Modular Forms Courses and Certifications

University of Chicago Department of Mathematics

The Ramanujan Conjecture for Modular Forms

Dive into the Ramanujan conjecture for modular forms, exploring its history and recent developments in a gentle overview suitable for all levels of mathematical background.

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

Institut des Hautes Etudes Scientifiques (IHES)

Towards mod p Local Global Compatibility for Partial Weight One Hilbert Modular Forms

Explore advanced number theory through mod p Hilbert modular forms, Galois representations, and local-global compatibility conjectures for totally real fields.

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

NCCR SwissMAP

Rigid Classes for SL(n) and p-adic Families of Modular Forms

Explore rigid classes for SL(n) and their connection to p-adic families of modular forms in this advanced mathematical presentation.

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

INI Seminar Room 2

Modular Forms and Black Holes in N=4 String Theories

Delve into advanced mathematical physics exploring modular forms, their relationship to black hole physics in N=4 string theories, and connections to K3 surfaces and Mathieu group symmetries.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Video

INI Seminar Room 2

Rademacher Expansions for False and Mock Modular Forms

Delve into advanced mathematical concepts exploring Rademacher expansions, examining their application to false and mock modular forms while uncovering connections to holomorphic modular theory.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Ramanujan, Modular Forms and Beyond

Explore Ramanujan's groundbreaking work on modular forms and mock theta functions, connecting number theory to modern mathematical applications in physics and geometry.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Iterated Integrals of Modular Forms in String Theory

Explore iterated integrals of modular forms in string theory, their connection to scattering amplitudes, and the concept of multiple modular values in physics.

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

Fields Institute

Hypergeometric Functions, Galois Representations, and Modular Forms

Explore connections between hypergeometric functions, Galois representations, and modular forms in advanced number theory and algebraic geometry.

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

Instituto de Matemática Pura e Aplicada

Single-valued Integrals and Modular Forms

Delve into advanced mathematical concepts exploring the relationship between single-valued integrals and modular forms, with applications in analytic number theory and complex analysis.

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

Institute for Advanced Study

Generalizations of Ohta's Theorem for Holomorphic Modular Forms on Certain Shimura Varieties

Delve into advanced arithmetic geometry through Ohta's theorem generalizations, exploring holomorphic modular forms and Shimura varieties with applications in Euler systems construction.

• YouTube
• 1 hour 7 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

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

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