Lectures related to Local structure of totally disconnected locally compact groups V

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

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Endomorphisms and automorphisms of totally disconnected locally compact groups I

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.

Local structure of totally disconnected locally compact groups I

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

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Local structure of totally disconnected locally compact groups III

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Local structure of totally disconnected locally compact groups II

Explores the local structure of totally disconnected locally compact groups, covering commensurated subgroups, completions, local automorphisms, and the quasi-centre.

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Homogeneous Spaces

Explores formogenic spaces, topological groups, quotients, and rotations on the unit sphere.

Topology: Separation Criteria and Quotient Spaces

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

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Harmonic Forms and Riemann Surfaces

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

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Local structure of totally disconnected locally compact groups IV

Explores the local structure of totally disconnected locally compact groups, focusing on pseudocomplements and normal subgroups.

Modular curves: Riemann surfaces and transition maps

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

Convergence and Compactness in R^n

Explores adhesion, convergence, closed sets, compact subsets, and examples of subsets in R^n.

Hadamard Factorisation

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.