In algebraic geometry, a geometric quotient of an algebraic variety X with the action of an algebraic group G is a morphism of varieties such that (i) For each y in Y, the fiber is an orbit of G.(ii) The topology of Y is the quotient topology: a subset is open if and only if is open.(iii) For any open subset , is an isomorphism. (Here, k is the base field.) The notion appears in geometric invariant theory. (i), (ii) say that Y is an orbit space of X in topology. (iii) may also be phrased as an isomorphism of sheaves . In particular, if X is irreducible, then so is Y and : rational functions on Y may be viewed as invariant rational functions on X (i.e., of X). For example, if H is a closed subgroup of G, then is a geometric quotient. A GIT quotient may or may not be a geometric quotient: but both are categorical quotients, which is unique; in other words, one cannot have both types of quotients (without them being the same). (Wikipedia).
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
How to determine the geometric mean between two numbers
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
Learn how to find the geometric mean between two numbers
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
Write the first five terms of the geometric sequence
👉 Learn how to find the first 5 terms of a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multiplyin
From playlist Sequences
Evaluate the expression of a term of a geometric sequence
👉 Learn how to find the nth term of a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multiplying/div
From playlist Sequences
How to find the first five terms of a geometric sequence
👉 Learn how to find the first 5 terms of a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multiplyin
From playlist Sequences
Given a geometric sequence determine the nth rule
👉 Learn how to find the nth term of a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multiplying/div
From playlist Sequences
Learn how to determine the sum of a geometric finite series
👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first term
From playlist Series
Evaluate the geometric sequence given two values
👉 Learn how to find the nth term of a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multiplying/div
From playlist Sequences
Talk by Emile Takahiro Okada (University of Oxford, UK)
The Wavefront Set of Spherical Arthur Representations
From playlist Seminars: Representation Theory and Number Theory
Ana Khukhro - Geometric rigidity of finite quotients of groups
The set of finite quotients of a group can provide a lot of information about the group if this set is sufficiently rich. This is the case for a residually finite group, and studying its finite quotients geometrically has many implications for algebraic and analytic aspects of the group
From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
The integral coefficient geometric Satake equivalence in mixed characteristic - Jize Yu
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: The integral coefficient geometric Satake equivalence in mixed characteristic Speaker: Jize Yu Affiliation: Member, School of Mathematics Date: November 16, 2020 For more video please visit http://video.ias
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Vincent LAFFORGUE - Stacks of Shtukas and spectral decompositions
https://ams-ems-smf2022.inviteo.fr/
From playlist International Meeting 2022 AMS-EMS-SMF
Moduli of Representations and Pseudorepresentations - Carl Wang Erickson
Carl Wang Erickson Harvard University May 2, 2013 A continuous representation of a profinite group induces a continuous pseudorepresentation, where a pseudorepresentation is the data of the characteristic polynomial coefficients. We discuss the geometry of the resulting map from the moduli
From playlist Mathematics
Dynamics on character varieties - William Goldman
Character Varieties, Dynamics and Arithmetic Topic: Dynamics on character varieties Speaker: William Goldman Affiliation: University of Maryland; Member, School of Mathematics Date: November 10, 2021 In these two talks, I will describe how the classification of locally homogeneous geomet
From playlist Mathematics
Jens Hemelaer: Toposes in arithmetic noncommutative geometry
Talk by Jens Hemelaer in Global Noncommutative Geometry Seminar (Americas) on February 5, 2021
From playlist Global Noncommutative Geometry Seminar (Americas)
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 3/4
We motivate, define and study Donaldson-Thomas invariants and Cohomological Hall algebras associated to quivers, relate them to the geometry of moduli spaces of quiver representations and (in special cases) to Gromov-Witten invariants, and discuss the algebraic structure of Cohomological H
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Hyperbolic surfaces and their Teichmüller spaces (Lecture - 02) by Subhojoy Gupta
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017
Pseudo-reductive groups by Brian Conrad
PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will
From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)
How to determine the rule for a geometric sequence given two values
👉 Learn how to write the explicit formula for a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multi
From playlist Sequences