Chapter 1 Singular Support of a Vertex Algebra and the Arc Space of Its Associated Scheme

Chapter 2 On Cacti and Crystals

Chapter 3 Quotients for Sheets of Conjugacy Classes

Chapter 4 About Polynomiality of the Poisson Semicentre for Parabolic Subalgebras

Chapter 5 On Dynkin Gradings in Simple Lie Algebras

Chapter 6 Multiplicative Slices, Relativistic Toda and Shifted Quantum Affine Algebras

Chapter 7 Some Properties of Orbital Varieties in Extremal Nilpotent Orbits

Chapter 8 On Involutions in the Weyl Group and B -Orbit Closures in the Orthogonal Case

Chapter 9 Proper Self-Similar Triangle Tiling and Representing Weight Diagrams in the Plane

Chapter 10 Closures of O n -Orbits in the Flag Variety for GL n

Chapter 11 The Spin Calogero-Sutherland Model at Infinity

Chapter 12 Semi-Direct Products Involving Sp 2 n or Spin n with Free Algebras of Symmetric Invariants

Chapter 13 Primitive Ideals of U ( 𝖘 𝖑 ( ∞ ) ) $${\mathrm {U}}(\mathfrak {sl}(\infty ))$$ and the Robinson–Schensted Algorithm at Infinity