Topology | Sheaf theory

Germ (mathematics)

In mathematics, the notion of a germ of an object in/on a topological space is an equivalence class of that object and others of the same kind that captures their shared local properties. In particular, the objects in question are mostly functions (or maps) and subsets. In specific implementations of this idea, the functions or subsets in question will have some property, such as being analytic or smooth, but in general this is not needed (the functions in question need not even be continuous); it is however necessary that the space on/in which the object is defined is a topological space, in order that the word local has some meaning. (Wikipedia).

Video thumbnail

Integers – Easy, Clear and Understandable Definition

TabletClass Math: https://tcmathacademy.com/ Math help with integers and real numbers. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes: https://ta

From playlist GED Prep Videos

Video thumbnail

Number theory Full Course [A to Z]

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio

From playlist Number Theory

Video thumbnail

Analyzing Sets of Data: Range, Mean, Median, and Mode

What does the word "average" mean to you? There are a lot ways we use that word, and even in math, it can imply a few different things. If we want to summarize a set of data in a meaningful way, we can talk about the mean, the median, or the mode, and one might be more useful than another

From playlist Mathematics (All Of It)

Video thumbnail

Finding Eigenvalues and Eigenvectors

In studying linear algebra, we will inevitably stumble upon the concept of eigenvalues and eigenvectors. These sound very exotic, but they are very important not just in math, but also physics. Let's learn what they are, and how to find them! Script by Howard Whittle Watch the whole Math

From playlist Mathematics (All Of It)

Video thumbnail

Theory of numbers: Gauss's lemma

This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di

From playlist Theory of numbers

Video thumbnail

Geometry: Ch 5 - Proofs in Geometry (2 of 58) Definitions

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and give examples of definitions. Next video in this series can be seen at: https://youtu.be/-Pmkhgec704

From playlist GEOMETRY 5 - PROOFS IN GEOMETRY

Video thumbnail

Quantum Mechanics -- a Primer for Mathematicians

Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w

From playlist Mathematics

Video thumbnail

Walter Neumann: Lipschitz embedding of complex surfaces

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

Video thumbnail

Volodymyr Nekrashevych: Contracting self-similar groups and conformal dimension

HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 20, 2021 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 Dynamical Systems and Ordinary Differential Equations

Video thumbnail

Logic: The Structure of Reason

As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be

From playlist Logic & Philosophy of Mathematics

Video thumbnail

Connor McCranie and Markus Pflaum (2/25/20): Catastrophe theory

Title: Catastrophe theory Abstract: We given an introduction to catastrophe theory by René Thom. After briefly defining what degenerate and non-degnerate critical points of a smooth function are we introduce the algebra of germs of smooth real-valued functions and describe singular germs

From playlist DELTA (Descriptors of Energy Landscape by Topological Analysis), Webinar 2020

Video thumbnail

Teach Astronomy - Cosmology

http://www.teachastronomy.com/ Cosmology is the study of the universe, its history, and everything in it. It comes from the Greek root of the word cosmos for order and harmony which reflected the Greek belief that the universe was a harmonious entity where everything worked in concert to

From playlist 22. The Big Bang, Inflation, and General Cosmology

Video thumbnail

Alex Wilkie: On complex continuations of functions definable in ℝan,exp with a diophantine [...]

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 Logic and Foundations

Video thumbnail

Jean Écalle - Resurgence’s two Main Types and Their Signature Complications...

Resurgence’s two Main Types and Their Signature Complications: Tessellation, Isography, Autarchy Quite specific challenges attend the move from equational resurgence (i.e. resurgence in a singular variable –the main type in frequency and importance) to coequational re

From playlist Resurgence in Mathematics and Physics

Video thumbnail

13. Contagionism versus Anticontagionsim

Epidemics in Western Society Since 1600 (HIST 234) The debate between contagionists and anticontagionists over the transmission of infectious diseases played a major role in nineteenth-century medical discourse. On the one side were those who believed that diseases could be spread by in

From playlist Epidemics in Western Society Since 1600 with Frank Snowden

Video thumbnail

2020.06.04 Alison Etheridge - Branching Brownian motion, mean curvature flow and hybrid zones

Hybrid zones are narrow regions in which two genetically distinct populations come together and interbreed, resulting in hybrids. They may be maintained by an abrupt change in the environment or because of natural selection against the hybrids, in which case the location of the zone can ch

From playlist One World Probability Seminar

Video thumbnail

Aurélien Tellier: Plant ecology influences population genetics: the role of seed banks in [...]

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 SPECIAL 7th European congress of Mathematics Berlin 2016.

Video thumbnail

Universality of Resurgence in Quantization Theories - 13 June 2018

http://crm.sns.it/event/433 Universality of Resurgence in Quantization Theories Recent mathematical progress in the modern theory of resurgent asymptotic analysis (using trans-series and alien calculus) has recently begun to be applied systematically to many current problems of interest,

From playlist Centro di Ricerca Matematica Ennio De Giorgi

Video thumbnail

Steven Kleiman - "Equisingularity of germs of isolated singularities"

Steven Kleiman delivers a research lecture at the Worldwide Center of Mathematics.

From playlist Center of Math Research: the Worldwide Lecture Seminar Series

Video thumbnail

The Bridge Between Math and Quantum Field Theory

Even in an incomplete state, quantum field theory is the most successful physical theory ever discovered. Nathan Seiberg, one of its leading architects, reveals where math and QFT converge. Read more at Quanta: https://www.quantamagazine.org/nathan-seiberg-on-how-math-might-reveal-quantum-

From playlist Inside the Mind of a Scientist

Related pages

Topological space | Almost ring | Algebraic structure | Rational function | Stalk (sheaf) | Vector space | Gluing axiom | Indicator function | Abuse of notation | Jet (mathematics) | Differentiable function | Continuous function | Topological vector space | Group (mathematics) | Map (mathematics) | Local property | Phase space | Ian R. Porteous | Weierstrass preparation theorem | Ordinal number | Asymptotic analysis | Neighbourhood (mathematics) | Riemann surface | Tangent vector | Lawvere theory | Equivalence class | Natural number | Catastrophe theory | Mathematics | Function (mathematics) | Set (mathematics) | Noetherian ring | Power series | Sheaf (mathematics) | Regular ring | Ring (mathematics) | Taylor series | Subset | Holomorphic function | Analytic continuation | Equivalence relation | Analytic function | Ascending chain condition on principal ideals | Hardy field | Local ring | Nicolas Bourbaki | Unique factorization domain | Abelian group | Singularity theory