Lectures related to Shell Components in Meromorphic Parameter Spaces

Local Homeomorphisms and Coverings

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.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Hadamard Factorisation

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

Holomorphic Functions: Taylor Series Expansion

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

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.

Harmonic Forms: Main Theorem

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

Functional Equation of Zeta

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

Bifurcation and fractals in complex dynamical systems

Explores bifurcation, fractals, Julia sets, Mandelbrot set, and self-similarity in complex dynamical systems.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Open Mapping Theorem

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

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Differential Forms Integration

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

Nonlinear Dynamics: Homoclinic Orbits and Bifurcations

Delves into homoclinic orbits, bifurcations, and limit cycles in nonlinear dynamics.

Proper Actions and Quotients

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

Mild Dissipative Surface Dynamics

Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Thermodynamic formalism for coarse expanding dynamical systems

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

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.