In dynamical systems, a spectral submanifold (SSM) is the unique smoothest invariant manifold serving as the nonlinear extension of a spectral subspace of a linear dynamical system under the addition of nonlinearities. SSM theory provides conditions for when invariant properties of eigenspaces of a linear dynamical system can be extended to a nonlinear system, and therefore motivates the use of SSMs in nonlinear dimensionality reduction. (Wikipedia).
Spectral Sequences 02: Spectral Sequence of a Filtered Complex
I like Ivan Mirovic's Course notes. http://people.math.umass.edu/~mirkovic/A.COURSE.notes/3.HomologicalAlgebra/HA/2.Spring06/C.pdf Also, Ravi Vakil's Foundations of Algebraic Geometry and the Stacks Project do this well as well.
From playlist Spectral Sequences
Elba Garcia-Failde - Quantisation of Spectral Curves of Arbitrary Rank and Genus via (...)
The topological recursion is a ubiquitous procedure that associates to some initial data called spectral curve, consisting of a Riemann surface and some extra data, a doubly indexed family of differentials on the curve, which often encode some enumerative geometric information, such as vol
From playlist Workshop on Quantum Geometry
Bertrand Eynard: Integrable systems and spectral curves
Usually one defines a Tau function Tau(t_1,t_2,...) as a function of a family of times having to obey some equations, like Miwa-Jimbo equations, or Hirota equations. Here we shall view times as local coordinates in the moduli-space of spectral curves, and define the Tau-function of a spect
From playlist Analysis and its Applications
For the latest information, please visit: http://www.wolfram.com Speaker: Paul Abbott When the eigenvalues of an operator A can be computed and form a discrete set, the spectral zeta function of A reduces to a sum over eigenvalues, when the sum exists. Belloni and Robinett used the “quan
From playlist Wolfram Technology Conference 2014
Semiclassical Eigenfunction Estimates - Melissa Tacy
Semiclassical Eigenfunction Estimates - Melissa Tacy Institute for Advanced Study October 29, 2010 ANALYSIS/MATHEMATICAL PHYSICS SEMINAR Concentration phenomena for Laplacian eigenfunctions can be studied by obtaining estimates for their LpLp growth. By considering eigenfunctions as quasi
From playlist Mathematics
Samson Shatashvili - 3/3 Supersymmetric Vacua and Integrability
"I review the relationship between supersymmetric gauge theories and quantum integrable systems. From the quantum integrability side this relation includes various spin chains, as well as many well-known quantum many body systems like elliptic Calogero-Moser system and generalisations. Fro
From playlist Samson Shatashvili - Supersymmetric Vacua and Integrability
Convergence and Riemannian bounds on Lagrangian submanifolds - Jean-Philippe Chassé
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Title: Convergence and Riemannian bounds on Lagrangian submanifolds Speaker: Jean-Philippe Chassé Affiliation: UdeM Date: October 8, 2021 Abstract: Recent years have seen the appearance of a plethora of possible metrics on
From playlist PU/IAS Symplectic Geometry Seminar
Klaus Frahm - Spectral properties of Google matrix and beyond
https://indico.math.cnrs.fr/event/3475/attachments/2180/2564/Frahm_GomaxSlides.pdf
From playlist Google matrix: fundamentals, applications and beyond
Raffaella Mulas - Spectral theory of hypergraphs
Hypergraphs are a generalization of graphs in which vertices are joined by edges of any size. In this talk, we generalize the graph normalized Laplace operators to the case of hypergraphs, and we discuss some properties of their spectra. We discuss the geometrical meaning of the largest an
From playlist Research Spotlight
Floer Theory and Framed Cobordisms Between Exact Lagrangian Submanifolds - Noah Porcelli
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Floer Theory and Framed Cobordisms Between Exact Lagrangian Submanifolds Speaker: Noah Porcelli Affiliation: Imperial College London Date: February 24, 2023 Lagrangian Floer theory is a useful tool for study
From playlist Mathematics
Stable Representation Theory and Spaces of Flat Connections by Daniel Ramras
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Determine the Fundamental Subspaces of a Matrix (2 by 3)
This video explains how to determine the 4 fundamental subspaces of a matrix.
From playlist Fundamental Subspaces of a Matrix
Path products in projective space - Nancy Hingston
Nancy Hingston The College of New Jersey February 6, 2015 We compute the mod 2 homology of the space of paths in ℂPnCPn with endpoints in ℝPnRPn, and its algebra structure with respect to the Pontryagin-Chas-Sullivan product. Our method combines Morse theory with geometry. Joint work with
From playlist Mathematics
Tarun Das - C^1 - generically continuum - wise expansive homoclinic classes are hyperbolic
PROGRAM: RECENT TRENDS IN ERGODIC THEORY AND DYNAMICAL SYSTEMS DATES: Tuesday 18 Dec, 2012 - Saturday 29 Dec, 2012 VENUE: Department of Mathematics,Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara PROGRAM LINK: http://www.icts.res.in/program/ETDS2012 DESCR
From playlist Recent Trends in Ergodic Theory and Dynamical Systems
Carlos Simpson - Spectral networks and harmonic maps to buildings
This is joint work with L. Katzarkov, A. Noll, and P. Pandit in Vienna. A boundary point of the character variety gives rise to a spectral curve, and a harmonic map to a building. The differential of the harmonic map is the real part of the multivalued tuple of differentials defined over t
From playlist 3e Séminaire Itzykson: Wall crossing in Hitchin integrable systems
Length and width of Lagrangian cobordisms - Joshua Sabloff
Princeton/IAS Symplectic Geometry Seminar Speaker: Joshua Sabloff Affiliation:Haverford College; Member, School of Mathematics Topic:Length and width of Lagrangian cobordisms For more videos, visit http://video.ias.edu
From playlist Mathematics
In this video, we introduce and discuss spectra (in the sense of homotopy theory). We explain how they generalise abelian groups. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further informa
From playlist Higher Algebra
Heaviness and Relative Symplectic Cohomology - Yuhan Sun
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Heaviness and Relative Symplectic Cohomology Speaker: Yuhan Sun Affiliation: Rutgers University Date: March 17, 2023 For a compact subset K of a closed symplectic manifold, Entov-Polterovich introduced the no
From playlist Mathematics