Homotopy theory | Surgery theory | Differential topology

Obstruction theory

In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants. In the original work of Stiefel and Whitney, characteristic classes were defined as obstructions to the existence of certain fields of linear independent vectors. Obstruction theory turns out to be an application of cohomology theory to the problem of constructing a cross-section of a bundle. (Wikipedia).

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Limit Theories and Higher Order Fourier Analysis - Balazs Szegedy

Balazs Szegedy University of Toronto; Member, School of Mathematics October 4, 2011 We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large comp

From playlist Mathematics

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Category Theory 1.2: What is a category?

What is a Category?

From playlist Category Theory

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Limit Theories and Higher Order Fourier Analysis - Balazs Szegedy

Balazs Szegedy University of Toronto; Member, School of Mathematics October 11, 2011 We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large com

From playlist Mathematics

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Limits and Limit Laws in Calculus

In introducing the concept of differentiation, we investigated the behavior of some parameter in the limit of something else approaching zero or infinity. This concept of limits is how calculus got started. As the field developed, new techniques arose such that we don't have to find limits

From playlist Calculus

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Calculus - The laws of limits

This video covers the laws of limits and how we use them to evaluate a limit. These laws are especially handy for continuous functions. More theorems about limits are introduced in later videos. For more videos visit http://www.mysecretmathtutor.com

From playlist Calculus

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Lower Bound on Complexity - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

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What is Reductionism?

There are two different types of reductionism. One is called methodological reductionism, the other one theory reductionism. Methodological reductionism is about the properties of the real world. It’s about taking things apart into smaller things and finding that the smaller things determ

From playlist Philosophy of Science

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08 Exercise problem

In this exercise problem we prove that the intersection of a set with the union of two other sets, is equal to the union of the intersection of the first and the second and the first and the third sets.

From playlist Abstract algebra

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Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 2/5

This course has 4 sections split over 5 lectures. The first section will be the longest, and hopefully useful for the other courses. - Sheaves, moduli and virtual cycles - Vafa-Witten invariants: stable and semistable cases - Techniques for calculation --- virtual degeneracy loci, cosecti

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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Category Theory: The Beginner’s Introduction (Lesson 1 Video 4)

Lesson 1 is concerned with defining the category of Abstract Sets and Arbitrary Mappings. We also define our first Limit and Co-Limit: The Terminal Object, and the Initial Object. Other topics discussed include Duality and the Opposite (or Mirror) Category. These videos will be discussed

From playlist Category Theory: The Beginner’s Introduction

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Gromov-Witten theory and gauge theory (Lecture 1) by Constantin Teleman

PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie

From playlist Vortex Moduli - 2023

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CTNT 2020 - Topology and Diophantine Equations - David Corwin

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Conference Videos

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The Mueller Report and Indictments. What Have We Learned? - Stanford Legal on Sirius XM Radio

The investigation into Russian interference into the 2016 U.S. presidential election led by Special Counsel Robert Mueller came to an end on March 22, with a 300+ page report and several high profiled indictments. In this live taping of the Stanford Legal podcast, Professor David Sklansky,

From playlist Stanford Legal podcast

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Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 5/5

This course has 4 sections split over 5 lectures. The first section will be the longest, and hopefully useful for the other courses. 1. Sheaves, moduli and virtual cycles 2. Vafa-Witten invariants: stable and semistable cases 3. Techniques for calculation --- virtual degeneracy loci, cose

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 3/5

The main topics will be the intersection theory of tautological classes on moduli space of curves, the enumeration of stable maps via Gromov-Witten theory, and the enumeration of sheaves via Donaldson-Thomas theory. I will cover a mix of classical and modern results. My goal will be, by th

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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Davesh Maulik - Stable Pairs and Gopakumar-Vafa Invariants 1/5

In the first part of the course, I will give an overview of Donaldson-Thomas theory for Calabi-Yau threefold geometries, and its cohomological refinement. In the second part, I will explain a conjectural ansatz (from joint work with Y. Toda) for defining Gopakumar-Vafa invariants via modul

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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Noncommutative Geometric Invariant Theory (Lecture 4) by Arvid Siqveland

PROGRAM :SCHOOL ON CLUSTER ALGEBRAS ORGANIZERS :Ashish Gupta and Ashish K Srivastava DATE :08 December 2018 to 22 December 2018 VENUE :Madhava Lecture Hall, ICTS Bangalore In 2000, S. Fomin and A. Zelevinsky introduced Cluster Algebras as abstractions of a combinatoro-algebra

From playlist School on Cluster Algebras 2018

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Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 2/5

The main topics will be the intersection theory of tautological classes on moduli space of curves, the enumeration of stable maps via Gromov-Witten theory, and the enumeration of sheaves via Donaldson-Thomas theory. I will cover a mix of classical and modern results. My goal will be, by th

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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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

Related pages

Topological manifold | Simplicial homology | Principal bundle | Differential structure | Postnikov system | Fiber bundle | Homotopy group | Invariant (mathematics) | Samuel Eilenberg | Hassler Whitney | Surgery theory | CW complex | Cohomology | Homotopy theory | Geometric topology | Characteristic class | N-skeleton | Poincaré duality | Mathematics | Diffeomorphism | Wall's finiteness obstruction | Section (fiber bundle) | N-sphere | Vector bundle | Mathematical theory | Normal invariant | Manifold | Fibration | Simplicial complex | Kirby–Siebenmann class | L-theory | Contractible space | Vector field | Homotopy fiber | Topological K-theory