Lattice (group)

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Related lectures (31)

Reciprocal lattice: Shape effects

Explains how sample geometry affects the size and shape of reciprocal lattice nodes in multiple beam scattering.

Reciprocal lattice: Fourier transform and Bravais lattice

Explains the Fourier transform for periodic functions and the reciprocal lattice in relation to the Bravais lattice.

Reciprocal Lattice: Diffraction Basics III

Explores the reciprocal lattice, diffraction patterns, and atomic structure extraction.

Diophantine Approximation: Minbowski's Theorem

Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.

Lattices: Theory and Applications

Explores the theory of lattices, their properties, and applications in different mathematical contexts, emphasizing local-global principles.

Borcherds' Proof: Strategy

Covers Borcherds' proof strategy, emphasizing the significance of simple roots and Weyl vectors.

E8 Lattice Optimality

Delves into the construction and optimality of the E8 lattice as the densest sphere packing in dimension eight.

Adelic Topology: Properties and Approximation

Explores adelic topology, lattice representation, and strong approximation properties.

Subset Sum: LLL Algorithm

Covers the Subset Sum problem and the efficient LLL algorithm for finding solutions in lattice basis reduction.

Atomic-scale Modeling: Interactive Exercises and Graded Assignments

Explores atomic-scale modeling through interactive exercises and graded assignments, covering crystallography, diffraction, defects, and regression models.

Mathematica Tutorial: Graphics and Functions

Introduces Mathematica basics, including graphics creation, list manipulation, and function definition.

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