Lectures in course MATH-603: Subconvexity, Periods and Equidistribution

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

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

Covers the relations between the ideal class group and proper fractional ideals.

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

Covers the properties and applications of modular forms and discusses equidistribution and modularity.

Explores quadratic forms, Hecke operators, eigenvalues, and compactly supported functions in matrix theory.

Explores the discriminant in matrices, ideal class groups, and optimal embeddings in mathematics.

Explores the Duality Principle for Radon measures and its applications.

Explores the discriminant's role in equations, symmetry, and orbits in mathematical spaces.

Covers the unit tangent bundle of hyperbolic spaces and geodesic flows.

Explores quadratic forms, symmetries, representations, and orthogonal sums in mathematics.

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

Explores integral representations, quadratic lattices, and the Hasse Principle.

Covers non-degenerate quadratic lattices, local representability, equidistribution, and the Siegel theorem.

Covers non-degenerate integral quadratic lattices and adèles, including their properties and definitions.

Explores integral Hasse principle, locally isometric lattices, and adèles rings.

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

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

Discusses the Godement Compactness Criterion in reductive groups and covolume computations.

Covers Haar measures, quotient functions, and their importance in group actions.