UNION OF BULGARIAN MATHEMATICIANS INSTITUTE OF MATHEMATICS AND INFORMATICS, BULGARIAN ACADEMY OF SCIENCES   NATIONAL MATHEMATICS COLLOQUIUM The next meeting of the National Mathematics Colloquium will be held on June 25, 2018 (Monday) at 16:00 in the Conference Room of the Institute of Mathematics and Informatics, Acad. G. Bonchev Street, Block 8 A talk on: On Kobayashi's conjecture for K3 surfaces and hyperkaehler manifolds Everybody is invited. Head of the Colloquium: Acad. P. Popivanov Abstract. The Kobayashi pseudometric on a complex manifold M is the maximal pseudometric such that any holomorphic map from the Poincare disk to M is distance-decreasing. Kobayashi conjectured that this pseudometric vanishes on Calabi-Yau manifolds. Using ergodicity of complex structures, we prove this conjecture for all K3 surfaces and for most [...]