Elliptic Curves Courses and Certifications

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Parabolic Bundles of Rank 3 on Elliptic Curves

Explore parabolic bundles of rank 3 on elliptic curves in this advanced mathematics lecture celebrating Frank Loray's 60th birthday at IMPA's specialized conference.

• YouTube
• 54 minutes
• Self-Paced
• 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
• Self-Paced
• 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
• 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

International Centre for Theoretical Sciences

Conjectural Asymptotics of Prime Orders of Points on Elliptic Curves Over Number

Explores conjectural asymptotics of prime orders of points on elliptic curves over number fields, advancing understanding in arithmetic geometry and modular curve theory.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Arithmetic Field Theory for Elliptic Curves by Minhyong Kim

Explore advanced arithmetic field theory for elliptic curves, focusing on rational points on modular curves, Chabauty methods, and computational aspects in arithmetic geometry.

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

International Centre for Theoretical Sciences

Diophantine Stability for Elliptic Curves on Average by Anwesh Ray

Explore Diophantine stability for elliptic curves, focusing on average-case analysis. Gain insights into arithmetic geometry and modular curves through advanced theoretical and computational approaches.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Iwasawa Theory for the Fine Selmer Group of Elliptic Curves Over Anticyclotomic

Explore Iwasawa theory for fine Selmer groups of elliptic curves over anticyclotomic extensions, delving into advanced arithmetic geometry concepts and their applications.

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

TheIACR

Double-Base Chains for Scalar Multiplications on Elliptic Curves

Explore efficient scalar multiplication on elliptic curves using double-base chains, enhancing cryptographic operations and improving performance in elliptic curve cryptography.

• YouTube
• 20 minutes
• Self-Paced
• Conference Talk

Fields Institute

One-level Densities in Families of Grossencharakters Associated to CM Elliptic Curves

Explore one-level densities in Grossencharakters families linked to CM elliptic curves, delving into advanced number theory concepts and their applications.

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

An Introduction to Number Theory

Explore quadratic fields, binary forms, and elliptic curves while mastering fundamental concepts in number theory and their applications to cryptography over 12 weeks.

• Swayam
• 12 weeks
• Self-Paced
• Free Online Course

Mathologer

Euler's and Fermat's Last Theorems, the Simpsons and CDC6600

Explore Fermat's last theorem, Euler's conjecture, and their connections to pop culture and computing history. Delve into mathematical proofs and historical insights.

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