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Concept

Lattice (discrete subgroup)

Related lectures (21)

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Adelic Topology: Properties and Approximation

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Ergodic properties of low complexity symbolic systems

Explores the influence of complexity on ergodic properties of symbolic systems, presenting the Curtis-Hedlund-Lyndon Theorem and constructions of minimal subshifts.

Quadratic Lattices: Properties and Equidistribution

Covers non-degenerate quadratic lattices, local representability, equidistribution, and the Siegel theorem.

Extremal Lattices

Explores extremal lattices, emphasizing bounds on shortest vectors and unique modular forms.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Explores dynamics on homogeneous spaces and their interactions with number theory, focusing on modular lattices and the Iwasawa decomposition theorem.

Lattices: Properties and Theta Functions

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Local structure of totally disconnected locally compact groups I

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Topology of Adeles

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Dotsenko-Fateev Approach: Correlation Functions in Quantum Field Theory

Covers the Dotsenko-Fateev approach to computing correlation functions in quantum field theory.

Automorphism groups of trees and graphs

Explores automorphisms of graphs, focusing on automorphism groups, Cayley-Abels graphs, and quasi-isometry.

Extreme Problems in Diophantine Approximation and Dynamics

Explores the Logarithmic Law, geodesic flows, hyperbolic surfaces, and rare events in probability.

Reciprocal lattice: basics and properties MOOC: Transmission Electron Microscopy for Materials Sciences

Covers the basics of the reciprocal lattice in electron diffraction, including diffraction vector geometry and properties of reciprocal lattice unit cell vectors.

Group Theory: Properties and Examples Log in to Mediaspace to watch this video

Introduces the concept of a group and its properties through illustrative examples.

Lattice Theory: Minkowski's Theorems Log in to Mediaspace to watch this video

Delves into lattice theory, emphasizing Minkowski's theorems and their implications on lattice structures.

Hermite Normal Form: Computation & Properties Log in to Mediaspace to watch this video

Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.

Minkowski's Theorems: Lattices and Volumes Log in to Mediaspace to watch this video

Explores Minkowski's theorems on lattices, volumes, and set comparisons.

Lattices: Theory and Applications Log in to Mediaspace to watch this video

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

Subset Sum: LLL Algorithm Log in to Mediaspace to watch this video

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

Number Fields: Embeddings and Ideal Classes Log in to Mediaspace to watch this video

Covers the embeddings of number fields and ideal classes with proofs and examples.