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PLEASE NOTE: If a candidate gives a layman's talk, the livestream will start fifteen minutes earlier.

The world around us is inherently complex, filled with problems that demand solutions. Every day, we face questions like, "How can I pack all of my groceries into my fridge?'', "How do I get to the Academiegebouw from the train station?'', "Where is the nearest bookstore that is open right now?''. More and more, we use computers to answer such questions, as these questions often become too complex to answer by hand. Many of these problems are geometric in nature: they deal with properties of space such as distance, shape, size, and position. In the field of computational geometry we study such geometric problems and formulate efficient solutions for them.

To do so, we must translate a geometric problem into a form that a computer can understand. In other words, we have to express the problem in the realm of mathematics: using numbers, formulas, and equations. We can then develop algorithms and data structures that support us in solving these problems.

When solving travel-related problems, we might not want to measure distances by the Euclidean distance between the points, but by the time it takes to travel. Furthermore, there are often other objects (e.g. buildings, rivers, roads, islands) that influence the shortest path between the sites. We can model such an environment using a polygonal domain: a polygon possibly containing some polygonal holes. Within a polygonal domain, we measure distances using the geodesic distance: the length of the shortest obstacle avoiding path. In this thesis, we study several central problems from computation geometry in this setting.