Simons Semester on Dynamics Courses

Disintegrating Cubic Measures for Sumsets

Explore advanced mathematical concepts in cubic measure disintegration and their applications to sumset analysis through Robertson's theoretical framework and methodologies.

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

An Extension of Result by Furstenberg and Glasner in Topological Dynamics

Delve into advanced mathematical concepts exploring extensions of Furstenberg and Glasner's work in topological dynamics and ergodic theory, presented by XiangDong Ye.

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

Infinite Arithmetic Configurations in Sets with Positive Density

Delve into advanced mathematical concepts exploring infinite arithmetic configurations and their relationship with positive density sets through rigorous theoretical analysis.

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

Free Nilspaces, Double Coset Nilspaces, and Gowers Norms

Explore advanced mathematical concepts of nilspaces, examining their relationships with double cosets and Gowers norms through rigorous theoretical analysis and proofs.

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

A Non-Flag Arithmetic Regularity Lemma and Counting Lemma

Delve into advanced mathematical concepts exploring arithmetic regularity and counting lemmas, featuring insights on nilpotent structures and topological dynamics in combinatorics.

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

Local Entropy Theory and Descriptive Complexity - Lecture 1

Dive into local entropy theory's foundations, exploring topological dynamics, combinatorial descriptions, and applications in understanding complex dynamical systems and homoclinic points.

• YouTube
• 1 hour 31 minutes
• On-Demand
• Free Video

Local Entropy Theory and Descriptive Complexity - Lecture 2

Delve into local entropy theory's fundamental concepts, exploring topological dynamics, combinatorial descriptions, and applications in understanding complex dynamical systems and homoclinic points.

• YouTube
• 1 hour 39 minutes
• On-Demand
• Free Video

Anti-holomorphic Dynamical Systems on a Torus - Applications to Weierstrass Functions

Explore complex dynamics through anti-holomorphic systems on a torus, examining Weierstrass zeta-functions and their applications to Green functions and constant curvature metrics.

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

Local Entropy Theory and Descriptive Complexity - Lecture 3

Delve into local entropy theory's fundamental concepts, exploring topological dynamics, combinatorial descriptions, and applications in understanding complex dynamical systems and homoclinic points.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Video

Almost Periodic Points and Quasifactors in Dynamical Systems

Explore the mathematical concepts of almost periodic points, minimal systems, and quasifactors in dynamical systems theory, focusing on their relationships and structural properties.

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

Beyond SL2(R): Time-Changes and Other Perturbations in Different Settings - Lecture 6

Delve into advanced mathematical concepts of horocycle flows, exploring their ergodic properties, mixing phenomena, and applications beyond SL2(R) in dynamical systems theory.

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

Introduction to Smooth Ergodic Theory - Lecture 3

Delve into smooth ergodic theory, exploring stable/unstable foliations in hyperbolic systems and their role in understanding statistical behaviors, SRB measures, and Hopf's argument for ergodicity.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Some Arguments in Equidistribution - Lecture 6

Delve into advanced concepts of equidistribution theory, exploring ergodic theorems, measure preservation, and flow dynamics on the 2-torus through detailed mathematical proofs and arguments.

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

Introduction to Smooth Ergodic Theory - Lecture 1

Delve into smooth ergodic theory, exploring statistical behavior of orbits, hyperbolic systems, and stable/unstable foliations. Learn about SRB measures and their role in understanding dynamical systems.

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

Introduction to Smooth Ergodic Theory - Lecture 2

Delve into smooth ergodic theory, exploring stable/unstable foliations in hyperbolic systems and their role in understanding statistical behaviors, SRB measures, and Hopf's argument for ergodicity.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video