Elliptic Curves Courses and Certifications

Hausdorff Center for Mathematics

A New Case of BSD Conjecture and Deformation of Line Bundles

Explores a new case of the BSD conjecture for elliptic curves and examines deformation of line bundles in positive and mixed characteristic, applying rigidity properties of variations of Hodge structures.

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

Harvard CMSA

Predicting Euler Factors of Elliptic Curves

Discover how machine learning models predict Euler factors of elliptic curves with surprising accuracy from limited data in this advanced mathematical research presentation.

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

Simons Foundation

Ranks of Elliptic Curves

Explore the fundamental question of whether elliptic curve ranks can be arbitrarily large through computational data, statistical models, and challenging outliers.

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

Harvard CMSA

Ranks of Elliptic Curves - A Survey of Rational Points and Group Structure

Explore the fundamental concepts of elliptic curves, their rational points, and group structures through an advanced mathematical examination of Mordell's theorem and contemporary research.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

Harvard CMSA

Learning Euler Factors of Elliptic Curves with Transformers

Explore how machine learning and transformers can predict Euler factors of elliptic curves, uncovering patterns in L-functions and their relationship to the BSD conjecture.

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

Instituto de Matemática Pura e Aplicada

Low Lying Zeros in Families Related to Complex Multiplication Elliptic Curves

Delve into advanced number theory concepts focusing on low-lying zeros and their relationship to CM elliptic curves, exploring mathematical patterns and theoretical frameworks in this specialized mathematical domain.

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

Instituto de Matemática Pura e Aplicada

L-functions of Elliptic Curves Over Real Quadratic Fields as Special Values of Automorphic Green's Functions

Delve into advanced number theory concepts exploring L-functions of elliptic curves over real quadratic fields and their relationship to automorphic Green's functions through expert mathematical analysis.

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