Rational Points Courses and Certifications

Institut Henri Poincaré

Reinventing Rational Points

Explore advanced techniques in arithmetic geometry, from Brauer-Manin obstructions to counting rational points on algebraic varieties through analytic and geometric methods.

• YouTube
• 2 days 3 minutes
• On-Demand
• Free Video

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 Video

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 Video

Centre International de Rencontres Mathématiques

Probabilistic Approaches to Rational Points on Algebraic Surfaces

Explore probabilistic methods for studying rational points on algebraic surfaces, delving into advanced mathematical concepts and recent research developments.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Counting Rational Points on Modular Curves of Genus 0 Over Number Fields by Peter Bruin

Explore techniques for counting rational points on modular curves of genus 0 over number fields, advancing understanding in arithmetic geometry and algebraic number theory.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

BIMSA

Sparsity of Rational Points on Curves - What is Known and What is Expected

Explore the known results and open questions surrounding the sparsity of rational points on curves, gaining insights into this mathematical concept.

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

International Centre for Theoretical Sciences

Rational Points on Modular Curves - Lecture 1

Explore advanced concepts in arithmetic geometry, focusing on rational points on modular curves. Gain insights into theoretical and computational aspects of this fascinating field of mathematics.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Rational Points on Modular Curves by Jan Vonk

Explore advanced techniques for studying rational points on modular curves, focusing on theoretical and computational aspects in arithmetic geometry.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Lower Bound on the Maximal Number of Rational Points on Curves over Finite Fields

Explore lower bounds on maximal rational points for curves over finite fields. Delve into strategies, Kzarnak Theory, and proofs in algebraic geometry.

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

Centre International de Rencontres Mathématiques

Algebraic Curves with Many Rational Points over Finite Fields

Explore algebraic curves with many rational points over finite fields, focusing on maximum curves, automorphisms, and their applications in coding theory.

• YouTube
• 49 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

International Centre for Theoretical Sciences

Rational Points on Modular Curves - Lecture 3

Explore advanced techniques for studying rational points on modular curves, focusing on geometry, Q-rational points, Chabauty methods, and computational aspects in arithmetic geometry.

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

International Centre for Theoretical Sciences

Rational Points on Modular Curves - Lecture 2

Explore advanced techniques for studying rational points on modular curves, focusing on geometry, Q-rational points, Chabauty methods, and computational aspects in arithmetic geometry.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Cohomological Obstructions to Rational Points

Explore cohomological obstructions proving varieties over number fields lack rational points, covering Brauer-Manin and descent obstructions in this advanced mathematics lecture.

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

International Centre for Theoretical Sciences

P-adic Adelic Metrics, P-adic Heights, and Rational Points on Curves by Padma Srinivasan

Explore P-adic adelic metrics, P-adic heights, and their applications in studying rational points on curves with expert Padma Srinivasan in this advanced mathematics lecture.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video