Topics in Nonlinear Dynamics
Explore nonlinear dynamics through critical points, Hamiltonian systems, bifurcations, limit cycles, discrete-time dynamics, and stochastic processes. Gain insights into complex system behaviors and analysis techniques.
Topics in Nonlinear Dynamics
This is a basic course in classical mechanics at the senior undergraduate/ master's level. It covers the standard topics in this subject, including the Lagrangian and Hamiltonian formalisms. It also places the subject in the broader context of classical…
Poisson Algebra, Combinatorics and Representations of Surface Groups
Dive into Poisson algebras, combinatorics, and surface group representations. Explore Goldman's Lie algebra construction and its applications to character varieties and Anosov representations.
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.
Stability of Periodic Orbits - Floquet Theory - Stable and Unstable Invariant Manifolds
Explore stability of periodic orbits using Floquet theory. Learn about monodromy matrices, Floquet multipliers, and invariant manifolds in Hamiltonian systems. Understand the foundations of chaos in dynamical systems.
Hamiltonian Systems Introduction - Why Study Them?
Explore Hamiltonian systems and their advantages in mechanics. Learn about generalized momentum, canonical equations, and the transformation from Lagrangian to Hamiltonian formalism.
Geometry and Topology of Hamiltonian Floer Complexes in Low-Dimension - Dustin Connery-Grigg
Explore Hamiltonian Floer complexes on surfaces, connecting dynamics to Floer chain structure. Discover a new symplectic norm and geometric interpretations of chain complexes using transverse foliations.
Asymmetry in Dynamics
Explore symmetries in dynamical systems and progress on Smale's conjecture about generic smooth systems having only trivial symmetries. Delve into complex analytic, Hamiltonian, and smooth dynamics.
Gromov-Hausdorff Convergence of Filtered A Infinity Categories
Explore Floer homology's dependence on Hamiltonian isotopy, its multiplicative structure, and connections to homological Mirror symmetry in formal deformation theory.
A New Interpretation of Laser Instabilities
Explore a novel mathematical approach to laser instabilities, uncovering their nearly Hamiltonian nature and the challenges in adiabatic elimination of atomic polarization.
On Fillings of Contact Links of Isolated Quotient Singularities - Workshop on Conservative Dynamics and Symplectic Geometry
Explore fillings of contact links in isolated quotient singularities. Delve into strong and exact fillings, tight criteria, terminal singularities, and orbifold symplectic cohomology in this advanced mathematics lecture.
Quantitative Refinements of Conjectures in 3D Reeb Dynamics - Workshop on Conservative Dynamics and Symplectic Geometry
Explore quantitative refinements of conjectures in 3D Reeb dynamics and related results. Delve into symplectic topology, Hamiltonian dynamics, and contact geometry with expert Umberto Hryniewicz.
Morse Type Theories with Differential Graded Coefficients - Workshop on Conservative Dynamics and Symplectic Geometry
Explore Morse type theories with differential graded coefficients in this advanced mathematics lecture. Gain insights into Conservative Dynamics and Symplectic Geometry from expert Mihai Damian.
Introduction to Modelling Gravitational Waves from Compact Binaries
Explore gravitational wave modeling techniques for compact binary systems, covering inspiral, merger, and ringdown phases. Learn about semi-analytic models crucial for detection and analysis.
Hamiltonian Geometry and Dynamics Behind Compressible Fluids
Explore Hamiltonian geometry and dynamics in relation to compressible fluids, delving into mathematical concepts and physical applications in fluid mechanics.
A Physics-Based Reduced Order Model Capturing the Topology of Dynamical Manifolds
Explore a transformational approach to dynamics using the Heisenberg Scattering Transformation, applied to create fast surrogate models for 2D pulsed power liner implosions in MagLIF.
A Theory of Trotter Error
Explores advanced theory of Trotter error in quantum simulation, providing tighter error bounds and improved algorithms for various quantum systems and observables.
Using Chaos to Characterize a Programmable Analog Quantum Simulator
Explore chaos in analog quantum simulators, uncovering random behavior, estimating fidelity, and learning noise models for large-scale entangled states using Rydberg atom arrays.
Symmetry and Asymmetry in Dynamics
Explore symmetry and asymmetry in dynamics, examining dynamical symmetry groups, Hamiltonian dynamics, and rigidity theorems. Gain insights into mathematical concepts and their applications.
Exact Lagrangians in Cotangent Bundles with Locally Conformally Symplectic Structure
Explore advanced concepts in locally conformally symplectic geometry, examining Lagrangian topology, Hamiltonian dynamics, and connections to contact geometry through theoretical frameworks and practical examples.
The Entropic Dynamics Approach to Quantum Mechanics
Explore the Entropic Dynamics framework for reconstructing Quantum Mechanics, focusing on ontic and epistemic variables, probability distributions, and the derivation of key quantum principles.