Lectures related to P-adic number

Conductor of X: Waldsparger Formula and Subconvexity Bound

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

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Rational Numbers Construction

Explores the construction of rational numbers, irreducible fractions, equivalence, and simplification rules.

Primes and Coprime

Explores prime numbers, coprime integers, and their properties in number theory.

Properties of Division

Covers the properties of division in integers and the relationship between divisibility and unique quotients.

RSA: Chinese Remainder Theorem

Covers RSA encryption and the Chinese Remainder theorem for secure communication.

Introduction to Finite Fields

Covers the basics of finite fields, including arithmetic operations and properties.

P-adic Expansion: Unique Representations and Power Series Log in to Mediaspace to watch this video

Explores p-adic expansion, unique representations, and power series for computing p-adic expansions.

Hensel's Lemma and Field Theory Log in to Mediaspace to watch this video

Covers the proof of Hensel's Lemma and a review of field theory, including Newton's approximation and p-adic complex numbers.

Invariant Definitions Log in to Mediaspace to watch this video

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

Algebraic Closure of Qp Log in to Mediaspace to watch this video

Covers the algebraic closure of Qp and the definition of p-adic complex numbers, exploring roots' continuous dependence on coefficients.

P-adic Numbers: Completion and Norm Log in to Mediaspace to watch this video

Explores the definition of Q_p and the completion of Q,1(p) to form Qp.

P-adic Expansion and Hensel's Lemma Log in to Mediaspace to watch this video

Covers the p-adic expansion theorem and Hensel's Lemma in Qp.

Standard Model Overview Log in to Mediaspace to watch this video

Provides an in-depth analysis of the Standard Model, covering topics such as the Higgs mechanism, gauge boson interactions, and the role of chirality in particle physics.

Torsion and Divisibility in Group Theory Log in to Mediaspace to watch this video

Explores the relationship between p-torsion and p-divisibility in group theory, highlighting implications of p-divisibility in exact sequences of abelian groups.

Integration on H_pxH and Arithme Log in to Mediaspace to watch this video

Covers integration on H_pxH and arithmetic topics, focusing on the Hensel Lemma and the process of finding R and S such that R.S-P=0.

Galois Theory of Qp Log in to Mediaspace to watch this video

Explores the Galois theory of Qp, covering algebraic extensions, inertia groups, and cyclic properties.

Fermat Equation: Solutions and Coprime Numbers Log in to Mediaspace to watch this video

Explores solutions of the Fermat equation and the importance of coprime numbers.

Quantum and nanocomputing Log in to Mediaspace to watch this video

Covers the basics of number theory, RSA encryption, and Shor's period finding algorithm.

Compact Manifolds Classification Log in to Mediaspace to watch this video

Covers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.