Geometric topology | 4-manifolds
In mathematics, the intersection form of an oriented compact 4-manifold is a special symmetric bilinear form on the 2nd (co)homology group of the 4-manifold. It reflects much of the topology of the 4-manifolds, including information on the existence of a smooth structure. (Wikipedia).
Manifolds 1.3 : More Examples (Animation Included)
In this video, I introduce the manifolds of product manifolds, tori/the torus, real vectorspaces, matrices, and linear map spaces. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5koj5
From playlist Manifolds
Multivariable Calculus | Interactions of lines in 3 dimensions.
We describe how two lines can interact in three dimensions. In addition, we give examples of intersecting, parallel, and skew lines. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Lines and Planes in Three Dimensions
Geometry - Ch. 4: Lines and Angles (3 of 37) What is a Transversal?
Visit http://ilectureonline.com for more math and science lectures! In this video I will define and explain the 4 angle relationships formed by transversals: alternate interior, alternative exterior, consecutive interior, corresponding angles. To donate: http://www.ilectureonline.com/don
From playlist GEOMETRY CH 4 LINES AND ANGLES
Jessica Purcell: Structure of hyperbolic manifolds - Lecture 1
Abstract: In these lectures, we will review what it means for a 3-manifold to have a hyperbolic structure, and give tools to show that a manifold is hyperbolic. We will also discuss how to decompose examples of 3-manifolds, such as knot complements, into simpler pieces. We give conditions
From playlist Topology
Jessica Purcell: Structure of hyperbolic manifolds - Lecture 3
Abstract: In these lectures, we will review what it means for a 3-manifold to have a hyperbolic structure, and give tools to show that a manifold is hyperbolic. We will also discuss how to decompose examples of 3-manifolds, such as knot complements, into simpler pieces. We give conditions
From playlist Topology
Jessica Purcell: Structure of hyperbolic manifolds - Lecture 2
Abstract: In these lectures, we will review what it means for a 3-manifold to have a hyperbolic structure, and give tools to show that a manifold is hyperbolic. We will also discuss how to decompose examples of 3-manifolds, such as knot complements, into simpler pieces. We give conditions
From playlist Topology
From playlist Intersection Theory
Calculus 3: Ch 2.2 Planes in 3-D Equation (13 of 22) How to Find the Line of Intersection - Planes
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will find the line of intersection of 2 planes given the general equation of the 2 planes. Next video in this series can be seen
From playlist CALCULUS 3 CH 2.2 PLANES IN 3-D
Intersection of circles and lines
Practice finding the intersection of a circle and a line
From playlist Geometry
Maggie Miller - The Price twist via trisections
June 20, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry The Price twist is a surgery operation on an RP^2 in a 4-manifold that may change the smooth structure of the 4-manifold. Akbulut showed that this ope
From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry I
Invariants of 4-manifolds - Tye Lidman
Short Talks by Postdoctoral Members Tye Lidman - September 24, 2015 http://www.math.ias.edu/calendar/event/88224/1443125700/1443126600 More videos on http://video.ias.edu
From playlist Short Talks by Postdoctoral Members
C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
In this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC manifold of dimension 4 (resp. 5) has vanishing π2 (resp. vanishing π2 and π3), then a finite co
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions (version temporaire)
In this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC manifold of dimension 4 (resp. 5) has vanishing π2 (resp. vanishing π2 and π3), then a finite co
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Symplectic fillings and star surgery - Laura Starkston
Laura Starkston University of Texas, Austin September 25, 2014 Although the existence of a symplectic filling is well-understood for many contact 3-manifolds, complete classifications of all symplectic fillings of a particular contact manifold are more rare. Relying on a recognition theor
From playlist Mathematics
Ana-Maria Brecan: Deformation theory of twistor spaces of K3 surfaces
Abstract: Twistor spaces of K3 surfaces are non-Kähler compact complex manifolds which play a fundamental role in the moduli theory of K3 surfaces. They come equipped with a holomorphic submersion to the complex projective line which under the period map corresponds to a twistor line in th
From playlist Algebraic and Complex Geometry
Machine- Learning the Landscape (Lecture 1) by Yang-Hui He
PROGRAM KAVLI ASIAN WINTER SCHOOL (KAWS) ON STRINGS, PARTICLES AND COSMOLOGY (ONLINE) ORGANIZERS Francesco Benini (SISSA, Italy), Bartek Czech (Tsinghua University, China), Dongmin Gang (Seoul National University, South Korea), Sungjay Lee (Korea Institute for Advanced Study, South Korea
From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology (ONLINE) - 2022
Developments in 4-manifold topology arising from a theorem of Donaldson's - John Morgan [2017]
slides for this talk: https://drive.google.com/file/d/1_wHviPab9klzwE4UkCOvVecyopxDsZA3/view?usp=sharing Name: John Morgan Event: Workshop: Geometry of Manifolds Event URL: view webpage Title: Developments in 4-manifold topology arising from a theorem of Donaldson's Date: 2017-10-23 @9:3
From playlist Mathematics
Homology Smale-Barden manifolds with K-contact and Sasakian structures by Aleksy Tralle
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Kenji Fukaya (Kyoto University). Plenary Lecture from the 1st PRIMA Congress, 2009. Plenary Lecture 3. Abstract: This is a survey of Lagrangian Floer homology which I developed together with Y.G.-Oh, Hiroshi Ohta, and Kaoru Ono. I will focus on its relation to (homological) mirror symmetr
From playlist PRIMA2009