Modular Curves Courses and Certifications

Fields Institute

Some Differential Operators on the Modular Curves with Infinite Level at P and Applications

Explore differential operators on modular curves with infinite level at p, their applications, and related concepts in algebraic geometry and number theory.

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

International Centre for Theoretical Sciences

Arakelov Self-Intersection Number on Modular Curves by Priyanka Mazumdar

Exploration of Arakelov self-intersection numbers on modular curves, examining their geometric and arithmetic properties in the context of rational points and arithmetic geometry.

• YouTube
• 27 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

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

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

On the Locally Analytic Vectors of the Completed Cohomology of Modular Curves

Explore locally analytic vectors in completed cohomology of modular curves through advanced mathematical analysis and geometric insights.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Modular Curves X1(n) as Moduli of Point Arrangements

Explore the mathematical theory of modular curves X1(n) as moduli of point arrangements, focusing on complex elliptic curves and their properties under Weierstrass embedding into CP2.

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

International Centre for Theoretical Sciences

Computing Local Galois Representations Modulo 2 by Shalini Bhattacharya

Explore techniques for computing local Galois representations modulo 2, focusing on arithmetic geometry and modular curves. Gain insights into advanced mathematical concepts and their applications.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

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 Video

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 Video

Hausdorff Center for Mathematics

P-adic Height Pairings of Geodesics on Modular Curves

Explore p-adic height pairings of real quadratic geodesics on modular curves, their relation to real quadratic singular moduli, and insights from triple product period interpretation.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Principle of Quadratic Chabauty and Nonsplit Cartan Modular Curves

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

• YouTube
• 1 hour 4 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

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 1

Explore modular forms, elliptic curves, and modular curves in this advanced lecture. Gain insights into arithmetic geometry and the study of rational points on varieties.

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