Lectures related to Motivic Knot Theory: Quadratic Linking Degree

The Quadratic Linking Degree

Introduces the quadratic linking degree in motivic knot theory, covering knot theory basics, algebraic geometry, and intersection theory.

Knot Theory: The Quadratic Linking Degree

Covers the quadratic linking degree in knot theory, exploring its definitions, properties, and significance in algebraic geometry.

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.

Algebraic Geometry: Forms and Maps

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.

Homology of Riemann Surfaces

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

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Affine Plane Curves

Covers the study of affine plane curves and their properties, including the concept of multiplicity and its applications.

Adjunctions and Applications

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Variety Defined as the Closure of VCA

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Tangent Spaces in Algebraic Geometry

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Analytical Geometry: Mixed Product and Determinant

Covers the analytical expression of the mixed product and its applications.

Analytical Geometry: Intersections and Medians

Covers Analytical Geometry, focusing on intersections and medians, providing step-by-step solutions for various cases.

Varieties with nef anti-canonical: Surjective Albanese

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

Regularity and Geometric Meaning

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.

Conformal Blocks: Functions on Moduli Spaces

Covers conformal blocks and their significance in complex structures and moduli spaces.

Geometric Analysis: Singularities in Architectural Design

Examines geometric singularities in architectural design through the analysis of spatial intersections.

Cartier Divisors and Invertible Sheaves

Covers Cartier divisors, invertible sheaves, and their properties in algebraic geometry.

Modern Algebraic Geometry: Schemes and Affine Schemes

Covers modern algebraic geometry, focusing on schemes and affine schemes, including a review of classical algebraic geometry and Bézout's theorem.

Quotient Criterion

Explores a criterion for computing quotients in algebraic geometry, emphasizing the importance of normality and g-invariant morphisms.