Lectures related to Lattice (order)

Equidistribution of CM Points

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Dynamics on Homogeneous Spaces and Number Theory

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

Hermite Normal Form: Computation & Properties

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

Lattices: Properties and Theta Functions

Explores lattices in Rd, Gram matrices, theta functions, and modular properties.

Local Global Duality

Explores local-global duality in lattices and joint equidistribution of CM points.

From Lattice Products to Tarski's Fixedpoint Theorem

Covers the combination of lattice elements, partial orders, complete lattices, and Tarski's Fixed Point theorem.

Quantization: Topological Operators

Covers the quantization of topological operators and Ising models on square lattices.

Equidistribution of CM Points

Explores the joint equidistribution of CM points and their properties in ergodic theory and homogeneous dynamics.

Lattices for Abstract Interpretation

Covers lattices, abstract interpretation, fixpoint analysis, Hoare logic, and partial orders with extreme elements.

Lattices: Theory and Applications

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

Lattice Theory: Minkowski's Theorems

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

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Crystallography: Describing Periodic Structures

Covers crystallography, lattice structures, vectors, and diffraction patterns.

Canonical Embedding: Fields and Lattices

Explores canonical embedding of #-fields, lattices, and finiteness of class groups.

Relations and Sequences

Covers relations, sequences, and posets, emphasizing properties like anti-symmetry and transitivity, and introduces arithmetic and geometric progressions.

Group Actions on Lattices

Explores group actions on lattices, emphasizing GL₂(Q) and GL₂(Ag) compatibility and alternative formulations.

Partial Ordering: Relations, Sequences, Summation

Introduces partial orderings, lattices, and lexicographic orderings on Cartesian products.

Embeddings of Number Fields

Explores embeddings of number fields, types, signatures, lattices, and determinants.

Lattices, Minkowski's Theorem

Explores lattices, Minkowski's Theorem, and properties of symmetric convex sets.

Number Fields: Embeddings and Ideal Classes

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