Lectures related to Group Actions: Theory and Examples

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

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Explores the use of for-expressions in Scala to simplify computations and solve problems like combinatorial search and N-Queens.

Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.

Covers special cases in group theory, focusing on group actions and functors.

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

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Explores creating dashboards in ServiceNow, focusing on advantages, transition from homepages, and important concepts like tasks and incidents.

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

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

Explores two definitions of group action and their equivalence through bijection in group homomorphisms.

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

Explores edge labels, skills like aggregation and deduction, and the structure of contents.

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

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

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

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

Covers aggregation queries and sorting of results in Geographic Information Systems.

Explores the motivations for studying actions through the universal action of bijections.