Number Theory Courses and Certifications

Institute for Advanced Study

The Unbounded Denominators Conjecture - Yunqing Tang

Explore the unbounded denominators conjecture in modular forms, its implications, and a new proof approach using arithmetic algebraization theorem.

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

Institute for Advanced Study

Ramanujan Conjecture and the Density Hypothesis - Shai Evra

Explore the Ramanujan Conjecture and Density Hypothesis in number theory, examining their evolution, generalizations, and connections to automorphic forms and classical groups.

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

Institute for Advanced Study

An Asymptotic Version of the Prime Power Conjecture for Perfect Difference Sets - Sarah Peluse

Explore prime power conjecture for perfect difference sets, focusing on asymptotic results and proof techniques in number theory and combinatorics.

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

Institute for Advanced Study

A Geometric View on Iwasawa Theory - Mladen Dimitrov

Explore a geometric perspective on Iwasawa theory, covering higher dimensions, periodic representations, and key concepts in number theory with Mladen Dimitrov from Université de Lille.

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

Institute for Advanced Study

Eisenstein Series and the Cubic Moment for PGL(2) - Paul Nelson

Explore Eisenstein series, cubic moments for PGL(2), and their applications in number theory. Gain insights into spectral expansions, hypergeometric functions, and improved bounds.

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

Institute for Advanced Study

Primes and Knots - Akshay Venkatesh

Explore surprising parallels between number theory and 3D geometry, uncovering connections that continue to shape mathematical research.

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

Hausdorff Center for Mathematics

Large Sieve Inequalities for Families of Automorphic Forms

Explore advanced large sieve inequalities for automorphic forms, focusing on GL_3 spectral cases and recent progress in higher rank families. Gain insights into measuring family understanding.

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

Hausdorff Center for Mathematics

Valentin Blomer - The Polynomial Method for Point Counting and Exponential Sums, Lecture III

Explore advanced techniques for counting points on curves over finite fields and estimating exponential sums using auxiliary polynomials and character sums.

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

Hausdorff Center for Mathematics

Spectral Approximation of Transfer Operators

Explore spectral approximation of transfer operators using Galerkin methods and Lagrange-Chebyshev interpolation, with applications in number theory and quantum chaos.

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

Hausdorff Center for Mathematics

Maxim Kirsebom - On a Limiting Distribution for Maximal Cusp Excursions of the Unipotent Flow

Exploring the unipotent flow on modular surfaces, focusing on cusp excursions and their probabilistic behavior using geometry of numbers and extreme value statistics.

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

Hausdorff Center for Mathematics

Panorama of Mathematics - Manjul Bhargava

Explore the Birch and Swinnerton-Dyer Conjecture with Fields Medalist Manjul Bhargava, delving into rational solutions of polynomial equations and the structure of points on cubic curves.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 3

Explore the deep connections between Rogers-Ramanujan identities and the icosahedron, spanning number theory, modular forms, combinatorics, and more. Uncover the beauty and complexity of these mathematical gems.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 2

Explore connections between Rogers-Ramanujan identities and icosahedron, linking number theory, modular forms, combinatorics, and conformal field theory in an accessible survey for mathematicians.

• YouTube
• 1 hour 45 minutes
• On-Demand
• Free Video

ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 1

Explore the deep connections between the Rogers-Ramanujan identities and the icosahedron, spanning number theory, modular forms, combinatorics, and more in this accessible mathematical lecture.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

On the Brumer-Stark Conjecture and Refinements

Explore recent advancements in the Brumer-Stark Conjecture, its connections to explicit class field theory, and the proof's completion, including implications for the Equivariant Tamagawa Number Conjecture.

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