Diophantine Approximation Courses and Certifications

BIMSA

Open Problems in Diophantine Approximation and Geometry of Numbers

Explore open problems in Diophantine Approximation and Geometry of Numbers, focusing on approximation of subspaces in R^d by rational subspaces and related mathematical concepts.

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

Simons Semester on Dynamics

The Dani Correspondence and Its Applications in Diophantine Approximation - Lecture 1

Explore the dynamic connection between ergodic theory and Diophantine approximation, focusing on Dirichlet's Theorem and its interpretation through orbital behavior in mathematical systems.

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

BIMSA

Homogeneous Dynamics and Probabilistic Diophantine Approximations - Cauchy Limit Laws for Linear Forms

Explore homogeneous dynamics and probabilistic Diophantine approximations, focusing on Cauchy limit laws for linear forms with random coefficients and lattice counting problems.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

On the Dani Correspondence and Its Applications - Lecture 3

Delve into ergodic theory and dynamics applications in Diophantine approximation, exploring Dani's correspondence and its impact on understanding rational number density patterns.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

On the Dani Correspondence and Its Applications - Lecture 2

Delve into Diophantine approximation through ergodic theory, exploring the Dani correspondence and its dynamic interpretation of rational number density in the real line.

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

Centre International de Rencontres Mathématiques

The Arithmetic of Power Series - Lecture 1

Explore advanced techniques for proving irrationality of periods using rational approximations and arithmetic holonomy theorems in this mathematical lecture.

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

Centre International de Rencontres Mathématiques

Balanced Fibonacci Word Rectangles

Explore the mathematical properties of balanced Fibonacci word rectangles using Hankel matrices and Walnut software to characterize their distribution patterns.

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

Centre International de Rencontres Mathématiques

The Arithmetic of Power Series - Lecture 2

Explore advanced Diophantine approximation through Thue hypergeometric Pade methods, multivalent holonomy bounds, and algebraic Apery limits with explicit proofs and S-unit equation applications.

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

Hausdorff Center for Mathematics

Osama Khalil- Diophantine Approximation on Fractals and Homogeneous Flows

Explore Diophantine approximation on fractals and homogeneous flows, examining exceptional sets and their connections to recurrence behavior. Discover new results on Hausdorff dimension of divergent orbits and self-similar measure projections.

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

International Centre for Theoretical Sciences

Hyperbolic Geometry, the Modular Group and Diophantine Approximation - Lecture 1

Explore hyperbolic geometry, modular groups, and Diophantine approximation in this advanced lecture. Delve into fundamental concepts, geodesic flows, and subgroups of SL(2,R), with proofs and examples.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 1

Explore Zariski-dense subgroups, number theory, and geometric applications in this lecture on bounded generation of linear groups and Diophantine approximation.

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

International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 2

Explore advanced topics in linear groups and Diophantine approximation, focusing on bounded generation and its applications in number theory and geometric analysis.

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

International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 3

Explore advanced concepts in linear groups and Diophantine approximation, focusing on bounded generation techniques and their applications in number theory and geometric analysis.

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

Institut Henri Poincaré

Random Walks and Asymptotic Geometry of Groups

Explore advanced mathematical concepts connecting random walks with asymptotic geometry of groups through expert lectures from leading researchers in the field.

• YouTube
• 16 hours 47 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Ergodic Theory and Dynamical Systems 2022

Explore advanced topics in ergodic theory and dynamical systems through expert lectures on Diophantine approximation, homogeneous dynamics, and measure theory applications.

• YouTube
• 1 day 16 hours 22 minutes
• On-Demand
• Free Video