Computational topology is a relatively new, but lively field

somewhere between computer science and mathematics. On the mathematical

side it is closely connected to topology. Topology is a somewhat loose

form of geometry, where sizes, distances, angles and other numerical

measures are not really important. Instead, objects are described using

qualitative measures like the number of connected pieces, the number of

holes of different shapes and of tunnels. Because of this, topological

methods have turned out as useful in several problems where too high

precision is unnecessary or even bad. Topological approaches and methods

are used for example for analyzing big data sets, for modelling

networks, reconstructing objects from samples, in robot motion planning,

distributing tasks among processors, and so on.

The course will

have a strong emphasis on student projects. Several typical problems

suitable for a topological approach will be described. Through solving

these problems, the basic topological concepts, structures and

algorithms will be introduced, and tested on real data.To successfully pass this course, the student has to complete 3 homework assignments (deadlines at the ends of months March, April, and May), one group project (in May), and pass a theoretical exam at the end of the semester.

- nosilec: Neža Mramor-Kosta
- nosilec: Žiga Virk