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Lecture
Points fixes et orbites
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Fixed points, orbits, and stabilizers
Covers fixed points, orbits, and stabilizers in G-varieties, including properties of closed subgroups and faithful actions.
Active Learning: Group Theory
Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.
Orbit of a G-ensemble
Explores orbits in a G-ensemble, functions of fixed points, and G-equivariance.
Functor Fixed Points and Orbital Functor
Explores defining functors on morphisms, fixed points, orbits, equivariance, and composition preservation.
Adjunctions: Trivial and Application Quotient
Explores adjunctions, emphasizing trivial and application quotient cases in functors, orbits, and fixed points.
Active Learning: Group Homomorphisms
Explores group homomorphisms, emphasizing surjective mappings and their impact on group questions.
Active Learning: Group Structures and Symmetric Actions
Explores active learning implications in understanding group structures and symmetric actions.
Proper Actions and Quotients
Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.
Points Fixes in G-sets
Explores fixed points in G-sets, applications between sets, and the construction of orbits.
Properties of Sylow Subgroups: Group Theory
Explores the beautiful properties of the p-Sylow subgroups of a finite group.