Lectures related to Singular point of an algebraic variety

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Applications of Residue Theorem in Complex Analysis

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

Smooth Projective Varieties

Covers regular and smooth projective varieties, hypersurfaces, and algebraic dimensions.

Algebraic Multiplicity, Geometric Multiplicity

Explores algebraic and geometric multiplicities of eigenvalues in linear algebra.

Laurent Series: Analysis and Applications

Explores Laurent series, regularity, singularities, and residues in complex analysis.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Homology of Riemann Surfaces

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Algebraic Varieties in Linear Algebra

Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.

Plane Curves: Singular Points and Multiplicities

Explores plane curves, focusing on singular points, multiplicities, and tangent lines.

Compact Manifolds Classification

Covers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.

Bessel Equation: First Frobenius Series Solution around x=0

Explores the Bessel equation solution method and the gamma function properties.

Elliptic Curves: Singular Points and Group Law

Explores singular points, the group law, and the ambiguity in defining the sum of a point with itself on elliptic curves.

Residues Theorem

Explores the Residues Theorem and the classification of holomorphic functions.

Residues Theorem Applications

Explores applications of the residues theorem in various scenarios, with a focus on Laurent series development.

Frobenius Method: General Case of Regular Singular Point

Explores deriving a second solution using the Frobenius series in differential equations.

Frobenius Method: General Case of Regular Singular Point

Explores the Frobenius method for regular singular points in ODEs, emphasizing the nature of roots and deriving solutions.

Tangent Spaces Insights

Explores the relationships between tangent spaces, dimensions, and sub-varieties in algebraic geometry.

Primary Decomposition: Behaviour and Localisation

Explores primary decomposition, recovering rings from spectra, and studying regular functions on spectra.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Dynamics of Singular Riemann Surface Foliations

Explores the dynamics of singular Riemann surface foliations near singular points and their relation to compact manifolds.