Lectures related to Quaternion Algebra and Hermite Space

Quaternion Algebra: Properties and Applications

Covers the properties and applications of quaternion algebra, including norm calculations and distribution in different spaces.

3D Rotations and Quaternions

Covers 3D rotations, quaternions, and matrices of direction cosines, providing an elegant solution to the limitations of rotation matrices.

Fourier Expansion and Quaternion Algebra

Discusses Fourier expansion, quaternion algebra, and Whittaker model in automorphic forms.

Quadratic Spaces and Quaternion Algebra

Explores quadratic spaces, norms, and quaternion algebra over fields.

Conductor of X: Waldsparger Formula and Subconvexity Bound

Covers the equidistribution of representations of integers by ternary forms and the conductor of X.

Fermat's Theorem: Sums of Squares

Explores Fermat's Theorem, factorization of integers, properties of Z[i], and Hurwitz quaternions.

Proof of Lagrange Theorem

Covers the proof of Lagrange Theorem and explores quaternions, prime numbers, and equations.

Mechanics: Introduction and Calculus

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Conformal Field Theory: Generators and Commutation Relations

Covers the definition of generators of the conformal group and the application of Wick's theorem.

Abelianization of Fundamental Group

Explores abelianization examples, homomorphisms, and isomorphisms in group theory.

Division Rings and Ideals

Covers division rings, fields, and ideals in commutative rings with examples in Z and quaternions.

Linear Projective Groups

Explores linear projective groups, quaternions, subgroup generation, and normality.

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Orthogonality and Gram-Schmidt Process

Explores orthogonality, Gram-Schmidt process, dot products, and solution minimization in systems.

Magnetic Induction

Explains magnetic induction, force on a dipole, torque, and applications in macroscopic systems.

Wave Equation: Euler-Paissan-Doubana

Covers the wave equation and introduces the Euler-Paissan-Doubana formula, emphasizing key concepts.

Studying Mechanics: Vector Calculus

Covers vector calculus, including scalar and vector products, with insights from Dr. Sylvain Bréchet.

Scalar Product and Vectors

Introduces vector components, scalar and vector products, and their properties, including colinear and coplanar vectors, and the rule of the right hand.

Scalar Product: Geometric Properties

Covers the definition and properties of the scalar product, including geometric interpretations and algebraic properties.

Group Homomorphisms

Explores group homomorphisms, constructing isomorphisms between groups using generators and relations.