What is a hyperkähler manifold?

Abstract: A hyperkähler structure is a geometric structure which occurs naturally in different fields such as algebraic geometry, theoretical physics and Riemannian geometry. For differential geometers, a hyperkähler manifold is a Riemannian manifold with three anti- commuting, parallel and orthogonal complex structures. The most prominent examples – Calabi-Yau manifolds – play an important role in string theory.

After discussing the definition and first properties of hyperkähler manifolds, we will explain some examples in detail. These examples are either constructed as hyperkähler quotients by adapting the symplectic reduction method to the Kähler forms or as the space of real holomorphic sections of the associated twistor spaces. If time permits, we will end the talk by referring to current research results.

algebraic geometrycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: learners

What is ...? Seminar

Series comments: The ``What is ... ? Seminar'' (WiSe) is a weekly Zoom mathematics seminar. The goal is to explain interesting things to each other in a casual manner. The name is inspired by the What is ...? column of the Notices of the American Mathematical Society. See the website for more details. If you want to receive the zoom link for the talks please fill out the form linked on the website or contact Anna at a.puskas@uq.edu.au.