Algebraic Number Theory Courses and Certifications

Algebraic Number Theory

Master advanced number theory concepts, from Diophantine equations to field extensions, exploring algebraic structures, class groups, and L-functions while building expertise in computational methods and proofs.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

Insights into Mathematics

Algebraic Number Theory and Rings - Math History II

Explores 19th-century algebraic number theory, focusing on extension fields, abstract rings, and algebraic integers. Discusses Gaussian integers, unique factorization, and foundational challenges in the field.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Insights into Mathematics

Algebraic Number Theory and Rings I - Math History - NJ Wildberger

Explore algebraic number theory and rings, focusing on extension fields, Gaussian integers, and the development of abstract ring theory in 19th-century mathematics.

• YouTube
• 48 minutes
• On-Demand
• Free Video

BIMSA

Structure in the Search for Structure - Algebraic Number Theory and Motivic Cohomology

Explore algebraic number theory through analogies between numbers and shapes, including quadratic reciprocity and linking numbers, leading to insights on Tate's 1966 conjecture.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Sato-Tate Conjecture for Bianchi Modular Forms

Explore potential automorphy results for Ramanujan and Sato-Tate conjectures in GL(2) over imaginary quadratic fields, extending previous work and introducing new mathematical concepts.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Class Field Theory - Lecture 1

Explore fundamental concepts of class field theory in this advanced mathematics lecture, delving into algebraic number theory and Galois theory.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

ICTP Mathematics

Bounds on the Number of Generators of Prime Ideals

Explore prime ideals and their generators, focusing on mathematical bounds and theoretical implications in algebraic geometry and commutative algebra.

• YouTube
• 35 minutes
• On-Demand
• Free Video

ICTP Mathematics

From Knots to Number Theory II

Explore connections between quantum knot invariants and number theory, covering topics like hyperbolic topology, Kashaev invariant, and quantum modularity. No prior knowledge required.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

Fields Institute

Hasse Principle for Function Fields

Explore the Hasse principle's application to function fields, delving into its mathematical implications and theoretical foundations.

• YouTube
• 37 minutes
• On-Demand
• Free Video

Fields Institute

Iwasawa Theory in a Family of Z_p-Extensions

Explore advanced number theory concepts, focusing on Iwasawa theory in Z_p-extensions families. Gain insights from expert Sujatha Ramdorai on this specialized mathematical topic.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Fields Institute

Exponential Relations Among Algebraic Integer Conjugates

Explore exponential relations between algebraic integer conjugates, delving into advanced number theory concepts and their implications in mathematical research.

• YouTube
• 17 minutes
• On-Demand
• Free Video

Fields Institute

Certain Polytopes Associated to Algebraic Integer Conjugates

Explore polytopes linked to algebraic integer conjugates, delving into their properties and applications in number theory.

• YouTube
• 40 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Local Tate Duality over Positive Characteristics

Explore Local Tate Duality in positive characteristic fields through advanced number theory concepts and their applications in arithmetic geometry.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Anisotropic Quadratic Forms Over Global Fields Are Diophantine

Discover how anisotropic quadratic forms over global fields can be classified as Diophantine using class field theory and uniform descriptions across field completions.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Rank Stability in Quadratic Extensions and Hilbert's 10th Problem

Explore recent proof showing rank stability in quadratic extensions of number fields, connecting abelian varieties to Hilbert's 10th problem with negative solutions.

• YouTube
• 53 minutes
• On-Demand
• Free Video