As requested by the organisers, the talk is an advanced (more differential geometry oriented) version of the talk I gave as a colloquium in November, but I assume that some of the people have not been there, and will talk from scratch, and the abstract is essentially the same (but people who attended the colloquium will also hear new stuff).

On Wednesday morning you are going to hear a bunch of stories about manifolds, focusing on two main characters: a compact holomorphic manifold and a Riemannian manifold. The talk consists of three seemingly independent parts. In the first part, the main character is going to be a compact holomorphic manifold, and as in every story, there will be some action going on. This time we act with the group of invertible complex numbers, or even better, with several copies of those. The spirit of late Andrzej Białynicki-Birula until this day helps us to understand what is going on. The second part is a tale of holonomies, it begins with "a long time ago,..." and concludes with "... and the last missing piece of this mystery is undiscovered till this day". The main character here is a quaternion-Kahler manifold, but the legacy of Marcel Berger is in the background all the time. In the third part we meet legendary distributions, which are subbundles in the tangent bundle of one of our main characters. Among others, distributions can be foliations, or contact distributions, which like yin and yang live on the opposite sides of the world, yet they strongly interact with one another. Ferdinand Georg Frobenius is supervising this third part. Finally, in the epilogue, all the threads and characters so far connect in an exquisite theorem on classification of low dimensional complex contact manifolds. In any dimension the analogous classification is conjectured by Claude LeBrun and Simon Salamon, while in low dimensions it is proved by Jarosław Wiśniewski, Andrzej Weber, in a joint work with the narrator.