Mathematics Around Integrable Hierarchies
Explore integrable hierarchies in mathematical physics with Professor Takashi Takebe, delving into advanced concepts and their applications.
Introdução à Mecânica Estatística - Aula 02
Explore sistemas hamiltonianos, teoremas fundamentais e conceitos avançados em mecânica estatística. Aprofunde-se em modelos como Ising e FK, transições de fase e teoria de Pirogov-Sinai.
Quantitative Almost-Existence in Dimension Four
Delve into advanced symplectic geometry concepts, exploring Hofer-Zehnder's theorem and the existence of closed characteristics in four-dimensional space through rigorous mathematical analysis.
Introduction to KAM Theory - Lecture 1
Delve into the fundamentals of Kolmogorov-Arnold-Moser (KAM) theory, exploring quasi-periodic motions, celestial mechanics stability, and analytical solutions for circle diffeomorphisms and Hamiltonian systems.
Introduction to KAM Theory - Lecture 2
Delve into the fundamentals of KAM theory and its application in celestial mechanics, exploring quasi-periodic motions, small divisors, and analytical circle diffeomorphisms in dynamical systems.
Convergence of Scattering Data and Non-Linear Fourier Transform - Part 1
Explore canonical systems, spectral problems, and Hilbert spaces of entire functions in this advanced mathematical analysis lecture on scattering data and non-linear Fourier transform.
Symplectic Geometry - Class 21
Explore advanced concepts in symplectic geometry with Professor Ben Webster, delving into complex mathematical theories and their applications in this comprehensive lecture.
Symplectic Geometry - Class 20
Explore advanced concepts in symplectic geometry with Professor Ben Webster, delving into complex mathematical theories and their applications in this comprehensive lecture.
Multiple Horn Problem in Hamiltonian Geometry
Explore the intricacies of the Multiple Horn problem in this mathematical lecture by Anton Alekseev, delving into advanced concepts in Hamiltonian geometry.
Some Reflections on the Moduli Spaces of Flat Connections with Involutions
Explore moduli spaces of flat connections with involutions, examining their geometric properties and mathematical implications in this advanced mathematical lecture.
Designing Conservative and Accurately Dissipative Numerical Integrators in Time
Explore innovative framework for structure-preserving time steppers using finite elements and auxiliary variables. Discover applications in Kepler, Kovalevskaya, Navier-Stokes, and Benjamin-Bona-Mahony problems.
Computational Mathematics: Dynamics, Geometry, and Algebra in Numerical Integration
Explore computational mathematics at the intersection of dynamics, geometry, and algebra, focusing on geometric numerical integration and structure-preserving discretization of differential equations.
Insights and Challenges in Symplectic Capacities
Explore key insights and challenges in symplectic capacities, delving into advanced mathematical concepts and their applications in geometric analysis.
Canonical Hamiltonian Systems in Symplectic Statistical Manifolds
Explore canonical Hamiltonian systems within symplectic statistical manifolds, delving into advanced mathematical concepts and their applications.
Nijenhuis Geometry Symmetries, Conservation Laws and Applications to Geodesically Equivalent Metrics
Explore Nijenhuis Geometry symmetries, conservation laws, and their applications to geodesically equivalent metrics. Gain insights from A. Bolsinov's expert perspective.
KAM Tori for the Nonlinear Klein-Gordon Equation in the Non-Relativistic Limit
Explore effective theories in classical and quantum particle systems, focusing on KAM tori for the Nonlinear Klein Gordon equation in the non-relativistic limit.
A Higher Dimensional Generalization of the Birkhoff Attractor
Explore higher-dimensional generalizations of the Birkhoff attractor using spectral metrics for conformal symplectic maps and damped Hamiltonian systems.
The Z/p Gysin Sequence in Symplectic Cohomology
Explore Z/p-equivariant symplectic cohomology and its Gysin sequence, connecting S^1 and Z/p versions. Discover applications to Seidel's conjecture on localized S^1-equivariant symplectic cohomology.
The Restricted Three-Body Problem and Holomorphic Curves - Lecture 3
Delve into advanced celestial mechanics, exploring holomorphic curves and their role in solving the restricted three-body problem through Birkhoff's conjecture and periodic orbits.
Entanglement Subvolume Law for 2D Frustration-Free Spin Systems
Explore entanglement entropy in 2D frustration-free spin systems, examining Hastings' proof, robust polynomials, and the Whole Screen Directivity Lemma.
Structure-Preserving Model Order Reduction of Hamiltonian Systems
Explore structure-preserving model order reduction for Hamiltonian systems, focusing on symplectic geometry and reduced basis algorithms. Learn about extensions to nonlinear problems and applications in plasma physics.