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Subject of the conference: Cohomology theories, Lie algebras and differential geometry are fondamental parts of modern mathematics related to almost any other mathematical subject. Cohomology theory makes a bridge from geometry and topology to algebra, it is a part of the universal beauty of mathematics. Lie algebra theory is a brickstone of contemporary mathematics. In particular, infinite dimensional Lie algebras consitute a subject which transformed mathematical physics and mathematics in general in the last decades. Infinite dimensional Lie algebras appear in differential geometry, integrable systems, cohomology theories and many other fields. Virasoro algebra is one of the best known examples of infinite dimensional Lie algebras. It was discribed by Gelfand and Fuchs in 1967, and since then it serves as an inspirational source for many mathematicaians and physicists in search of new algebraic structures appearing in mathematics and physics. This conference is dedicated to Claude Roger for his contribution to the subject. Claude Roger is at the origins of the fondamental developpements in the field. He is also one of the two authors of the the most complete and diverse book on the Virasoro algebra. The conference has an ambitious aim to reunite the most prominent experts in the subject, who have also interacted with Claude Roger in the course of his mathematical career.