Lectures related to Multicorrelation Sequences and Primes

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Orthogonal Projections and Reflections

Covers the analytical expression of orthogonal projections and reflections in 2D space.

Orthogonal Projection: Vector Decomposition

Explains orthogonal projection and vector decomposition with examples in particle trajectory analysis.

Orthogonality and Projection

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Applications of Ergodic Theory to Combinatorics

Explores the applications of ergodic theory to combinatorics and number theory, including Szemerédi's Theorem and the Erdős-Kac Theorem.

Elementary Algebra: Numeric Sets

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

QR Factorization: Least Squares System Resolution

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

Prime Numbers: Euclid's Theorem

Explores prime numbers and Euclid's Theorem through a proof by contradiction.

Orthogonal Projection: Theory and Applications

Covers the theory of orthogonal projection in vector spaces and its practical applications.

Prime Numbers and Primality Testing

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

Orthogonal Projection Theorems

Covers the theorems related to orthogonal projection and orthonormal bases.

Prime Number Theorem

Explores the proof of the Prime Number Theorem and its implications in number theory.

Orthogonal Families and Projections

Explains orthogonal families, bases, and projections in vector spaces.

Number Theory: More Facts about Primes

Covers the distribution of primes, arithmetic progressions, Mersene primes, and Goldbach's Conjecture.

Harmonic Forms and Riemann Surfaces

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Orthogonal Projection: Uniqueness and Properties

Explores the uniqueness and properties of orthogonal projection, including decomposition, associated matrix, linearity, and practical examples.

Subspaces, Spectra, and Projections

Explores subspaces, spectra, and projections in linear algebra, including symmetric matrices and orthogonal projections.

Linear Algebra: Orthogonal Projection and QR Factorization

Explores Gram-Schmidt process, orthogonal projection, QR factorization, and least squares solutions for linear systems.

Primes in Arithmetic Progression

Explores primes in arithmetic progression, focusing on L-functions, characters, and the divergence of the sum of 1 over p for p congruent to a modulo q.