Monday 27th of February 2023, 15:15-16:15 in HG03.085
Kevin Zwart
Representation theory and the Mathieu conjecture.
In the '90s, Olivier Mathieu published a paper in which he proposed a proof for the famous Jacobian
conjecture. To prove this, he unfortunately needed another conjecture (which is very creatively named
'the Mathieu conjecture') that up to this day is still open. His conjecture involved representation theory
of compact connected Lie groups. There have been attempts to generalize Mathieu's conjecture and prove
those instead, but these attempts all turned out to be false. The original Mathieu conjecture itself
however is still an open question.
In this talk, we will discuss the Mathieu conjecture. To do that, we need some representation theory of
compact connected Lie groups. We will start with the definitions, and state the Peter-Weyl theorem.
Next we will discuss the Mathieu conjecture in more detail, and the progress made since Mathieu stated
the conjecture. As this is my research topic, I will close by talking about my own findings. The only
prerequisites for this talk is some knowledge of group theory and linear algebra.