Lectures related to Incidence Geometry & Elliptic Curves

Explores Bézout's theorem and Cayley-Bacharach, discussing intersection multiplicities and linear combinations in projective geometry.

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

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

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

Explores the complement problem for hypersurfaces in projective spaces and discusses isomorphism based on their complements.

Covers the concept of connected sums in RP2 and how to compute them.

Introduces Euclidean elements, explores infinity uniqueness, parallel lines, and different geometries like Euclidean, hyperbolic, and spherical.

Covers the homology of projective space, focusing on cohomology and exact sequences.

Explores homogeneous ideals, regular rings, N-graded rings, and closed sets in projective geometry.

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

Covers separated spaces, saturation properties, and projective spaces, including the real projective plane and compactness.

Explores the historical and practical applications of geometry in architecture, emphasizing key geometric principles in architectural design.

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Introduces vector definitions, displacement, addition, and applications in geometry.

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.

Introduces projective space and algebraic sets, discussing homogeneous coordinates, ideals, and generators.

Explores geometric transformations, invariant properties, and mean relationships in modern geometry.

Explores modern geometric transformations and invariances, focusing on projective geometry and historical developments.