Finite Maps: Morphism of Schemes

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Adjunctions and Applications

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Linear Lie Groups: Definitions and Theorems

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Finite Differences Method: Error Division and Schemes

Covers error division and schemes for solving differential equations.

Algebraic Geometry: Regularity and Divisors

Explores regularity, divisors, prime divisors, and uniqueness in algebraic geometry.

Functors: Definition

Introduces functors in category theory and explains their composition.

Modern Algebraic Geometry: Schemes and Affine Schemes

Covers modern algebraic geometry, focusing on schemes and affine schemes, including a review of classical algebraic geometry and Bézout's theorem.

Affine Varieties

Introduces affine varieties and covers morphisms between them and their coordinate rings.

Group Operations and Homomorphisms in Abelian Groups

Explores operations on abelian groups, Homomorphisms, adjoints, and morphisms in group theory.

Mixing Time Changes of Nilflows

Delves into mixing time changes in nilflows, emphasizing the delicate nature of mixing and its dependence on singularities.

Quasi-coherence in Algebraic Geometry

Covers the concept of quasi-coherence in algebraic geometry, discussing the lifting of functions, sections of sheaves, and push forwards of coherent sheaves.