Lattice (discrete subgroup)

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Related lectures (21)

Dynamics on Homogeneous Spaces and Number Theory

Covers dynamical systems on homogeneous spaces and their interactions with number theory.

Adelic Topology: Properties and Approximation

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

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.

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.

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.

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

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.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Number Fields: Embeddings and Ideal Classes

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

Topology of Adeles

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

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.

Policy Gradient Methods in Reinforcement Learning

Covers policy gradient methods in reinforcement learning, focusing on optimization techniques and practical applications like the cartpole problem.

Extreme Problems in Diophantine Approximation and Dynamics

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

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