Symmetries of Manifolds - Lecture 3
Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.
Symmetries of Manifolds - Lecture 2
Delve into symmetries of manifolds, exploring classical and recent results on spaces of symmetries for simple manifolds like spheres and discs, with insights into emerging conjectural perspectives.
Symmetries of Manifolds - Lecture 1
Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.
Renormalization in Dimension Two - Lecture 1
Explore renormalization theory in two-dimensional dynamical systems, extending techniques from one-dimensional cases to higher dimensions using non-uniformly partially hyperbolic systems.
Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 1
Dive into chain recurrence classes of generic diffeomorphisms, exploring advanced concepts in dynamical systems and topology.
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.
Mild Dissipative Diffeomorphisms of the Disk with Zero Entropy - Lecture 3
Explore zero entropy surface diffeomorphisms, their dynamics, and bifurcations. Examine volume-contracting systems, renormalization concepts, and extensions to different domains like the annulus.
Mild Dissipative Diffeomorphisms of the Disk with Zero Entropy - Lecture 2
Explore zero entropy surface diffeomorphisms, their dynamics, and bifurcations. Examine volume-contracting systems, renormalization concepts, and extensions to different domains like the annulus.
Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 1A
Delve into chain recurrence classes and Conley's theory of Lyapunov functions in dynamical systems, exploring robust non-hyperbolic diffeomorphisms and their relationship with aperiodic classes and adding machines.
Renormalization in Dimension Two - Lecture 1B
Explore advanced renormalization theory in two-dimensional dynamical systems, focusing on self-similarity, non-uniform partial hyperbolicity, and the extension of unimodal map concepts to higher dimensions.
Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 2B
Delve into chain recurrence classes in diffeomorphisms, exploring Conley's theory, Lyapunov functions, and the properties of periodic points in relation to homoclinic classes through advanced mathematical analysis.
Renormalization Theory in Two-Dimensional Dynamical Systems - Lecture 2A
Delve into advanced renormalization theory for two-dimensional dynamical systems, exploring self-similarity, non-uniform partial hyperbolicity, and geometric control at microscopic scales.
Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 2A
Delve into chain recurrence classes in dynamical systems, exploring Conley's theory, Lyapunov functions, and robust non-hyperbolic diffeomorphisms. Learn about aperiodic classes and adding machines in generic systems.
Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 1B
Delve into chain recurrence classes in diffeomorphisms, exploring Conley's theory, Lyapunov functions, and robust non-hyperbolic examples leading to aperiodic classes and adding machines in dynamical systems.
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.
Renormalization in Dimension Two - Lecture 2B
Delve into advanced renormalization theory for two-dimensional dynamical systems, exploring self-similarity, non-uniform partial hyperbolicity, and geometric control at microscopic scales.
Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 3a
Delve into advanced concepts of chain recurrence classes, exploring viral chain properties, flexible periodic points, and filtrating Markov partitions in diffeomorphisms and dynamical systems.
Singularities and Diffeomorphism - IPAM at UCLA
Explore singularities and diffeomorphism in calculus of variations, covering special cases, classification, and applications in probability and geometry.
Research Seminar - Arc-Connectedness of the Space of 1-Dimensional Commuting Diffeomorphisms
Explore arc-connectedness in 1D commuting diffeomorphisms with Andrés Navas. Gain insights into group actions, community spaces, and rotational concepts in this advanced mathematics seminar.
On the Nielsen Realization Problem and Cohomology of Mapping Class Groups of Non-orientable Surfaces
Exploración del problema de realización de Nielsen y cohomología de grupos de clases de mapeo en superficies no orientables, con aplicaciones en topología y teoría de grupos.
Subtly Knotted Surfaces Separated by Many Internal Stabilizations
Exploration of smoothly knotted surfaces in 4-manifolds, focusing on isotopy, internal stabilizations, and diffeomorphisms. Discusses infinite collections of surfaces with unique properties and infinite stabilization diameter.