Some new counter-examples to the integral Hodge conjecture (Location: Endnicher Allee 60!)

The Hodge conjecture is one of the major open problems in algebraic geometry. Hodge's original question was stated with integral coefficients, which is nowadays called the integral Hodge conjecture (IHC). The IHC was shown to be false by Atiyah and Hirzebruch more than 50 years ago. Since then many new counter-examples have been constructed and various theories were developed to explain the failure of IHC. In this talk, I will report some recent developments.