Intersection theory | Duality theories | Generalized manifolds | Cohomology theories | Algebraic topology

Intersection homology

In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well-suited for the study of singular spaces, discovered by Mark Goresky and Robert MacPherson in the fall of 1974 and developed by them over the next few years. Intersection cohomology was used to prove the Kazhdan–Lusztig conjectures and the Riemann–Hilbert correspondence. It is closely related to L2 cohomology. (Wikipedia).

Video thumbnail

What is an Intersection? (Set Theory)

What is the intersection of sets? This is another video on set theory in which we discuss the intersection of a set and another set, using the classic example of A intersect B. We do not quite go over a formal definition of intersection of a set in this video, but we come very close! Be su

From playlist Set Theory

Video thumbnail

What are the Angle Relationships for Parallel Lines and a Transversal

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

Video thumbnail

What are parallel lines and a transversal

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

Video thumbnail

When do vector functions intersect?

Free ebook http://tinyurl.com/EngMathYT Example discussing intersection of curves of two vector functions on one variable.

From playlist Engineering Mathematics

Video thumbnail

What is the Alternate Exterior Angle Converse Theorem

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

Video thumbnail

What is the Consecutive Interior Angle Converse Theorem

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

Video thumbnail

What is the Alternate Interior Angle Converse Theorem

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

Video thumbnail

How To Determine If Two Lines are Parallel to Apply Angle Theorems

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

Video thumbnail

Symplectic implosion - Lisa Jeffrey

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Symplectic implosion Speaker: Lisa Jeffrey Affiliation: University of Toronto Date: January 14, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Classification of n-component links with Khovanov homology of rank 2^n - Boyu Zhang

Symplectic Dynamics/Geometry Seminar Topic: Classification of n-component links with Khovanov homology of rank 2^n Speaker: Boyu Zhang Affiliation: Princeton University Date: February 24, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Anthony Henderson: Hilbert Schemes Lecture 9

SMRI Seminar Series: 'Hilbert Schemes' Lecture 9 Correspondences in homology Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students intereste

From playlist SMRI Course: Hilbert Schemes

Video thumbnail

Big fiber theorems and ideal-valued measures in symplectic topology - Yaniv Ganor

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Big fiber theorems and ideal-valued measures in symplectic topology Speaker: Yaniv Ganor Affiliation: Technion Date: October 22, 2021 In various areas of mathematics there exist "big fiber theorems", these a

From playlist Mathematics

Video thumbnail

Loop products, closed geodesics and self-intersections - Nancy Hingston

Workshop on Geometric Functionals: Analysis and Applications Topic: Loop products, closed geodesics and self-intersections Speaker: Nancy Hingston Affiliation: The College of New Jersey Date: March 6, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

String topology and the intersection product - Nathalie Wahl

Members’ Seminar Topic: String topology and the intersection product Speaker: Nathalie Wahl Affiliation: University of Copenhagen; Member, School of Mathematics Date: March 22, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Emilie Purvine (5/2/21): Homology of Graphs and Hypergraphs

Graphs and hypergraphs are typically studied from a combinatorial perspective. A graph being a collection of vertices and pairwise relationships (edges) among the vertices, and a hypergraph capturing multi-way or groupwise relationships (hyperedges) among the vertices. But both of these ob

From playlist TDA: Tutte Institute & Western University - 2021

Video thumbnail

Noncommutative resolutions and intersection cohomology for quotient singularities - Tudor Padurariu

Short Talks by Postdoctoral Members Topic: Noncommutative resolutions and intersection cohomology for quotient singularities Speaker: Tudor Padurariu Affiliation: Member, School of Mathematics Date: September 23, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Generation criteria for the Fukaya category - Mohammed Abouzaid

Generation criteria for the Fukaya category Mohammed Abouzaid MIT May 11, 2011

From playlist Mathematics

Video thumbnail

Primoz Skraba (2/28/18): An approximate nerve theorem

The Nerve Theorem is an implicit tool in most applications of topological data analysis relating the topological type of a suitably nice space with a combinatorial description of the space, namely, the nerve of a cover of that space. It is required that it is a good cover, that each elemen

From playlist AATRN 2018

Video thumbnail

What is the Corresponding Angle Converse Theorem

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

Related pages

Mixed Hodge structure | Topology | Floor and ceiling functions | Hausdorff space | Armand Borel | Simplex | Poincaré duality | Perverse sheaf | Intersection theory | Singular homology | Riemann–Hilbert correspondence | Connected space | Mathematics | Henri Poincaré | Orientability | Bilinear form | Compact space | Manifold | Constructible sheaf | Borel–Moore homology | Elliptic curve | General position | Simplicial complex | Verdier duality | Paracompact space | Resolution of singularities | Singularity theory