Algebraic Geometry

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Related lectures (28)

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Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Integration on H_pxH and Arithmetic

Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.

Vector Spaces: Properties and Examples

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Complex Roots and Polynomials

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Complex Roots: Conjugate Pairs and Quadratic Equations

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Weil Conjectures: Rationality and Function Equation

Covers the Weil conjectures on rationality, functional equation, and the Riemann hypothesis, exploring properties of varieties in algebraic geometry.

Polynomials: Theory and Operations

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

Linear Combinations and Vector Spaces

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Integration of Rational Functions

Covers the integration of rational functions, focusing on decomposing functions into simpler elements.