Erlend Raa Vågset

Field of work

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I am an Associate Professor of Computer Science and Mathematics at HVL in Førde. My work is divided between research and teaching.

My research is at the intersection of computational topology and parameterized complexity theory. Both are quite theoretical fields: the first is concerned with shape and structure in data, while the second asks what makes some computational problems easy and others hard. I am particularly interested in homology, topological structure in data, and computational hardness. Further down the page, I have linked to a few short videos for readers who want a more intuitive introduction. My most recent paper is on discrete Morse theory. 

In teaching, I try to create ways of working in which students think, investigate, and solve problems together. That is why I use discussion, work at the board, and hands-on activities, not only to make abstract ideas more tangible, but also to build a learning community in which motivation can grow through collaboration, participation, and shared responsibility. The goal is not simply for students to learn a particular solution, but to understand why it works, develop a greater sense of ownership over their work, and become more confident when tackling new problems. I am inspired by traditions of democratic education and by pedagogical ideas that emphasize thinking, community, responsibility, and freedom, and I try to let such ideas take practical form within the framework of Norwegian higher education.

Three videos about my field

It may be easier to get a first impression of what I work on through these three videos than through a long written explanation.

This open problem taught me what topology is
One of the best introductions to topology that I know. It gives a concrete and visual sense of what topological thinking is, without making the subject artificially simple.

FTDA: Intro to Topological Data Analysis
A good introduction to how topological ideas can be used to understand data, and to the part of my work that deals with shape, structure, and patterns in complex datasets.

P = NP? | Complexity Theory Explained Visually
A clear and accessible introduction to complexity theory, and to the question of why some problems can be solved efficiently while others become difficult very quickly.

Three videos about teaching

These three videos reflect some of the ideas that shape how I think about teaching.

John Dewey’s 4 Principles of Education
A short and clear introduction to some of the ideas behind the view of learning as something we do, not simply something we receive.

Peter Liljedahl: Å bygge tenkende klasserom
What I like about this one is how concrete it is. It is not just about students being “active,” but about how teaching can be structured so that they actually think, investigate, and collaborate.

Summerhill School: Leavers Interview
What is most interesting here is hearing former students describe how freedom, responsibility, and trust shape learning. The video points to something important about independence and finding one’s own path.