In mathematics, and especially algebraic geometry, stability is a notion which characterises when a geometric object, for example a point, an algebraic variety, a vector bundle, or a sheaf, has some desirable properties for the purpose of classifying them. The exact characterisation of what it means to be stable depends on the type of geometric object, but all such examples share the property of having a minimal amount of internal symmetry, that is such stable objects have few automorphisms. This is related to the concept of simplicity in mathematics, which measures when some mathematical object has few subobjects inside it (see for example simple groups, which have no non-trivial normal subgroups). In addition to stability, some objects may be described with terms such as semi-stable (having a small but not minimal amount of symmetry), polystable (being made out of stable objects), or unstable (having too much symmetry, the opposite of stable). (Wikipedia).
Stability Analysis, State Space - 3D visualization
Introduction to Stability and to State Space. Visualization of why real components of all eigenvalues must be negative for a system to be stable. My Patreon page is at https://www.patreon.com/EugeneK
From playlist Physics
The structure of instability in moduli theory - Daniel Halpern-Leistner
Daniel Halpern-Leistner Member, School of Mathematics October 21, 2014 In many examples of moduli stacks which come equipped with a notion of stable points, one tests stability by considering "iso-trivial one parameter degenerations" of a point in the stack. To such a degeneration one can
From playlist Mathematics
Fixed points and stability: one dimension
Shows how to determine the fixed points and their linear stability of a first-order nonlinear differential equation. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org
From playlist Differential Equations
Stability for functional and geometric inequalities - Robin Neumayer
Short talks by postdoctoral members Topic: Stability for functional and geometric inequalities Speaker: Robin Neumayer Affiliation: Northwestern University; Member, School of Mathematics Date: Oct 1, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Stabilizer in abstract algebra
In the previous video we looked at the orbit of a set. To work towards the orbit stabilizer theorem, we take a look at what a stabilizer is in this video.
From playlist Abstract algebra
algebraic geometry 14 Dimension
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the dimension of a topological space, algebraic set, or ring.
From playlist Algebraic geometry I: Varieties
Algebraic geometry 44: Survey of curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives an informal survey of complex curves of small genus.
From playlist Algebraic geometry I: Varieties
An introduction to algebraic curves | Arithmetic and Geometry Math Foundations 76 | N J Wildberger
This is a gentle introduction to curves and more specifically algebraic curves. We look at historical aspects of curves, going back to the ancient Greeks, then on the 17th century work of Descartes. We point out some of the difficulties with Jordan's notion of curve, and move to the polynu
From playlist Math Foundations
Alessio Figalli - Quantitative Stability in Geometric and Functional Inequalities - IPAM at UCLA
Recorded 08 February 2022. Alessio Figalli of ETH Zurich presents "Quantitative Stability in Geometric and Functional Inequalities" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: Geometric and functional inequalities play a crucial role in several problems
From playlist Workshop: Calculus of Variations in Probability and Geometry
Degenerations and moduli spaces in Kähler geometry – Song Sun – ICM2018
Geometry Invited Lecture 5.10 Degenerations and moduli spaces in Kähler geometry Song Sun Abstract: We report some recent progress on studying degenerations and moduli spaces of canonical metrics in Kähler geometry, and the connection with algebraic geometry, with a particular emphasis o
From playlist Geometry
Arend Bayer: Stability and applications to birational and hyperkaehler geometry - lecture 1
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Maxim Kontsevich - 3/4 Bridgeland Stability over Non-Archimedean Fields
Bridgeland stability structure/condition on a triangulated category is a vast generalization of the notion of an ample line bunlde (or polarization) in algebraic geometry. The origin of the notion lies in string theory, and is applicable to derived categories of coherent sheaves, quiver re
From playlist Maxim Kontsevitch - Bridgeland Stability over Non-Archimedean Fields
Stability conditions in symplectic topology – Ivan Smith – ICM2018
Geometry Invited Lecture 5.8 Stability conditions in symplectic topology Ivan Smith Abstract: We discuss potential (largely speculative) applications of Bridgeland’s theory of stability conditions to symplectic mapping class groups. ICM 2018 – International Congress of Mathematicians
From playlist Geometry
David Rydh. Local structure of algebraic stacks and applications
Abstract: Some natural moduli problems, such as moduli of sheaves and moduli of singular curves, give rise to stacks with infinite stabilizers that are not known to be quotient stacks. The local structure theorem states that many stacks locally look like the quotient of a scheme by the act
From playlist CORONA GS
Robert BRYANT - Algebraically Constrained Special Holonomy Metrics...
Robert BRYANT - Algebraically Constrained Special Holonomy Metrics and Second-order Associative 3-folds There are various methods known now for constructing more-or-less explicit metrics with special holonomy; most of these rely on assumptions of symmetry and/or reduction. Another promisi
From playlist Riemannian Geometry Past, Present and Future: an homage to Marcel Berger
Ruadhai Dervan: Moduli of algebraic varieties
Abstract: One of the central problems in algebraic geometry is to form a reasonable (e.g. Hausdorff) moduli space of smooth polarised varieties. I will show how one can solve this problem using canonical Kähler metrics. This is joint work with Philipp Naumann. Recording during the meeting
From playlist Algebraic and Complex Geometry
Infinite-Dimensional Geometric Invariant Theory and Gauged Gromov–Witten... by Dan Halpern-Leistner
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
Exploring Moduli: basic constructions and examples (Lecture 1) by Carlos Simpson
INFOSYS-ICTS RAMANUJAN LECTURES EXPLORING MODULI SPEAKER: Carlos Simpson (Université Nice-Sophia Antipolis, France) DATE: 10 February 2020 to 14 February 2020 VENUE: Madhava Lecture Hall, ICTS Campus Lecture 1: Exploring Moduli: basic constructions and examples 4 PM, 10 February 2020
From playlist Infosys-ICTS Ramanujan Lectures
Corey Jones: "Anomalous symmetries of C*-algebras"
Actions of Tensor Categories on C*-algebras 2021 "Anomalous symmetries of C*-algebras" Corey Jones - North Carolina State University Abstract: A fusion category is called pointed if every simple object is invertible under the monoidal product. These are described by finite groups togethe
From playlist Actions of Tensor Categories on C*-algebras 2021
algebraic geometry 15 Projective space
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It introduces projective space and describes the synthetic and analytic approaches to projective geometry
From playlist Algebraic geometry I: Varieties