In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and since their introduction by Jean Leray , they have become important computational tools, particularly in algebraic topology, algebraic geometry and homological algebra. (Wikipedia).
Spectral Sequences 02: Spectral Sequence of a Filtered Complex
I like Ivan Mirovic's Course notes. http://people.math.umass.edu/~mirkovic/A.COURSE.notes/3.HomologicalAlgebra/HA/2.Spring06/C.pdf Also, Ravi Vakil's Foundations of Algebraic Geometry and the Stacks Project do this well as well.
From playlist Spectral Sequences
Spectral Sequences 01: How to read them.
How to read a spectral sequence.
From playlist Spectral Sequences
What is the definition of a geometric sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What is the alternate in sign sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What is the difference between finite and infinite sequences
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What is the definition of an arithmetic sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Evaluate the geometric sequence given two values
👉 Learn how to find the nth term of a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multiplying/div
From playlist Sequences
Stable Homotopy Seminar, 20: Computations with the Adams Spectral Sequence (Jacob Hegna)
Jacob Hegna walks us through some of the methods which have been used to compute the E_2 page of the Adams spectral sequence for the sphere, a.k.a. Ext_A(F_2, F_2), where A is the Steenrod algebra. The May spectral sequence works by filtering A and first computing Ext over the associated g
From playlist Stable Homotopy Seminar
Lecture 12: Topological periodic homology
In this video, we introduce another refinement of THH, the topological periodic homology TP. We see how it is an analogue of HP, how it is related to negative cyclic homology, and how to compute it for the field F_p. Feel free to post comments and questions at our public forum at https:/
From playlist Topological Cyclic Homology
Dianel Isaksen - 3/3 Motivic and Equivariant Stable Homotopy Groups
Notes: https://nextcloud.ihes.fr/index.php/s/4N5kk6MNT5DMqfp I will discuss a program for computing C2-equivariant, ℝ-motivic, ℂ-motivic, and classical stable homotopy groups, emphasizing the connections and relationships between the four homotopical contexts. The Adams spectral sequence
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Stable Homotopy Seminar, 16: The Whitehead, Hurewicz, Universal Coefficient, and Künneth Theorems
These are some generalizations of facts from unstable algebraic topology that are useful for calculating in the category of spectra. The Whitehead and Hurewicz theorems say that a map of connective spectra that's a homology isomorphism is a weak equivalence, and that the lowest nonzero hom
From playlist Stable Homotopy Seminar
Jeremy Hahn : Prismatic and syntomic cohomology of ring spectra
CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR
From playlist Topology
Álvaro Torras Casas (8/5/20): The Persistence Mayer-Vietoris spectral sequence
Title: The Persistence Mayer Vietoris spectral sequence Abstract: In this talk, I will give a brief introduction to the persistent Mayer-Vietoris spectral sequence. The original motivation for studying this object comes from the need to parallelize persistent homology computations. The st
From playlist AATRN 2020
Stable Homotopy Seminar, 12: The Atiyah-Hirzebruch Spectral Sequence (Caleb Ji)
Caleb Ji gives us an overview of spectral sequences, focusing on the example of the Leray-Serre spectral sequence which is used to prove the equivalence of cellular and singular homology. He then defines the Atiyah-Hirzebruch spectral sequence, which is used to compute extraordinary cohomo
From playlist Stable Homotopy Seminar
Calculations in the stable homotopy categories - Hana Jia Kong
Short Talks by Postdoctoral Members Topic: Calculations in the stable homotopy categories Speaker: Hana Jia Kong Affiliation: Member, School of Mathematics Date: September 28, 2022
From playlist Mathematics
Stable Homotopy Seminar, 19: The Adams spectral sequence (D. Zack Garza)
This talk by D. Zack Garza is all about the Adams spectral sequence, which is a powerful tool for computing homotopy classes of maps of spectra in terms of their cohomology for some cohomology theory E. The spectral sequence looks like: Ext_{E^*}(E^*Y, E^*X) ⇒ (a completion of) [X, Y]. We'
From playlist Stable Homotopy Seminar
Determine if a sequence is geometric or not
👉 Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque
From playlist Sequences
Determine if a sequence is geometric or not
👉 Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque
From playlist Sequences
Mike Hill - Real and Hyperreal Equivariant and Motivic Computations
Foundational work of Hu—Kriz and Dugger showed that for Real spectra, we can often compute as easily as non-equivariantly. The general equivariant slice filtration was developed to show how this philosophy extends from 𝐶2-equivariant homotopy to larger cyclic 2-groups, and this has some fa
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory