Simons Semester on Dynamics Courses

Dimension of Stationary Measures - Lecture 2

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

Dimension of Stationary Measures - Lecture 4

Delve into the dimension of stationary measures in random walks on matrix groups, exploring flag spaces, Oseledets measures, and configuration space dynamics.

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

Methods for Studying Abelian Actions and Centralizers - Lecture 6

Explore centralizer rigidity and classification in accessible examples of dynamical systems. Gain insights into the non-generic situations where smooth centralizers form larger groups, particularly in algebraic systems.

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

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

Nicolas Gourmelon (Université de Bordeaux)

Explore a lecture on total renormalizations of perturbations of identity presented by Nicolas Gourmelon from Université de Bordeaux as part of the Simons Semester on Dynamics. Delve into the concept of total renormalization, defined as a transformation F…

• YouTube
• 1 hour 4 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

Newhouse Phenomenon in the Complex Hénon Family

Explore the Newhouse phenomenon in complex Hénon maps, focusing on stable homoclinic tangencies and intersections between dynamical Cantor sets generated by conformal IFSs.

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

Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 3

Delve into spectrum rigidity and joint integrability for Anosov systems on tori. Explore the equivalence between geometric rigidity and dynamical spectral rigidity in Anosov diffeomorphisms, focusing on irreducible cases with split stable bundles.

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

On the Algebraic Structure of Groups of Area-Preserving Homeomorphisms - Lecture 3

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 their role in solving these problems.

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

Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 2

Explore the global rigidity properties of irreducible Anosov diffeomorphisms on T^d satisfying center bunching conditions in this advanced mathematics lecture. Delve into how joint integrability of strong stable and full unstable subbundles leads to dyna…

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

Collapsed Anosov Flows - Lectures 3 and 4

Explore partially hyperbolic systems and collapsed Anosov flows in dynamical systems. Gain insights into accessibility, ergodicity, and self-orbit equivalences of Anosov flows in 3-manifolds.

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

On the Algebraic Structure of Groups of Area-Preserving Homeomorphisms - Lecture 2

Explore the algebraic structure of area-preserving homeomorphism groups, focusing on Fathi's question and the simplicity conjecture for compact surfaces. Discover link spectral invariants and their role in solving this problem.

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