Elliptic Curves Courses and Certifications

Hausdorff Center for Mathematics

Hilbert Tenth Problem for Finitely Generated Rings

Explore advanced techniques for constructing elliptic curves with prescribed rank to resolve Hilbert's tenth problem for finitely generated rings using diophantine methods.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Quasi Jacobi Forms and Moduli Space of Enhanced Elliptic Curves - GADEPs Conference III

Explore quasi Jacobi forms and moduli space of enhanced elliptic curves in this advanced mathematics lecture by Jin Cao, part of the GADEPs conference on Noether-Lefschetz and Hodge loci.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Centre de recherches mathématiques - CRM

An Equation of Diophantus - Introduction to Torsion and Ranks of Elliptic Curves

Explore Diophantus' equation and its impact on number theory, from ancient times to modern developments in elliptic curves and their torsion and ranks.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Moments of Families of Elliptic Curves

Explore new developments in higher moment sums of elliptic curve families, their connections to modular forms, and applications to rigid Calabi-Yau threefolds and intermediate Jacobians.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Centre International de Rencontres Mathématiques

Quadratic Twist Families of Elliptic Curves with Unusual 2∞-Selmer Groups

Explore quadratic twist families of elliptic curves with unusual 2∞-Selmer groups in this advanced mathematics talk by Alexander Smith at CIRM's Arithmetic Statistics meeting.

• YouTube
• 1 hour
• Self-Paced
• Free Video

TheIACR

Isogenies and Elliptic Curves in Cryptography

Explore advanced cryptographic concepts focusing on isogenies and elliptic curves in this comprehensive session from Crypto 2024, chaired by Francisco Rodríguez-Henríquez.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 1

Explore modular forms, elliptic curves, and modular curves in this advanced lecture. Gain insights into arithmetic geometry and the study of rational points on varieties.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 2

Explore advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Gain insights into rational points and their significance in number theory.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 4

Explore advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Gain insights from expert Eknath Ghate in this in-depth lecture.

• YouTube
• 1 hour 37 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 3

Explores advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Builds on previous lectures to deepen understanding of these fundamental objects.

• YouTube
• 1 hour 30 minutes
• Self-Paced
• Free Video

Fields Institute

Ranks of Elliptic Curves in Cyclic Sextic Extensions of Q

Explore elliptic curve ranks in cyclic sextic extensions of Q, delving into advanced number theory concepts and their applications in algebraic geometry.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

There Are Infinitely Many Elliptic Curves Over the Rationals of Rank 2

Explore the proof of infinitely many elliptic curves over the rationals with rank 2, using explicit models, 2-descent methods, and Tao-Ziegler theorem, with insights on rank stability.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Fields Institute

Torsion of Rational Elliptic Curves over the Cyclotomic Extensions of Q

Explore the torsion behavior of rational elliptic curves when extended to cyclotomic fields in this advanced number theory seminar by Omer Avci from Bogazici University.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Groups from Elliptic Curves - Isomorphism Testing and the PORC Conjecture

Explore finite groups from elliptic curves, isomorphism testing methods, and connections to Higman's PORC conjecture in algebraic geometry and group theory.

• YouTube
• 43 minutes
• Self-Paced
• Free Video