Rational Points Courses and Certifications

International Mathematical Union

Olivier Wittenberg- Some Aspects of Rational Points and Rational Curves

Explore rational points and curves in algebraic geometry, examining their properties and connections to other mathematical concepts.

• YouTube
• 45 minutes
• On-Demand
• Free Online Course

International Mathematical Union

The Number of Rational Points on a Curve of Genus at Least Two

Explore the intriguing mathematical concept of rational points on higher genus curves, delving into advanced number theory and algebraic geometry.

• YouTube
• 45 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

The Variance of a General Class of Multiplicative Functions in Short Intervals

Explore the variance of multiplicative functions in short intervals, applying Fourier analysis and rational point counting to derive asymptotic estimates for k-free numbers and other functions.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

AGRA IV - Diophantine Equations with Few Solutions - Lecture 2

Exploración avanzada de ecuaciones diofantinas con soluciones limitadas, enfocándose en técnicas analíticas y algebraicas para abordar problemas complejos en teoría de números.

• YouTube
• 58 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 1

Explore advanced techniques for studying rational points on modular curves, focusing on the Chabauty-Coleman-Kim method and its theoretical and practical applications in arithmetic geometry.

• YouTube
• 1 hour 54 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 4

Explore advanced techniques in arithmetic geometry, focusing on the Chabauty-Coleman-Kim method for studying rational points on modular curves. Gain insights into theoretical foundations and practical applications.

• YouTube
• 1 hour 52 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

Classical and Quadratic Chabauty - Lecture 3

Explore advanced techniques in arithmetic geometry: Classical and Quadratic Chabauty methods for studying rational points on modular curves, with applications to elliptic curves.

• YouTube
• 1 hour 47 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

Classical and Quadratic Chabauty - Lecture 3

Explore advanced techniques in arithmetic geometry: Classical and Quadratic Chabauty methods for studying rational points on modular curves, with applications to elliptic curves.

• YouTube
• 1 hour 51 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 2

Explore advanced techniques in arithmetic geometry, focusing on the Chabauty-Coleman-Kim method for studying rational points on modular curves. Gain insights into theoretical foundations and practical applications.

• YouTube
• 1 hour 58 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 3

Exploring advanced techniques in arithmetic geometry for analyzing rational points on modular curves, focusing on the Chabauty-Coleman-Kim method and its practical applications.

• YouTube
• 1 hour 51 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

Computational Aspects of Nonabelian Chabauty - Lecture 1

Explore computational techniques for Nonabelian Chabauty methods in arithmetic geometry, focusing on rational points on modular curves and advanced number theory concepts.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Online Course

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
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

Automorphic Lefschetz Properties and L-Values

Explore automorphic Lefschetz properties and L-values in arithmetic geometry with expert Arvind Nair. Gain insights into advanced concepts and their applications in number theory.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

On the Harris-Venkatesh Conjecture by Loic Merel

Exploration of the Harris-Venkatesh conjecture in arithmetic geometry, focusing on rational points on modular curves and their implications for elliptic curves and modular forms.

• YouTube
• 3 hours 54 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

A Chabauty-Coleman-Caro-Pasten Bound in Higher Dimensions by Netan Dogra

Explore advanced techniques in arithmetic geometry, focusing on rational points on modular curves and higher-dimensional varieties using Chabauty-Coleman-Caro-Pasten methods.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Online Course