Watch a 38-minute lecture from Harvard CMSA's Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry where USTC's Bailin Song explores the global sections of chiral de Rham complexes on compact Calabi-Yau manifolds. Delve into complex mathematical concepts including local structures, coordinate changes, and sub-algebras of W(V), while examining holomorphic sections in both special and general cases. Learn about the actions of algebraic vector fields, loop algebras, and their invariants, along with the theoretical framework behind differential operators and super commutative algebras. Gain insights into the intricate relationship between vertex algebras and complex manifolds through detailed mathematical proofs and theoretical demonstrations.
The Global Sections of Chiral de Rham Complexes on Compact Calabi-Yau Manifolds
Harvard CMSA via YouTube
Overview
Syllabus
Intro
Global sections
Local structure
Change of the Coordinates
Sub algebra of W(V)
Hermitian form
Globally defined operators
Holomorphic sections: special cases
Holomorphic sections: general cases
Action of algebraic vector fields on W(V)
Invariants under the actions of Special series and Hamiltonian series
The action of loop algebra on SW(V)
Invariants under the actions of the loop algebra
Sketch proof of the theorem
A bundle of the super commutative algebras
The differential operator
Sketch proof of theorem
Taught by
Harvard CMSA
