Simons Semester on Dynamics Courses

Classifying Pseudo-Anosov Flows on 3-Manifolds - Lecture 2

Explore a 55-minute lecture on classifying pseudo-Anosov flows on 3-manifolds, delivered by Kathryn Mann from Cornell University as part of the Simons Semester on Dynamics. Delve into the collaborative work with Barthelmé, Fenley, and Frankel, focusing o…

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

Classifying Pseudo-Anosov Flows on 3-Manifolds - Lecture 1

Explore the intricacies of classifying pseudo-Anosov flows on 3-manifolds in this engaging lecture by Kathryn Mann from Cornell University. Delve into the collaborative work with Barthelmé, Fenley, and Frankel as they tackle this complex topic. Discover…

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

Non-classifiability of K-automorphisms - Lecture on Measure-Preserving Transformations

Delve into K-automorphisms, exploring their mixing properties, classification challenges, and the impossibility of Borel invariant classification. Gain insights into measure-preserving transformations and descriptive set theory.

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

Hölder Continuity of the Lyapunov Exponent for Markov Cocycles

Explore the Hölder continuity of Lyapunov exponents in ergodic theory, focusing on Markov cocycles and transition kernels.

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

Birkhoff Sums as Distributions in Dynamical Systems

Explore Birkhoff sums as distributions in dynamical systems, examining regularity results for hyperbolic systems and applications to deformation theory in one-dimensional dynamical systems.

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

Methods for Studying Abelian Actions and Centralizers - Lecture 1

Explore rigidity in dynamical systems, focusing on abelian actions and centralizers. Delve into methods for studying smooth coordinate changes, algebraic systems, and partially hyperbolic dynamics across six comprehensive lectures.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Dimension of Stationary Measures in Random Walks on Matrix Groups - Lecture Series

Explore the dimension of stationary measures in random walks, focusing on matrix group actions over flag spaces. Gain insights into exact dimensions, partial answers, and the intricate structure of flag spaces.

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

Metric and Ergodic Properties of Partially Hyperbolic Diffeomorphisms with Topological Neutral Center

Explore metric and ergodic properties of partially hyperbolic diffeomorphisms with topological neutral center. Gain insights into recent findings, including a dichotomy between atomicity and the Bernoulli property.

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

Infinite Renormalizability and Non-Uniform Partial Hyperbolicity in Two-Dimensional Dynamical Systems

Dive into the renormalization theory of dynamical systems, exploring its extension to two-dimensional settings and the concept of infinite renormalizability in diffeomorphisms.

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

Strong Positive Recurrence for Diffeomorphisms

Explore strong positive recurrence in diffeomorphisms, its implications for entropy-maximizing measures, and its equivalence to Lyapunov exponent continuity. Gain insights into smooth diffeomorphisms on compact surfaces.

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

Prediction of Dynamical Systems from Time-Delayed Measurements with Self-Intersections

Explore new versions of Takens time-delay embedding theorem for predicting dynamical systems from one-dimensional measurements, including deterministic and probabilistic settings with error decay rates.

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

Algebraic Structure of Area-Preserving Homeomorphism Groups - Lecture 4

Explore the algebraic structure of area-preserving homeomorphism groups, focusing on Fathi's question and the simplicity conjecture for compact surfaces. Delve into link spectral invariants and Lagrangian Floer homology.

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

Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 4

Delve into spectrum rigidity and joint integrability for Anosov systems on tori. Explore topological conjugacy of non-invertible Anosov maps on 2-torus and its implications for smooth conjugacy along stable foliations.

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

Collapsed Anosov Flows - Lecture 5

Delve into collapsed Anosov flows, exploring their attributes, classification, and dynamical properties in partially hyperbolic systems. Gain insights into recent developments and examples in this field of mathematics.

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

Symplectic Blenders and Persistence of Homoclinics to Saddle-Center Periodic Orbits

Explore symplectic blenders and their role in persistent homoclinic intersections for saddle-center periodic orbits in dynamical systems. Gain insights into C^r symplectic diffeomorphisms and Hamiltonian systems.

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