Number Theory Courses and Certifications

Hausdorff Center for Mathematics

Geometric Eisenstein Series and Torsion Vanishing

Explores torsion vanishing in cohomology of Shimura varieties, combining geometric Eisenstein series, Fargues-Scholze local Langlands correspondence, and Hecke correspondences to extend previous results.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Progress on Local Shtukas

Explore recent advancements in local shtukas, including joint research findings and their compatibility with global shtukas in characteristic p mathematics.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

An Introduction to Geometric Sen Theory

Explore geometric Sen theory, its applications to Shimura varieties, and connections with proétale cohomology. Learn about solid locally analytic representations and perfectoid Shimura varieties.

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

Hausdorff Center for Mathematics

Anticyclotomic P-adic L-functions for Rankin-Selberg Motives

Explore anticyclotomic p-adic L-functions for Rankin-Selberg motives, their construction, conjectures, and progress towards the Iwasawa main conjecture in this advanced mathematics lecture.

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

Hausdorff Center for Mathematics

Generalised Eigenvalues via Flach Classes

Explore the connection between generalized eigenvalues for mod p cusp forms and Galois cohomology classes, focusing on Flach's geometric construction and its implications for Hecke algebra actions.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 1

Explore advanced techniques for studying rational points on modular curves, focusing on the Chabauty-Coleman-Kim method and its theoretical and practical applications in arithmetic geometry.

• YouTube
• 1 hour 54 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Classical and Quadratic Chabauty - Lecture 3

Explore advanced techniques in arithmetic geometry: Classical and Quadratic Chabauty methods for studying rational points on modular curves, with applications to elliptic curves.

• YouTube
• 1 hour 51 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 2

Explore advanced techniques in arithmetic geometry, focusing on the Chabauty-Coleman-Kim method for studying rational points on modular curves. Gain insights into theoretical foundations and practical applications.

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

International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 4

Explore advanced techniques in arithmetic geometry, focusing on the Chabauty-Coleman-Kim method for studying rational points on modular curves. Gain insights into theoretical foundations and practical applications.

• YouTube
• 1 hour 52 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Classical and Quadratic Chabauty - Lecture 3

Explore advanced techniques in arithmetic geometry: Classical and Quadratic Chabauty methods for studying rational points on modular curves, with applications to elliptic curves.

• YouTube
• 1 hour 47 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 3

Exploring advanced techniques in arithmetic geometry for analyzing rational points on modular curves, focusing on the Chabauty-Coleman-Kim method and its practical applications.

• YouTube
• 1 hour 51 minutes
• Self-Paced
• Free Video

ICTP Mathematics

The Variance of a General Class of Multiplicative Functions in Short Intervals

Explore the variance of multiplicative functions in short intervals, applying Fourier analysis and rational point counting to derive asymptotic estimates for k-free numbers and other functions.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

International Mathematical Union

Points on Shimura Varieties Modulo Primes

Explore the intricacies of Shimura varieties modulo primes, delving into advanced mathematical concepts and their applications in number theory and algebraic geometry.

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

IMSA

Khajuraho's Magic Square and Hypercube Symmetries - General Seminar

Explore the symmetries of Khajuraho's Magic Square, its connection to hypercube movements, and broader implications for magic structures in this intriguing mathematical lecture.

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

IMSA

A Construction of Apéry Constants from Landau Ginzberg Models

Explores construction of Apéry constants from Landau-Ginzberg models, linking quantum differential equations of Fano threefolds to mirror symmetry and geometric higher normal functions.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video