Lecture

Coxeter Groups: Root System Classification and Fundamental Regions

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Explores Coxeter groups, reflections, fundamental regions, and classification by Coxeter graphs.

Explores symmetry in modern geometry, emphasizing reflections, rotations, and practical applications in computer-aided design.

Reviews Coxeter groups, reflections, rotations, and fundamental regions in finite orthogonal transformations.

Explores projections on lines and symmetries in 2D space, emphasizing fixed points and symmetric matrices.

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Explores the modern definition of symmetry and its practical applications.

Delves into modern geometry, covering transformations, isometries, and symmetries.

Covers the concept of distance in the plane, distance axioms, triangle construction, and triangle side properties.

Explores the definitions and symmetries of regular polyhedra, focusing on the five known convex regular polyhedra from ancient times.

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Explores the consequences of symmetry, focusing on the Noether Theorem and coordinated charges in Lie groups.

Explores the definitions and symmetries of regular polyhedra, shedding light on ancient geometry and modern mathematical formalization.

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Explores the dynamical consequences of symmetry, emphasizing conservation laws and the role of Noether currents.

Introduces the fundamentals of Euclidean geometry, covering equilateral triangles, symmetries, radical axes, and ancient architectural figures.

Explores the calculation of correlation energy and CSF's in electronic structure calculations.

Covers Exercise Set 3 on Symmetry and Group Theory, focusing on chiral molecules, point groups, conjugacy, and group properties.

Explains the inertia tensor, main axes, principal moments, and balancing of rotating solids.

Explores the modern definition and practical applications of symmetry in geometry.

Explores the symmetries of Navier-Stokes equations in periodic boxes, including translations, transformations, rotations, and scaling.