hand, by probability theory (random measures, point processes, random sets) and, on the other hand, by convex and integral geometry. In the lecture, we will introduce and study several fundamental models, including germ-grain models (e.g. the Boolean model) and random tesselations.


Prerequisites

The lecture requires a sound knowledge of measure theoretic probability.


Information on the procedure

Online teaching
Due to the current situation concerning Covid-19, we plan to start the course online. In the Ilias workspace of this course, we will provide lecture notes (in English) as well as some weekly instructions which parts of these lecture notes you should study. Moreover, the instructions will contain some exercises which you should do. You are invited to submit your solutions to us for feedback (on a voluntary basis). We also intend to offer online office hours for your questions concerning the lectures and exercises. Further information will be provided solely in Ilias.

Our 'exit strategy'
Should the authorities, during the time of lectures, allow for regular courses in the seminar rooms, we will turn to the above schedule and give the lectures and exercises in person as usual (starting with the week following the official permission). Of course, we will make a corresponding announcement beforehand on this website and in the Ilias workspace in case of such an event.