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New Professor in Algebra joins the Department of Mathematics

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Published on Monday, 30 August 2021

Pieter Belmans has recently joined the University of Luxembourg as Assistant Professor, specialised in algebraic geometry.

Prof. Pieter Belmans shares with us his background, research activities and future challenge

1) Could you introduce yourself?

"I am a mathematician, interested in algebraic geometry and its many interactions with noncommutative algebra and representation theory. I have just started working at the University of Luxembourg as an assistant professor. I have held postdoc positions at the University of Bonn, the University of Antwerp and the Max Planck Institute in Bonn. I obtained a joint PhD in mathematics from the University of Antwerp and the University of Hasselt. Before that, I studied computer science and mathematics at the University of Antwerp, Ghent University and Ecole Polytechnique in Paris. Besides research and teaching, I am very interested in outreach and science communication. It is often very hard to communicate with non-experts about recent results in abstract mathematics. But e.g. in chemistry one has the periodic table of elements which is a succinct description of a complicated classification, and even without fully understanding all of its details, an outsider can get a feeling for what is going on. Mathematics and algebraic geometry in particular also has interesting classification results of a very similar nature, and making these accessible to outsiders is a very rewarding activity. And in my experience this creates an interesting feedback loop too, inspiring new research and novel ways of teaching!"

2) What is your research field?

"My work combines ideas and tools from algebraic geometry with noncommutative algebra and representation theory. Algebraic geometry starts as the study of solutions to polynomial equations. This goes back all the way to the ancient Greeks studying conic sections (ellipses, parabolas and hyperbolas), which correspond to a single equation of degree two in two variables. By increasing the degree, the number of variables and the number of equations one can obtain many more geometric objects. In the 21th century a whole machinery exists to study these objects. Representation theory concerns highly symmetric objects and develops tools to study them, whilst noncommutative algebra concerns objects in which the order of multiplication is important. All three subjects have many ties to neighbouring fields of mathematics, but also mathematical physics. My own interests are then deformation theory and moduli spaces, which concerns: trying to construct new objects out of old objects, possibly classifying all these objects and studying which properties are (not) preserved amongst different elements of the classification."

3) Why did you join the University of Luxembourg?

"The Department of Mathematics at the University of Luxembourg provides an excellent environment to further develop my research interests. There is ample expertise in deformation quantisation, algebraic geometry and topology which allows for many interesting interactions. They also welcome science communication, and I look forward to further developing the initiatives I am involved in. The University of Luxembourg (and the Fonds National de la Recherche) moreover provides an excellent research environment, with ample support for activities and developing a research group."