Nonlinear Dynamics in an Age of Heuristic Science
Explore nonlinear dynamics through combinatorial topology, offering efficient computational methods and new perspectives for multiscale systems and data-driven science in biology and engineering.
Tomoo Yokoyama - Generalizations of Morse Graph of Flows and Reeb Graph of Hamiltonian Flows
Generalizations of Morse and Reeb graphs for flows, exploring connections between dynamical systems, topological structures, and abstract orbit spaces. Insights into Conley theory and topological invariants.
Pawel Dlotko - A Few Simple Stories on Topology in Action
Explore practical applications of computational topology in material science, dynamical systems, and brain research. Learn how theory and algorithms work together to solve real-world problems.
SRB Measures and Young Towers - Lecture 3 of 4
Explore SRB measures and Young towers in dynamical systems, focusing on nonuniformly hyperbolic systems and their statistical properties. Learn about recent advances in this field of mathematics.
Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 4
Explore advanced techniques in nonuniformly hyperbolic dynamics, focusing on symbolic coding and statistical properties of complex systems using Markov Partitions and Young Towers.
Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 3 of 5
Explores advanced techniques in nonuniformly hyperbolic systems, focusing on symbolic dynamics and Markov partitions. Covers key concepts, challenges, and recent developments in the field of dynamical systems.
Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 2 of 5
Explores advanced techniques in symbolic dynamics for nonuniformly hyperbolic systems, focusing on graph transforms, recurrence properties, and Markov partitions to analyze complex dynamical behaviors.
Fractal Dimensions in Nature and Mathematics - 2019
Explore fractal dimensions in nature and math, from intuitive integer dimensions to non-integer fractals. Learn alternative definitions, simple examples, and applications in dynamical systems.
Rotations of the Circle and Renormalization
Explore circle rotations, renormalization, and dynamical systems with Corinna Ulcigrai. Learn key concepts, proofs, and applications in this advanced mathematics lecture.
Taylor McAdam- Almost-Prime Times in Horospherical Flows
Explore effective results in horospherical flows, their applications to number theory, and connections to Sarnak's Mobius disjointness conjecture in this advanced mathematics lecture.
Michael Baake - A Cocycle Approach to the Fourier Transform of Rauzy Fractals
Explore Fourier transforms of Rauzy fractals and their role in analyzing spectra of Pisot inflation tilings, with applications to diffraction theory and dynamical systems.
The Dynamical Systems Approach to Spatially Homogenous Einstein-Vlasov Cosmology
Explore spatially homogenous Einstein-Vlasov cosmology using dynamical systems analysis. Investigate asymptotic solutions near singularities and expanding futures, focusing on Kantowski-Sachs models with Vlasov matter.
Dynamics of Smooth Surface Diffeomorphisms - Spectral Gap and Stochastic Properties
Explore surface diffeomorphisms, spectral gaps, and stochastic properties in smooth dynamics. Gain insights into symbolic models, entropy continuity, and hyperbolic systems.
Chance and Chaos - How to Predict the Unpredictable by Jens Marklof
Explore chaos theory, unpredictability, and mathematical tools for analyzing chaotic systems. Discover applications in weather forecasting, statistical physics, and everyday phenomena like coin tosses and bread kneading.
About Dulac's Problem in R3 for Perturbations of Linear Non-Degenerated Centers
Explora el problema de Dulac en R^3 para perturbaciones de centros lineales no degenerados, analizando mapas de retorno, conjuntos de ciclos y técnicas de explosión para sistemas dinámicos.
Hilbert's 16th Problem and O-Minimality - Lecture 1
Explore the topology of cycles, limit cycles, and related mathematical concepts in this advanced graduate-level lecture on Hilbert's 16th problem and o-minimality.
Vector Bundles for Data Alignment and Dimensionality Reduction
Explore vector bundles in data science, focusing on synchronization problems and topology-preserving dimensionality reduction. Applications in computational chemistry and dynamical systems are presented.
Residual Dynamic Mode Decomposition- Rigorous Data-Driven Computation of Spectral Properties of Koopman Operators for Dynamical Systems
Explore rigorous data-driven methods for computing spectral properties of Koopman operators in dynamical systems, focusing on Residual Dynamic Mode Decomposition and its applications.
Mini-course on Blaschke Products and Inner Functions - Part 1
Explore Blaschke products and inner functions in complex analysis, covering definitions, singular inner functions, and dynamical properties in this advanced mathematics lecture.
Symmetric Spaces by Pralay Chatterjee
Explore symmetric spaces in this advanced lecture on geometry, groups, and dynamics. Delve into modern research aspects and connect with cutting-edge theories in the field.
The Topology of the 3 Body Problem & Space
Explore the topological structure of invariant manifolds in the 3-body problem and its applications in space missions, dynamical astronomy, and celestial body impacts.