Coimbra - May 2024

May 10, 2024, Mathematics Department / CMUC of Faculdade de Ciências e Tecnologia, Universidade de Coimbra

Speaker: Gonçalo Oliveira (Instituto Superior Técnico)
Title: Special Lagrangians and mean curvature flow on Gibbons-Hawking manifolds
Abstract: Mirror symmetry is a somewhat mysterious phenomenon that relates the geometry of two distinct Calabi-Yau manifolds. In the realm of trying to understand this relationship several conjectures on the existence of so-called special Lagrangian submanifolds appeared. In this talk, I will report on joint work with Jason Lotay on which we prove versions of the Thomas and Thomas-Yau conjectures regarding the existence of these special Lagrangian submanifolds and the role of Lagrangian mean curvature flow as a way to find them. I will also report on some more recent work towards proving more recent conjectures due to Joyce.

Speaker: Lucile Vandembroucq (Universidade do Minho)
Title: On the (higher) topological complexity of manifolds with abelian fundamental group
Abstract: The topological complexity and its higher versions are homotopy invariants which were introduced by Farber and Rudyak in order to give a topological measure of the complexity of the motion planning problem. We will discuss some properties of these invariants for closed manifolds with abelian fundamental group. In particular, we will give sufficient conditions for the (higher) topological complexity of such a manifold to be non-maximal. This is based on joint works with N. Cadavid, D. Cohen, J. González and S. Hughes.

Speaker: Leander Stecker (Instituto Superior Técnico)
Title: Canonical Submersions and 3-(α, δ)-Sasaki geometry
Abstract: We introduce the classical results of de Rham and Berger on the holonomy of a Riemannian manifold. We compare these to the situation of parallel skew-torsion, where we obtain Riemannian submersions from reducible holonomy. If time permits I will give an introduction to 3-(α, δ)-Sasaki manifolds and their submersion onto quaternionic Kahler manifolds.