Lectures related to Curve of Genus 2: Very Ample Divisors

Explores the applications of Serre duality in Enriques-Severi-Zariski lemma, foliations, and Riemann-Roch theorem.

Albanese and Fourier Transform: Positive Characteristic

Explores Albanese varieties, Fourier-Mukai transforms, and positive characteristic applications.

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

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.

Regularity of Curves

Explores the regularity of curves over a field and the importance of specific properties for curve regularity.

Topology of Riemann Surfaces

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

Curves with Poritsky Property and Liouville Nets

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

Curves in Space: Parametric Equations and Surfaces

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Varieties with nef anti-canonical: Surjective Albanese

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Curvilinear Coordinates: Calculations and Examples

Covers curvilinear coordinates and area calculations using double integrals with examples of different curves.

Surface of Revolution

Explains the parametric equations of surfaces of revolution generated by curves in space.

Curves and Surfaces

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

Geometric Areas: Integrals and Regions

Covers the calculation of areas using integrals for geometric regions defined by curves and parametric equations.

Curves: Parameterized Curves and Tangent Vectors

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

Spatial Curves: Singularities and Mechanisms

Explores spatial curves, singularities, and mechanisms, analyzing their geometric properties and applications.

Parameterization of Curves

Explores parameterization of curves, emphasizing continuous settings and accurate curve representation through various examples.

Taylor Expansions: First Order

Explores Taylor expansions of first order in optimization on manifolds.

Algebraic Curves: Normalization

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

Introduction to Rhino Surfaces and Meshes

Introduces working with surfaces, polysurfaces, and solids in Rhino, covering rendering, material editing, and mesh creation.

Advanced Analysis II: Isoclines Method

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