Modular Curves Courses and Certifications

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Smooth Plane Models for Modular Curves of Shimura Type

Explore smooth plane models for modular curves of Shimura type, delving into advanced mathematical concepts and their applications in number theory.

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

NCCR SwissMAP

Elliptic Curves and Meromorphic Modular Forms

1 review

Explore the intricate relationship between elliptic curves and meromorphic modular forms in this advanced mathematical presentation from a leading researcher at MPIM Bonn.

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

Instituto de Matemática Pura e Aplicada

Commutative Algebra and Algebraic Geometry: Modular Space of Curves - Lecture 15

Explore modular spaces of curves, intersection theory, and dual graphs in algebraic geometry. Delve into pseudostable curves and Matthews theorem with expert insights.

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

Stony Brook Mathematics

Counting Curves and Surfaces in Calabi-Yau Threefolds and Modular Forms

Explore the S-duality modularity conjecture from string theory, connecting D-brane counting problems in Calabi-Yau threefolds to modular forms through advanced algebraic geometry.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Point-Counting and the Zilber-Pink Conjecture - Lecture 1

Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.

• YouTube
• 1 hour 51 minutes
• On-Demand
• Free Video

Fields Institute

The Glamorous Variety

Explore the aesthetic virtue of glamour in mathematics, focusing on semistable curves, modular curves, perfectoid rings, and connections to the Langlands program.

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

Hausdorff Center for Mathematics

Modular Regulators and Multiple Modular Values

Explore recent advancements in computing Goncharov regulator integrals for K_4 classes on modular curves, relating them to multiple modular values and single L-values of modular forms.

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

Institut des Hautes Etudes Scientifiques (IHES)

Point-Counting and the Zilber-Pink Conjecture - Lecture 4

Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.

• YouTube
• 1 hour 52 minutes
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Explicit Motivic Chabauty-Kim Method by David Corwin

Explore the Explicit Motivic Chabauty-Kim Method for studying rational points on modular curves, combining advanced arithmetic geometry with computational techniques.

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