Perspectives in Lie Theory

Part I. Lecture Notes

1. Introduction to Vertex Algebras, Poisson Vertex Algebras, and Integrable Hamiltonian PDE
Victor Kac

2. An Introduction to Algebras of Chiral Differential Operators
Fyodor Malikov

3. Representations of Lie Superalgebras
Vera Serganova

4. Introduction to W-Algebras and Their Representation Theory
Tomoyuki Arakawa

Part II. Contributed Papers

5. Representations of the Framisation of the Temperley–Lieb Algebra
Maria Chlouveraki, Guillaume Pouchin

6. Some Semi-Direct Products with Free Algebras of Symmetric Invariants
Oksana Yakimova

7. On Extensions of Affine Vertex Algebras at Half-Integer Levels
Dražen Adamović, Ozren Perše

8. Dirac Cohomology in Representation Theory
Jing-Song Huang

9. Superconformal Vertex Algebras and Jacobi Forms
Jethro Ekeren

10. Centralizers of Nilpotent Elements and Related Problems, a Survey
Anne Moreau

11. Pluri-Canonical Models of Supersymmetric Curves
Giulio Codogni

12. Report on the Broué–Malle–Rouquier Conjectures
Ivan Marin

13. A Generalization of the Davis-Januszkiewicz Construction and Applications to Toric Manifolds and Iterated Polyhedral Products
A. Bahri, M. Bendersky, F. R. Cohen, S. Gitler

14. Restrictions of Free Arrangements and the Division Theorem
Takuro Abe

15. The Pure Braid Groups and Their Relatives
Alexander I. Suciu, He Wang

16. Homological Representations of Braid Groups and the Space of Conformal Blocks
Toshitake Kohno

17. From Totally Nonnegative Matrices to Quantum Matrices and Back, via Poisson Geometry
S. Launois, T. H. Lenagan

Avainsanat: Mathematics, Non-associative Rings and Algebras, Mathematical Physics, Algebraic Topology, Combinatorics