Lectures related to Connected Components

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.

Algebraic Geometry: Forms and Maps

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Group Theory: Isomorphism and Semi-Direct Product

Covers group theory concepts like isomorphism and semi-direct product through examples and proofs.

Networked Control Systems: Consensus Algorithms in Digraphs

Explores consensus algorithms in digraphs, focusing on scenarios where the digraph is not strongly connected.

Isomorphism of Groups

Covers bijections between automorphisms and equivariant bijections in group isomorphisms.

Meromorphic Functions & Differentials

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

Isomorphism in Categories

Covers the concept of isomorphism in categories, defining morphisms with inverses and exploring automorphisms and groupoids.