Lectures related to DVR and Irreducible Plane Curves

Topology of Adeles

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Cohomology Real Projective Space

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

Algebraic Structures: Classes and Cyclic Groups

Explores algebraic structures, classes of examples, and properties of cyclic groups.

Topology of Riemann Surfaces

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

Dedekind Rings: Integral Extensions and Noetherian Rings

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

Irreducible Polynomials: Degree and Roots

Explores irreducible polynomials, focusing on their degree and roots in different fields.

Algebraic Curves: Normalization

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

Integration on H_pxH and Arithmetic

Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.

Projective Varieties: An Algebraic Study

Covers the study of projective varieties and their relation to compact manifolds.

Proper Actions and Quotients

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

Equidistribution of CM Points

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Projective Geometry: Tangent Lines

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

Limits and Operations on Limits

Covers limits, algebraic operations, and infinite limits with examples of functions' behavior near limit points.

Variety Defined as the Closure of VCA

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

Albanese and Fourier Transform: Positive Characteristic

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

Affine Varieties and Hypersurfaces

Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

Affine Algebraic Sets

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Regularity and Noetherian Local Rings

Covers the concepts of regularity and Noetherian local rings in algebraic structures.

Modern Algebraic Geometry

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

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.