Lectures related to Projective Plane Curves

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Algebraic Curves: Normalization

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

Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Tangent vectors without embedding space: Making tangent spaces linear

Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.

Analyse 2: Division euclidienne

Explores the process of division euclidienne in polynomials, emphasizing the importance of polynomial degrees during operations.

Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Parametric Curves: Descartes' Folium

Covers Descartes' Folium, a parametric curve with specific equations and properties, including domain boundaries and tangent vector analysis.

Projective Geometry: Tangent Lines Log in to Mediaspace to watch this video

Discusses the correction of tangent lines and projective plane curves, exploring topological applications and curve structure.

Elliptic Curves: Theory and Applications Log in to Mediaspace to watch this video

Covers the theory and applications of elliptic curves in cryptography and number theory.

Intersection Numbers: Algebraic Counting Solutions Log in to Mediaspace to watch this video

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

Tangent Lines and Equality Log in to Mediaspace to watch this video

Explores the intersection multiplicity of curves and the absence of common tangent lines.

Plane Curves: Singular Points and Multiplicities Log in to Mediaspace to watch this video

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

Curves and Surfaces Log in to Mediaspace to watch this video

Covers the representation of plane curves and the nature of obtained curves.

Differential Geometry: Parametric Curves & Surfaces Log in to Mediaspace to watch this video

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Polynomials on a Field: Basics and Operations Log in to Mediaspace to watch this video

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Advanced Analysis II: Isoclines Method Log in to Mediaspace to watch this video

Explores the Isoclines Method and solutions of differential equations with tangents.

Curves: Parameterized Curves and Tangent Vectors Log in to Mediaspace to watch this video

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Surfaces in R^3: Curves and Regular Surfaces Log in to Mediaspace to watch this video

Covers curves in R^2, regular surfaces in R^3, and geometric properties of edges.

Characteristic Polynomials and Similar Matrices Log in to Mediaspace to watch this video

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