Semiclassical Measures for Laplacian Eigenfunctions and Quantum Cat Maps
Dive into semiclassical measures for Laplacian eigenfunctions and quantum cat maps, exploring quantum chaos and high-energy limit behavior in mathematics.
Courant, Bezout, and Persistence - Lecture 2
Explore spectral geometry through persistence modules and barcodes, examining oscillation of functions and applications to Courant's nodal domain theorem and Bezout's theorem in eigenfunctions.
Courant, Bezout, and Persistence in Spectral Geometry - Lecture 1
Explore spectral geometry and topological persistence, focusing on oscillation of functions, Courant's nodal domain theorem, and Bezout's theorem in the context of eigenfunctions.
Dimension of Stationary Measures - Lecture 3
Delve into the dimension of stationary measures in random walks on matrix groups, exploring flag spaces, Oseledets measures, and configuration space dynamics. Gain insights into entropy and dimension addition.
Methods for Studying Abelian Actions and Centralizers - Lecture 4
Explore partially hyperbolic conservative dynamics, focusing on volume disintegration along foliations and the relationship between large centralizers and pathological center foliations.
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.
Non-hyperbolic Measures of Maximally Possible Entropy in Transitive Dynamical Systems
Explore the dynamics of nonhyperbolic partially hyperbolic diffeomorphisms, focusing on skew products of circle diffeomorphisms and their implications for ergodic measures and entropy in dynamical systems.
Volume Entropy for Flat Surfaces
Explore volume entropy in flat surfaces, its relation to negative curvature surfaces, and its minimum value on SL(2,R)-orbits in specific cases.
Methods for Studying Abelian Actions and Centralizers - Lecture 5: Transitive Centralizer and Fibered Partially Hyperbolic Systems
Explore transitive centralizers and fibered partially hyperbolic systems in dynamical systems. Gain insights into advanced concepts in smooth ergodic theory and their applications to centralizer rigidity.
Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 1
Dive into chain recurrence classes of generic diffeomorphisms, exploring advanced concepts in dynamical systems and topology.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.