Perspectives in Lie Theory

Part I Lecture notes. - 1 Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian PDE.- 2 An introduction to algebras of chiral differential operators.- 3 Representations of Lie Superalgebras.- 4 Introduction toW-algebras and their representation theory. Part II Contributed papers.- 5 Representations of the framisation of the Temperley-Lieb algebra.- 6 Some semi-direct products with free algebras of symmetric invariants.- 7 On extensions of affine vertex algebras at half-integer levels.- 8 Dirac cohomology in representation theory.- 9 Superconformal Vertex Algebras and Jacobi Forms.- 10 Centralizers of nilpotent elements and related problems.- 11 Pluri-Canonical Models of Supersymmetric Curves.- 12 Report on the Broué-Malle-Rouquier conjectures.- 13 A generalization of the Davis-Januszkiewicz construction.- 14 Restrictions of free arrangements and the division theorem.- 15 The pure braid groups and their relatives.- 16 Homological representations of braid groups and the space of conformal blocks.- 17 Totally nonnegative matrices, quantum matrices and back, via Poisson geometry.