Location: INF 205 (Mathematikon), SR 2
Date: Friday, 11:00 - 13:00 c.t. (c.t. means Cum Tempore, i.e. start at 11:15 !!! )
Preliminary discussion: Friday, 22.04.2022, 11.00-13.00 ct, INF 205 (Mathematikon), SR 2.
Cancer is one of the leading causes of disease-related death worldwide. In recent years, rapid increase in the molecular understanding of cancer has unraveled significant additional complexity of the disease. Although large amounts of data on cancer genetics and molecular characteristics are available and accumulating with increasing speed, adequate interpretation of these data still represents a major bottleneck. This is exactly where mathematics can be applied to oncology: Through mathematical modeling of complex biological processes we are able to gain novel, unprecedented medical insights. The fields of application of mathematical models include the analysis of biological concepts and medical hypotheses about cancer evolution, and the prediction of clinical outcomes using existing clinical and molecular information. On the other hand, the medical applications give rise to mathematical challenges, which can lead to new methods and algorithms in various fields of mathematics, like data analysis, mathematical modeling and machine learning. Therefore, applying mathematics in the field of oncology facilitates data interpretation and improve our understanding of the underlying processes which lead to cancer.
During this seminar, we will have a closer look at the main areas of current research in mathematical oncology, starting with the description of the first mutated cell over the growing tumor and the influence of the immune system thereon. We will look at different mathematical approaches: stochastic modeling, ordinary differential equations, partial differential equations, graph theory. The goal is to answer the following questions:
- How can each of these processes be modeled mathematically?
- Which mathematical tools can be used for modeling?
- Which numerical methods are needed for solving these problems?
- How can we compare the different models?
- What is the medical implication of the mathematical results?
- How can our medical colleagues benefit from these models?
In this seminar, 12 different topics are provided. Each interested Master student can create a list of three topics of his/her choice (prioritized). The 12 topics will be distributed in order to match the interests of the participants as good as possible. The maximum number of students is 12. Therefore, if more students should be interested, the topics will be distributed by random selection of the students which attend the preliminary discussion on 22 April 2022. Later applications can only be considered if not all topics have been distributed.
The prerequisites for each seminar talk depend on the chosen topics. The latter are based on:
- Knowledge in numerical mathematics (esp. ordinary and partial differential equations)
- Knowledge in stochastic (esp. random variables, probability densities, stochastic processes, expectation, Markov processes)
- Knowledge in graph theory (esp. directed acyclic graphs, trees)
- Knowledge in programming is optional
Please note the following requirements for the award of credit points: regular participation in the seminar, presentation with handout, and written summary of the presentation. Details will be announced at the preliminary meeting.