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178 videos
The Riemann-Roch theorem for curves
Properties of tensors products of vector spaces
Number field - Function field analogy
Manifolds - Intrinsic Geometry
Complex Analysis and algebraic geometry
Limits of Sequences: Formal Definition
Why Vector Bundles
Introduction to tensors in linear algebra
Modules
Connectedness
Tensor products. Coordinate free version.
You already know some Galois theory!
Homotopy
Galois groups of topological covers
The Galois group
The fundamental group and higher homotopy groups
Geometry of blowups
Applications of Riemann-Roch to Classifying Low genus curves
Constructing regular polygons
Finite fields via Galois theory
Sheaf cohomology
Recurrence Relations and Generating Functions
Serre duality and the adjunction formula
The Galois correspondence
Infinite Galois theory
The Riemann-Roch Theorem for Surfaces
Separable and Galois extensions
The Artin-Castelnuovo contraction theorem
Linear systems projections
Cech cohomology
The Galois correspondence in topology
Localisation in commutative algebra
The Riemann Hurwitz formula.
Central simple algebras as twisted forms of matrix algebras
ExponentialGenerating Functions
Lifting properties of covers and deck transformations
Zeta functions for varieties over finite fields
The simply connected or universal covering space
Differential forms and integration on manifolds
Weil's insight: A Lefschetz fixed point formula for varieties?
Etale cover - open cover analogy
Linear Ordinary Differential Equations
Cauchy Completeness and existence of limits.
Catalan numbers
What are the Weil conjectures about?
Analytic Power Series
Ratio test for convergence
Difference Operator
Counting and bijections
Galois cohomology and descent data
