Lectures related to Proof of Existence

Natural Transformations in Group Theory

Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.

Monster Group Construction

Explores the construction of the Fischer-Greiss monster group, emphasizing its key properties and the process involved.

Subsets and subgroups associated with an action

Explores subsets and subgroups related to group actions on sets.

Simplicial and Cosimplicial Objects: Examples and Applications

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

Groups and Numbers: Mathematical Elements on Groups

Explores fundamental properties of groups and numbers, emphasizing equivalence classes and subgroup concepts.

Topology: Free Groups and Their Properties

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

Lagrange Theorem: Applications and Proofs

Covers the application and proof of the Lagrange theorem in group theory.

Group Theory Fundamentals

Introduces the basics of group theory, defining groups, categories, and groupoids.

Composition of Applications in Mathematics

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

Monstrous Moonshine

Explores Monstrous Moonshine, focusing on the 1979 discovery and its mathematical connections.

Pushouts in Group Theory: Universal Properties Explained

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

Endomorphisms and automorphisms of totally disconnected locally compact groups

Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing the properties of flat groups and free abelian subgroups.

Group Theory: Restriction Functor

Explores the restriction functor in group theory, focusing on its properties.

Construction of Alpha and Beta

Covers the construction of alpha and beta in group theory, emphasizing commutativity and natural transformations.

Set Union: Properties and Operations

Explains the union of sets, its properties, operations, and intersection.

Categories and Functors: An Introduction

Provides an overview of categories, functors, and natural transformations in mathematics.

Morphism of Groups

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Functor Hom: Abelian Groups

Explores the Hom functor in Abelian groups, focusing on its construction and properties.

Active Learning: Functors and Geometric Realization

Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.