Concept
Lattice (discrete subgroup)
Related lectures (32)
Group Theory: Properties and Examples
Introduces the concept of a group and its properties through illustrative examples.
Lattice Theory: Minkowski's Theorems
Delves into lattice theory, emphasizing Minkowski's theorems and their implications on lattice structures.
Hermite Normal Form: Computation & Properties
Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.
Minkowski's Theorems: Lattices and Volumes
Explores Minkowski's theorems on lattices, volumes, and set comparisons.
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.
Lattices: Theory and Applications
Explores the theory of lattices, their properties, and applications in different mathematical contexts, emphasizing local-global principles.
Lattices: Properties and Theta Functions
Explores lattices in Rd, Gram matrices, theta functions, and modular properties.
Subset Sum: LLL Algorithm
Covers the Subset Sum problem and the efficient LLL algorithm for finding solutions in lattice basis reduction.
Number Fields: Embeddings and Ideal Classes
Covers the embeddings of number fields and ideal classes with proofs and examples.