On December 30, 2020, Paul Seymour from Princeton University was the speaker of the Virtual Discrete Math Colloquium. He presented his recent breakthrough on the Erdős-Hajnal conjecture with Maria Chudnovsky, Alex Scott, and Sophie Spirkl, which in particular proves that the Erdős-Hajnal conjecture holds for the cycle of length 5. The title of his talk was “The Erdős-Hajnal conjecture is true for excluding a five-cycle“.