Simons Semester on Dynamics Courses

Some Arguments in Equidistribution - Lecture 3

Delve into advanced concepts of ergodic theory, including measure preservation, Birkhoff's theorem, and ergodicity of flows on the 2-torus, with applications to hyperbolic automorphisms.

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

Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 1

Delve into random matrix products theory, exploring Lyapunov exponents, stationary measures, and probability measures on projective space through dynamic systems and ergodic theory perspectives.

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

Some Arguments in Equidistribution - Lecture 2

Delve into advanced mathematical concepts of ergodic theory, measure preservation, and equidistribution, exploring key theorems and their applications in dynamic systems and torus flows.

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

Some Arguments in Equidistribution - Lecture 1

Explore fundamental concepts of ergodic theory, from measure-preserving systems to Birkhoff's theorem, with applications to circle rotations and flows on the 2-torus.

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

Ergodic and Mixing Properties of Horocycle Flows - Lecture 1

Delve into the mathematical foundations of horocycle flows and their time-changes, exploring ergodic theory, mixing properties, and applications in hyperbolic geometry through advanced theoretical concepts.

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

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
• Self-Paced
• Free Video

Noncommutative Maximal Inequality and Ergodic Theorem for Actions of Amenable Groups

Delve into noncommutative maximal inequality and ergodic theorem, exploring measure-preserving transformations and actions of amenable groups in advanced mathematical theory.

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

Recent Progress on Dimension Drop Conjecture

Delve into recent advances in dimension drop conjecture, exploring self-similar sets, Hochman's theorem, and exponential separation in fractal geometry with applications to algebraic parameters.

• YouTube
• 1 hour 50 minutes
• Self-Paced
• Free Video

One-Parameter Families of Hyperbolic Iterated Function Systems on the Line - Lecture 3

Delve into hyperbolic iterated function systems and their dimensional properties, exploring transversality methods for analyzing one-parameter families and their applications in measure theory and dynamics.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Estimating Dimension and Lyapunov Exponents - Lecture 2A

Explore advanced mathematical concepts in dimension theory, including Hausdorff dimensions, Lyapunov exponents, and their applications to number theory and geometric systems.

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

Estimating Dimension and Lyapunov Exponents - Lecture 2B

Explore advanced mathematical concepts in dimension theory, including Hausdorff dimensions, Lyapunov exponents, and their applications to number theory and geometric systems.

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

One-Parameter Families of Hyperbolic Iterated Function Systems on the Line - Lecture 2B

Delve into hyperbolic iterated function systems and their dimensional properties, exploring transversality methods for analyzing one-parameter families and their geometric characteristics.

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

One-Parameter Families of Hyperbolic Iterated Function Systems on the Line - Lecture 2A

Delve into hyperbolic iterated function systems and their dimensional properties, exploring transversality methods for analyzing one-parameter families and their geometric characteristics in mathematical dynamics.

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

Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 3B

Delve into advanced dynamical systems theory, exploring chain recurrence classes, viral chain properties, flexible periodic points, and filtrating Markov partitions in diffeomorphisms.

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

Self-affine Systems and Hausdorff Dimension Theory - Lecture 2A

Delve into the dimension theory of self-affine systems, exploring Hausdorff dimensions, Falconer's results, and recent developments in non-conformal transformations and planar self-affine sets.

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