Peter Scholze: On topological cyclic homology
The lecture was held within the framework of the Hausdorff Trimester Program : Workshop "K-theory in algebraic geometry and number theory" Abstract: Topological cyclic homology is an approximation to algebraic K-theory that has been very useful for computations in algebraic K-theory. Rece
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
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
Computing homology groups | Algebraic Topology | NJ Wildberger
The definition of the homology groups H_n(X) of a space X, say a simplicial complex, is quite abstract: we consider the complex of abelian groups generated by vertices, edges, 2-dim faces etc, then define boundary maps between them, then take the quotient of kernels mod boundaries at each
From playlist Algebraic Topology
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
Introduction to Homotopy Theory- Part 5- Transition to Abstract Homotopy Theory
Credits: nLab: https://ncatlab.org/nlab/show/Introdu... Animation library: https://github.com/3b1b/manim Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name: "Remember (Extended Mix)" • YouTube Track Link: https://bit.ly/31Ma5s0 • Spotify Track Link: https://spoti.fi/
From playlist Introduction to Homotopy Theory
Algebraic Topology - 11.3 - Homotopy Equivalence
We sketch why that the homotopy category is a category.
From playlist Algebraic Topology
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
Eugene Gorsky - Algebra and Geometry of Link Homology 2/5
Khovanov and Rozansky defined a link homology theory which categorifies the HOMFLY-PT polynomial. This homology is relatively easy to define, but notoriously hard to compute. I will discuss recent breakthroughs in understanding and computing Khovanov-Rozansky homology, focusing on connecti
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Chromatic homotopy theory - Irina Bobkova
Short talks by postdoctoral members Topic: Chromatic homotopy theory Speaker: Irina Bobkova Affiliation: Member, School of Mathematics Date: September 26, 2017
From playlist Mathematics
Lecture 3: Classical Hochschild Homology
In this video, we introduce classical Hochschild homology and discuss the HKR theorem. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-muenster.de/IVV5WS/Web
From playlist Topological Cyclic Homology
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
Teena Gerhardt - 1/3 Algebraic K-theory and Trace Methods
Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Jennifer Hom - Knot concordance in homology cobordisms
June 22, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry We consider the group of knots in homology spheres that bound homology balls, modulo smooth concordance in homology cobordisms. Answering a question o
From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry I
Homological algebra 3: Tor over rings
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We define Tor(A,B) for modules A,B over a ring, and comment that it generalizes homology of groups, homology of Lie algebras,
From playlist Commutative algebra
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
Weil conjectures 6: etale cohomology of a curve
We give an overview of how to calculate the etale cohomology of a nonsinguar projective curve over an algebraically closed field with coefficients Z/nZ with n invertible. We simply assume a lot of properties of etale cohomology without proving (or even defining) them.
From playlist Algebraic geometry: extra topics
Lecture 4: The Connes operator on HH
Correction: The formula we give for the Connes operator B is slightly wrong, there needs to be a '+' instead of a '-' in between the two summands. In this video, we discuss the Connes operator on Hochschild homology. Feel free to post comments and questions at our public forum at https:
From playlist Topological Cyclic Homology
Categorical non-properness in wrapped Floer theory - Sheel Ganatra
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Categorical non-properness in wrapped Floer theory Speaker: Sheel Ganatra Affiliation: University of Southern California Date: April 02, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
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
M. Pflaum: Localization in Hochschild homology and convolution algebras of circle actions
Talk by Shintaro Nishikawa in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on July 29, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)