Simons Semester on Dynamics Courses

Collapsed Anosov Flows - Lecture 1: Basic Definitions and Main Results

Explore the concept of collapsed Anosov flows in this first lecture of a mini-course on partially hyperbolic systems. Delve into basic definitions and the characterization of collapsed Anosov flows, including stronger variants. Examine examples and key r…

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

Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 1

Explore the spectrum rigidity and joint integrability of Anosov systems on tori in this lecture from the Simons Semester on Dynamics. Delve into the strong rigidity properties arising from joint integrability in Anosov diffeomorphisms on tori, focusing o…

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

Rose Elliott Smith (University of Chicago)

Explore a 28-minute lecture on uniformly expanding random walks on manifolds, presented by Rose Elliott Smith from the University of Chicago as part of the Simons Semester on Dynamics. Delve into the dynamical property of uniform expansion, which indicat…

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

Salvador Zanata (Ime Usp)

Syllabus: Salvador Zanata (Ime Usp)

• YouTube
• 57 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

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

Methods for Studying Abelian Actions and Centralizers - Lecture 2

Explore local and global rigidity for abelian actions and centralizer rigidity. Examine examples and basic invariant structures, delving into the foundations of dynamical systems theory and its applications.

• YouTube
• 1 hour 2 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

Methods for Studying Abelian Actions and Centralizers - Lecture 3

Explore two methods for studying abelian actions and centralizers: linearization and non-linearization. Delve into cohomology concepts and their applications in dynamical systems analysis.

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