Lectures related to Regular 4-polytope

Hamiltonian dynamics on convex polytopes

Explores Hamiltonian dynamics on convex polytopes, covering symplectic capacities, EHZ capacity, and systolic ratio maximizers.

Regular Polyhedra: Definitions and Symmetries

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

Regular Polyhedra: Definitions and Symmetries

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

Regularity of Weak Solutions

Explores elliptic PDEs, weak solutions, regularity, and strong solutions, with a focus on classical solutions and proof techniques.

Construction of Solutions by Dirichlet-Laplace

Explores the construction of solutions by Dirichlet-Laplace in general domains.

Surface Integrals: Regular Parametrization

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.

Impossibility Result: Atomic SRSW Register

Explores the impossibility of implementing an atomic SRSW register using bounded regular registers.

Geodesic Curves: Minimizing Distance and Constant Speed

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Regular Polyhedra: Symmetries & Generation

Explores the properties of regular polyhedra, their symmetries, generation, and historical misconceptions.

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Implicit Surfaces: Regular Points

Explains regular points on implicit surfaces and their relationship with gradients and tangent planes.

Platonic Solids: Misinterpretations and Correspondences

Explores misinterpretations of Platonic solids and their correspondence with elements, emphasizing the importance of rigor in mathematical integration into architectural culture.

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Polygons & Polyhedra: Regular & Starred

Explores polygons, polyhedra, regularity, and starred configurations in Euclidean geometry, highlighting historical context and limitations.

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Closed Surfaces and Integrals

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

Quantum Physics: Coulomb Potentials

Delves into quantum physics, emphasizing Coulomb potentials and their effects on particles.

Symmetries of Regular Polyhedra

Explores the historical background and significance of symmetries in regular polyhedra, shedding new light on Euclid's Elements.

Geometry of the Lasso

Explores the geometric explanation of why Lasso solutions are sparse and how coefficients change with the regularization parameter.

Intersection of Manifolds in Exercise 8.2

Covers the intersection of manifolds in exercise 8.2 and fiscal year 8.8.