Lectures related to Dynamics on Homogeneous Spaces and Number Theory

Hermite Normal Form: Computation & Properties

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

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

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.

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A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Lattices: Properties and Theta Functions

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

Nilpotent Lie Groups

Covers the properties of nilpotent Lie groups and the construction of non-degenerate alternating 2-forms.

Lie Algebra: Vector Space and Multiplication Law

Covers Lie Algebra, focusing on vector space and multiplication law.

Symmetry in Quantum Field Theory

Explores associativity, Lie algebra, Lie groups, relativity, and symmetry preservation in quantum field theory.

Equidistribution of CM Points

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

Equidistribution of CM Points

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

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

Lie Algebra: Group Theory

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

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.

Smooth Dynamics: Bernoulli and K Properties

Explores Bernoulli and K properties in smooth dynamics, including equivalence, examples, and implications.

Macdonald identities

Delves into Macdonald identities, covering affine root systems, modular forms, and Lie algebras.

General Fields: Lorentz Representations

Covers the representation of Lorentz transformations through general fields and the consequences of symmetry.

Jacobi Identity in Lie Algebra

Explores the significance of the Jacobi identity in Lie algebra and its impact on linear vector spaces.

Complete Reducibility of Complex Representations

Covers the complete reducibility of complex representations and the relation between Lie algebras and Lie groups.

Symmetry: Noether Theorem

Explores the consequences of symmetry, focusing on the Noether Theorem and coordinated charges in Lie groups.