Title: A geometric approach to the Weyl group
Abstract: I will introduce the Weyl group and the Weyl resolution of a Poisson (or Dirac) manifold of proper type. In the case of the dual of a compact Lie algebra (or compact Lie group), one obtains an alternative geometric definition of the Weyl group, without appealing to any structure theory, as the orbifold fundamental group of an integral affine orbifold. This talk is based on the preprint “Poisson manifolds of compact type” (arXiv:2504.06447), joint work with Marius Crainic and David Martínez Torres.