Algebraic Number Theory Courses and Certifications

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

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

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

IIT Kanpur;  NPTEL

Modern Algebra

Explore groups and rings in modern algebra, covering fundamental concepts, properties, and applications. Gain essential knowledge for advanced mathematics and teaching careers.

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

Pondicherry University;  CEC

Algebra

Comprehensive exploration of algebraic structures, group theory, and ring theory, providing a strong foundation for advanced mathematics and teaching careers.

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

ICTP Mathematics

From Knots to Number Theory I

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

• YouTube
• 1 hour 33 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Two Mathematicians, Their Work and Career Experiences - Radhika Ganapathy and Purvi Gupta

Explore cyclotomic fields in number theory and convexity in complex analysis through lectures by two accomplished mathematicians, offering insights into their research and career experiences.

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

TheIACR

Mildly Short Vectors in Ideals of Cyclotomic Fields Without Quantum Computers - MathCrypt 2022

Explore norm relations in cyclotomic fields and their applications to cryptography, focusing on finding short vectors in ideals without quantum computers.

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

Hausdorff Center for Mathematics

Local Fields in Lean

Explore local fields using the Lean theorem prover, focusing on mathematical foundations and practical applications in number theory and algebraic geometry.

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

Hausdorff Center for Mathematics

K2 of Elliptic Curves over Non-Abelian Cubic and Quartic Fields

Explore K_2 of elliptic curves over non-Abelian fields, including constructions, integral elements, and numerical verification of Beilinson's conjecture. Joint work with Brunault, Hang, and Rodriguez Villegas.

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

Institute for Advanced Study

Determinants of Cohomology for Number Fields

Explore determinants of cohomology in number fields, delving into advanced mathematical concepts and their applications in algebraic number theory.

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

Centre International de Rencontres Mathématiques

Counting S4 and S5 Extensions Satisfying the Hasse Norm Principle

Explore counting techniques for S4 and S5 extensions satisfying the Hasse norm principle in this advanced mathematical lecture by Rachel Newton.

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

Centre International de Rencontres Mathématiques

An Invitation to Globally Valued Fields

Explore globally valued fields in mathematics through an in-depth lecture by Ehud Hrushovski, delving into advanced concepts and their applications.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Existential Closedness of Qalg as a Globally Valued Field

Explore existential closedness of Qalg as a globally valued field in advanced mathematical theory. Delve into complex concepts with expert Michal Szachniewicz.

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

Centre International de Rencontres Mathématiques

Finite Flat Group Schemes over Z

Explore finite flat group schemes over Z with René Schoof in this advanced arithmetic geometry lecture from the CIRM Symposium.

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