Lectures related to Topology of Adeles

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Finite Abelian Groups: Classification Theorem

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Equidistribution of CM Points

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

Topology: Separation Criteria and Quotient Spaces

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

Modular curves: Riemann surfaces and transition maps

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Symmetries and Groups in Quantum Mechanics

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Open Balls and Topology in Euclidean Spaces

Covers open balls in Euclidean spaces, their properties, and their significance in topology.

Topology: Compactness and Continuity

Explores compactness, continuity, and quotient spaces in topology, emphasizing the topology of lines in R² and the properties of compact sets.

Topology: Free Groups and Their Properties

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

The Jordan Curve Theorem

Explores the Jordan Curve Theorem, illustrating the division of a plane by a simple closed curve into two regions.

Compact Subsets of R^n

Explores compact subsets of R^n, convergence theorems, and set properties.

Topology: Exploring Cohomology and Quotient Spaces

Covers the basics of topology, focusing on cohomology and quotient spaces, emphasizing their definitions and properties through examples and exercises.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Properties of Convergence: Sequences and Topology

Discusses the properties of sequences, convergence, and their relationship with topology and compactness.

Topology of Riemann Surfaces

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

Knot Theory: The Quadratic Linking Degree

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

Topology: Open Sets, Compactness, and Connectivity

Explores open sets, compactness, and connectivity in topology, covering topological spaces and compact sets.