808 G Grassmanians, Flag Manifolds, And Schubert Calculus

• Intro
• Projective Space
• More Projective Space
• Projective Algebraic Sets
• Embedding Manifolds
• Vector Bundle
• Vector Bundle Example
• Vector Space Construction On Bundles
• Vector Bundle Morphisms
• Sections Of Bundles
• Partial Flag Varieties
• Coordinate Charts On Flags
• Plucker Embedding
• Untitled
• Plucker Relations And Varieties
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• Push forward And Pullback Of Cohomology Classes Of Varieties
• Intersection Of Varieties
• Chow Groups
• Schubert Cells On Grassmanians
• Schubert Variety And Classes
• Partitions And Schubert Cells
• Opposite flags
• Schuberts Duality Theorem
• Pieiri Rule
• Cartier Divisors
• Weil Divisors
• Chow Group And Examples
• Intro To Chern Classes
• Chern Classes Of Line Bundles
• Higher Chern Classes
• Untitled
• Splitting Principle
• Chern Roots
• Chern Character
• Cohomology If Complete Flag Bundle
• Bundles Over Points
• Symmetric Functions
• Monomial And Symmetric Bases Of Symmetric Functions
• More Elementary Symmetric Functions
• Complete Symmetric Functions
• Straightening Lemma
• Mirror Identities
• Pieri Rule
• Classical Schur Polynomials And Raising
• Kostka Numbers
• "dual" Pieri Rule
• Littlewood Formula
• Skew Schur Functions
• Cauchy Formula
• Inner Product On Symmetric Functions
• Degree Formula And Tableaux Counting
• Content And Hook Length Formulas
• Schur Functors
• Untitled
• Length Of Permutation
• Bruhat Order On Permutations
• Recognizing Bruhat Order
• Exchange Lemma
• Schubert Polynomial
• Stability Of Schubert Polynomials
• Schubert Polynomials Of Strongly Dominated And Grassmanian Permutations
• Using Schubert Polynomials As Basis
• Background For Schubert Polynomials And Cells
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• Schubert Classes And Polynomials
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• Botc Residue Formula
• Bott Formula And Grassmanians
• General Bott Residue Formulas
• Lagrangian Grassmanian
• Cohomology Of Lagrangian Grassmanian
• Week Group Of Lagrangian Grassmanian
• Lagrangian Schubert Cells
• Schubert Calculus On LG(n,2n)
• IG(n-k,n)
• Sequences In IG
• Symmetric Polynomials In IG