Rational Points Courses and Certifications

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
• On-Demand
• Free Online Course

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 Online Course

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
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

A Simple Dichotomy in Serre's Uniformity Question by Davide Lombardo

Explore Serre's Uniformity Question in arithmetic geometry, focusing on rational points on modular curves and their implications for elliptic curves and number theory.

• YouTube
• 2 hours 4 minutes
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

Roger Heath Brown - The Determinant Method, Lecture III

Explore variants of the determinant method and its application to consecutive "powerful" numbers in algebraic number theory.

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

International Centre for Theoretical Sciences

Towards Strong Uniformity for Isogenies of Prime Degree by Barinder Singh Banwait

Explores strong uniformity for prime degree isogenies in arithmetic geometry, focusing on modular curves and rational points. Advances theoretical understanding and computational methods in this specialized field.

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

International Centre for Theoretical Sciences

Quadratic Twist of Epsilon Factor of Symmetric Cube Transfers of Modular Form by Sudipa Mondal

Explores quadratic twists of epsilon factors for symmetric cube transfers of modular forms, delving into advanced concepts in arithmetic geometry and number theory.

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

International Centre for Theoretical Sciences

On the Pseudonullity of Fine Selmer Groups Over Function Fields by Sohan Ghosh

Explores pseudonullity of fine Selmer groups over function fields, advancing understanding in arithmetic geometry and modular curves. Contributes to research on rational points and algebraic structures.

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

International Centre for Theoretical Sciences

Uniform Versions of Shafarevich Conjecture by Plawan Das

Exploring uniform versions of Shafarevich Conjecture in arithmetic geometry, focusing on rational points on modular curves and their implications for elliptic curves and modular forms.

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

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 Online Course

International Centre for Theoretical Sciences

Classical and Quadratic Chabauty - Lecture 1

Explore advanced techniques for studying rational points on modular curves, focusing on classical and quadratic Chabauty methods in arithmetic geometry.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

Singular Moduli for Real Quadratic Fields - An Update by Jan Vonk

Explore singular moduli for real quadratic fields with Jan Vonk. Learn about recent developments, theoretical insights, and computational aspects in this advanced arithmetic geometry lecture.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

Equidistribution of Matrix Valued Gauss Sums by C. S. Rajan

Explore equidistribution of matrix-valued Gauss sums in this advanced mathematics lecture, delving into arithmetic geometry and modular curves.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Online Course

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 Online Course

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
• On-Demand
• Free Online Course