Combinatorics | Finite geometry
A finite geometry is any geometric system that has only a finite number of points.The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based on the graphics displayed on a computer screen, where the pixels are considered to be the points, would be a finite geometry. While there are many systems that could be called finite geometries, attention is mostly paid to the finite projective and affine spaces because of their regularity and simplicity. Other significant types of finite geometry are finite Möbius or inversive planes and Laguerre planes, which are examples of a general type called Benz planes, and their higher-dimensional analogs such as higher finite inversive geometries. Finite geometries may be constructed via linear algebra, starting from vector spaces over a finite field; the affine and projective planes so constructed are called Galois geometries. Finite geometries can also be defined purely axiomatically. Most common finite geometries are Galois geometries, since any finite projective space of dimension three or greater is isomorphic to a projective space over a finite field (that is, the projectivization of a vector space over a finite field). However, dimension two has affine and projective planes that are not isomorphic to Galois geometries, namely the non-Desarguesian planes. Similar results hold for other kinds of finite geometries. (Wikipedia).
The Geometry of Finite Geometric Sums (visual proof; series)
This is a short, animated visual proof demonstrating the finite geometric for any ratio x with x greater than 1. This series (and its infinite analog when x less than 1) is important for many results in calculus, discrete mathematics, and combinatorics. #mathshorts #mathvideo #math #cal
From playlist Finite Sums
Self Similar Geometric Series: Sums of powers of 7 (and all integers larger than 3)
This is a short, animated visual proof demonstrating the finite geometric sum formula for any integer n with n greater than 3 (explicitly showing the cases n=7 and n=9 with k=3). This series (and its infinite analog when x less than 1) is important for many results in calculus, discrete ma
From playlist Finite Sums
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
Infinite Limits With Equal Exponents (Calculus)
#Calculus #Math #Engineering #tiktok #NicholasGKK #shorts
From playlist Calculus
This video is about compactness and some of its basic properties.
From playlist Basics: Topology
Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
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
Math 101 Introduction to Analysis 112515: Introduction to Compact Sets
Introduction to Compact Sets: open covers; examples of finite and infinite open covers; definition of compactness; example of a non-compact set; compact implies closed; closed subset of compact set is compact; continuous image of a compact set is compact
From playlist Course 6: Introduction to Analysis
Pseudo-finite dimensions, modularity, and generalisations (...) - M. Bays - Workshop 1 - CEB T1 2018
Martin Bays (Münster) / 29.01.2018 Pseudo-finite dimensions, modularity, and generalisations of Elekes–Szab´o. Given a system of polynomial equations in m complex variables with solution set V of dimension d, if we take finite subsets Xi of C each of size N, then the number of solutions
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Emily Stark: Action rigidity for free products of hyperbolic manifold groups
CIRM VIRTUAL EVENT Recorded during the meeting"Virtual Geometric Group Theory conference " the May 22, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Virtual Conference
Ian Agol University of California, Berkeley; Distinguished Visiting Professor, School of Mathematics October 12, 2015 http://www.math.ias.edu/calendar/event/89554/1444672800/1444676400 I'll review recent progress on properties of 3-manifold groups, especially following from geometric pr
From playlist Members Seminar
Tame topology and Hodge theory (Lecture 1) by Bruno Klingler
Discussion Meeting Complex Algebraic Geometry ORGANIZERS: Indranil Biswas, Mahan Mj and A. J. Parameswaran DATE:01 October 2018 to 06 October 2018 VENUE: Madhava Lecture Hall, ICTS, Bangalore The discussion meeting on Complex Algebraic Geometry will be centered around the "Infosys-ICT
From playlist Complex Algebraic Geometry 2018
Cornelia Drutu - Connections between hyperbolic geometry and median geometry
The interest of median geometry comes from its connections with property (T) and a-T-menability and, in its discrete version, with the solution to the virtual Haken conjecture. In this talk I shall explain how groups endowed with various forms of hyperbolic geometry, from lattices in rank
From playlist Geometry in non-positive curvature and Kähler groups
Bruno Klingler - 1/4 Tame Geometry and Hodge Theory
Sorry for the re upload due to a technical problem on the previous version Hodge theory, as developed by Deligne and Griffiths, is the main tool for analyzing the geometry and arithmetic of complex algebraic varieties. It is an essential fact that at heart, Hodge theory is NOT algebraic.
From playlist Bruno Klingler - Tame Geometry and Hodge Theory
Grothendieck Pairs and Profinite Rigidity - Martin Bridson
Arithmetic Groups Topic: Grothendieck Pairs and Profinite Rigidity Speaker: Martin Bridson Affiliation: Oxford University Date: January 26, 2022 If a monomorphism of abstract groups H↪G induces an isomorphism of profinite completions, then (G,H) is called a Grothendieck pair, recalling t
From playlist Mathematics
Hodge Theory, between Algebraicity and Transcendence (Lecture 3) by Bruno Klingler
DISCUSSION MEETING TOPICS IN HODGE THEORY (HYBRID) ORGANIZERS: Indranil Biswas (TIFR, Mumbai, India) and Mahan Mj (TIFR, Mumbai, India) DATE: 20 February 2023 to 25 February 2023 VENUE: Ramanujan Lecture Hall and Online This is a followup discussion meeting on complex and algebraic ge
From playlist Topics in Hodge Theory - 2023
Jessica Purcell - Lecture 3 - Knots in infinite volume 3-manifolds
Jessica Purcell, Monash University Title: Knots in infinite volume 3-manifolds Classically, knots have been studied in the 3-sphere. However, many examples of knots arising in applications lie in broader classes of 3-manifolds. These include virtual knots, which lie within thickened surfa
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Reconstruction in Algebraic Geometry - Peter Haine
Spring Opportunities Workshop 2023 Topic: Reconstruction in Algebraic Geometry Speaker: Peter Haine Affiliation: IAS Date: January 12, 2023 A classical theorem of Neukirch and Uchida says that number fields are completely determined by their absolute Galois groups. One might wonder abou
From playlist Spring Opportunities Workshop 2023
Geometric Sequences and their Sums [Discrete Math Class]
This video is not like my normal uploads. This is a supplemental video from one of my courses that I made in case students had to quarantine. In this video, we define and investigate geometric sequences. We see how to find both recursive formulas and closed formulas for arithmetic sequence
From playlist Finite Sums