A joint meeting of the Algebra and Logic Seminar and the Joint Seminar on Analysis, Geometry and Topology will be held on March 12, 2021 (Friday) at 4:30 pm. A talk on Algebraic Non-hyperbolicity of Hyperkähler Manifolds will be delivered by Ljudmila Kamenova (Stony Brook University, USA). Abstract. A projective manifold is algebraically hyperbolic if the degree of any curve is bounded from above by its genus times a constant, which is independent from the curve. This is a property which follows from Kobayashi hyperbolicity. We prove that hyperkahler manifolds are not algebraically hyperbolic when the Picard rank is at least 3, or if the Picard rank is 2 and the SYZ conjecture on existence of Lagrangian fibrations is true. We also prove that if [...]