Rational Points Courses and Certifications

Institute for Advanced Study

Points on Rational Normal Curves and the ABCT Variety

Delve into the mathematical exploration of rational normal curves and ABCT variety, examining their fundamental properties and relationships in combinatorial physics.

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

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

Fields Institute

Hasse Principle for Function Fields

Explore the Hasse principle's application to function fields, delving into its mathematical implications and theoretical foundations.

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

International Centre for Theoretical Sciences

Ribet's Lemma in Residually Indistinguishable Case by Mahesh Kakde

Exploration of Ribet's Lemma in the context of residually indistinguishable cases, delving into advanced concepts in arithmetic geometry and modular curves theory.

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

International Centre for Theoretical Sciences

Iwasawa Theory for Rankin-Selberg L-Function at an Eisenstein Prime

Explores Iwasawa theory for Rankin-Selberg L-functions at Eisenstein primes, delving into advanced arithmetic geometry concepts and their applications in number theory.

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

International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 2

Explore advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Gain insights into rational points and their significance in number theory.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 4

Explore advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Gain insights from expert Eknath Ghate in this in-depth lecture.

• YouTube
• 1 hour 37 minutes
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Sections of Fano Fibrations Over Curves

Explores Manin's conjecture on rational points in Fano varieties, focusing on exceptional sets and their impact on moduli spaces of sections in Fano fibrations, particularly del Pezzo fibrations.

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

International Centre for Theoretical Sciences

On the Local Constancy of Certain Mod P Galois Representations by Suneel Kumar

Exploration of local constancy in mod p Galois representations, focusing on theoretical aspects and implications for arithmetic geometry and modular curves.

• YouTube
• 30 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

International Centre for Theoretical Sciences

On a Local-Global Principle for Quadratic Twists of Abelian Varieties by Francesc Fite

Explore a local-global principle for quadratic twists of abelian varieties in this advanced mathematics lecture, delving into arithmetic geometry and number theory concepts.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video