Lectures related to Open Mapping Theorem

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

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

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

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Differential Forms Integration

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

Fundamental Groups

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

Topology of Riemann Surfaces

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

Modular curves: Riemann surfaces and transition maps

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

Topology of Riemann Surfaces

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

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Local structure of totally disconnected locally compact groups I

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

Building surfaces from equilateral triangles

Explores the construction of Riemann surfaces from equilateral triangles and the dynamics of finite-type maps.

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.

Topology: Separation Criteria and Quotient Spaces

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

Homology of Riemann Surfaces

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

Thermodynamic formalism for coarse expanding dynamical systems

Explores thermodynamic formalism for weakly coarse expanding dynamical systems, covering equilibrium states, visual metrics, and symbolic coding.

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.

Shell Components in Meromorphic Parameter Spaces

Explores shell components in transcendental parameter planes and attracting cycles.

Local structure of totally disconnected locally compact groups III

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

Properties of X/G

Explores the properties of the quotient space X/G when X is compact and sometimes separated.