In mathematics, a complete set of invariants for a classification problem is a collection of maps (where is the collection of objects being classified, up to some equivalence relation , and the are some sets), such that if and only if for all . In words, such that two objects are equivalent if and only if all invariants are equal. Symbolically, a complete set of invariants is a collection of maps such that is injective. As invariants are, by definition, equal on equivalent objects, equality of invariants is a necessary condition for equivalence; a complete set of invariants is a set such that equality of these is also sufficient for equivalence. In the context of a group action, this may be stated as: invariants are functions of coinvariants (equivalence classes, orbits), and a complete set of invariants characterizes the coinvariants (is a set of defining equations for the coinvariants). (Wikipedia).
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
Sets might contain an element that can be identified as an identity element under some binary operation. Performing the operation between the identity element and any arbitrary element in the set must result in the arbitrary element. An example is the identity element for the binary opera
From playlist Abstract algebra
Eva Gallardo Gutiérrez: The invariant subspace problem: a concrete operator theory approach
Abstract: The Invariant Subspace Problem for (separable) Hilbert spaces is a long-standing open question that traces back to Jonhn Von Neumann's works in the fifties asking, in particular, if every bounded linear operator acting on an infinite dimensional separable Hilbert space has a non-
From playlist Analysis and its Applications
An introduction to Invariant Theory - Harm Derksen
Optimization, Complexity and Invariant Theory Topic: An introduction to Invariant Theory Speaker: Harm Derksen Affiliation: University of Michigan Date: June 4, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Determine Sets Given Using Set Notation (Ex 2)
This video provides examples to describing a set given the set notation of a set.
From playlist Sets (Discrete Math)
Find a Set with Least Cardinality that has Two Given Subsets (Lists)
This video explains how to determine a set with least cardinality that has two given subsets.
From playlist Sets (Discrete Math)
11. Two more invariant problems
Part of a series of videos in which I (usually) solve problems in real time from a list of 60 problems that require the finding of invariants. Here I solve numbers 16 and 17. The first one I manage to do quite systematically. With the second, I see my way to the end fairly early on but it
From playlist Thinking about maths problems in real time: mostly invariants problems
15 Properties of partially ordered sets
When a relation induces a partial ordering of a set, that set has certain properties with respect to the reflexive, (anti)-symmetric, and transitive properties.
From playlist Abstract algebra
Every Compact Set in n space is Bounded
Every Compact Set in n space is Bounded If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Advanced Calculus
Hülya Argüz - Gromov-Witten Theory of Complete Intersections 1/3
I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. This uses a monodromy analysis, as well as new degeneration and splitting formulas for nodal Gromov--Witten invariants
From playlist Workshop on Quantum Geometry
Amos Nevo: Representation theory, effective ergodic theorems, and applications - 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 Dynamical Systems and Ordinary Differential Equations
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
Complete Statistical Theory of Learning (Vladimir Vapnik) | MIT Deep Learning Series
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From playlist AI talks
Counting and Constraining Gravitational Scattering matrices (Lecture 2) by Shiraz Minwalla
RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online lectures
From playlist Recent Developments in S-matrix Theory (Online)
Curtis T. McMullen: Coupled rotations and snow falling on cedars
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 Dynamical Systems and Ordinary Differential Equations
Lie Groups and Lie Algebras: Lesson 38 - Preparation for the concept of a Universal Covering Group
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From playlist Lie Groups and Lie Algebras
The Monge - Ampère equations, the Bergman kernel, and geometry (Lecture 5) by Kengo Hirachi
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Giuseppe De Nittis : Topological nature of the Fu-Kane-Mele invariants
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From playlist Mathematical Physics
Find How Many Sets Are a Subset of a Given Set and Have a Given Subset
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From playlist Sets (Discrete Math)