Lecture 14: The Definition of TC
In this video, we finally give the definition of topological cyclic homology. In fact, we will give two definitions: the first is abstract in terms of a mapping spectrum spectrum in cyclotomic spectra and then we unfold this to a concrete definition on terms of negative topological cyclic
From playlist Topological Cyclic Homology
Algebraic Topology - 11.3 - Homotopy Equivalence
We sketch why that the homotopy category is a category.
From playlist Algebraic Topology
Stable Homotopy Seminar, 18: The Steenrod Algebra (Liam Keenan)
Liam defines the Steenrod algebra, as the endomorphisms of the Eilenberg-MacLane spectrum HF_p. This naturally acts on the mod p cohomology of any space (or spectrum), and we look at the example of the mod 2 cohomology of RP^infinity. He states some of its fundamental properties allowing u
From playlist Stable Homotopy Seminar
Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS
The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t
From playlist Introduction to Homotopy Theory
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Homological Algebra(Homo Alg) 4 by Graham Ellis
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Cohomology in Homotopy Type Theory - Eric Finster
Eric Finster Ecole Polytechnique Federal de Lausanne; Member, School of Mathematics March 6, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
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
Sergey Melikhov, Steklov Math Institute (Moscow) Title: Fine Shape Abstract: A shape theory is something which is supposed to agree with homotopy theory on polyhedra and to treat more general spaces by looking at their polyhedral approximations. Or if you prefer, it is something which is s
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Stable Homotopy Seminar, 21: Computing Homotopy Groups with the Adams Spectral Sequence (Zach Himes)
Zachary Himes constructs the May spectral sequence, a tool using a filtration of of the dual Steenrod algebra that calculates the E2 page of the Adams spectral sequence. May's original insight was that the associated graded of the dual Steenrod algebra is a primitively generated Hopf algeb
From playlist Stable Homotopy Seminar
Homotopy type theory: working invariantly in homotopy theory -Guillaume Brunerie
Short talks by postdoctoral members Topic: Homotopy type theory: working invariantly in homotopy theory Speaker: Guillaume Brunerie Affiliation: Member, School of Mathematics Date: September 26, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Jeremy Dubut: Natural homology computability and Eilenberg Steenrod axioms
The lecture was held within the framework of the Hausdorff Trimester Program : Applied and Computational Algebraic Topology
From playlist HIM Lectures: Special Program "Applied and Computational Algebraic Topology"
This lecture is part of an online course on the Zermelo Fraenkel axioms of set theory. This lecture gives an overview of the axioms, describes the von Neumann hierarchy, and sketches several approaches to interpreting the axioms (Platonism, von Neumann hierarchy, multiverse, formalism, pra
From playlist Zermelo Fraenkel axioms
Lecture 8: Bökstedt Periodicity
In this video, we give a proof of Bökstedts fundamental result showing that THH of F_p is polynomial in a degree 2 class. This will rely on unlocking its relation to the dual Steenrod algebra and the fundamental fact, that the latter is free as an E_2-Algebra. Feel free to post comments a
From playlist Topological Cyclic Homology
Introduction to Fiber Bundles part 1: Definitions
We give the definition of a fiber bundle with fiber F, trivializations and transition maps. This is a really basic stuff that we use a lot. Here are the topics this sets up: *Associated Bundles/Principal Bundles *Reductions of Structure Groups *Steenrod's Theorem *Torsor structure on arith
From playlist Fiber bundles
Anibal Medina, "Persistence Steenrod modules"
The talk is part of the Workshop Topology of Data in Rome (15-16/09/2022) https://www.mat.uniroma2.it/Eventi/2022/Topoldata/topoldata.php The event was organized in partnership with the Romads Center for Data Science https://www.mat.uniroma2.it/~rds/about.php The Workshop was hosted and
From playlist Workshop: Topology of Data in Rome
You Could Have Invented Homology, Part 1: Topology | Boarbarktree
The first video in my series "You Could Have Invented Homology" Become a patron: https://patreon.com/boarbarktree
From playlist You Could Have Invented Homology | Boarbarktree
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, ... 1
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Digression: Hochschild Homology of Schemes
We define and study Hochschild homology for schemes. This video is a slight digression from the rest of the lecture course and we assume familiarity with schemes. The exercise might be a bit tricky... Feel free to post comments and questions at our public forum at https://www.uni-muenste
From playlist Topological Cyclic Homology