Lecture 5: Periodic and cyclic homology
In this video, we construct periodic and cyclic homology and compute examples. 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/WebHop/user
From playlist Topological Cyclic Homology
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
This is a short overview of the main content of our course on Topological Cyclic Homology. 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
From playlist Topological Cyclic Homology
Lecture 11: Negative Topological cyclic homology
Correction: In the definition of stable ∞-categories at the very beginning, we forgot the condition that C has a zero object, i.e. the initial and terminal objects agree via the canonical morphism between them. Sorry for the confusion! In this video we define negative topological cyclic h
From playlist Topological Cyclic Homology
In this video, we give an important motivation for studying Topological Cyclic Homology, so called "trace methods". 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://w
From playlist Topological Cyclic Homology
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"
Cyclic homology and S1S1-equivariant symplectic cohomology - Sheel Ganatra
Sheel Ganatra Stanford University November 21, 2014 In this talk, we study two natural circle actions in Floer theory, one on symplectic cohomology and one on the Hochschild homology of the Fukaya category. We show that the geometric open-closed string map between these two complexes is S
From playlist Mathematics
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
Cyclic Groups, Generators, and Cyclic Subgroups | Abstract Algebra
We introduce cyclic groups, generators of cyclic groups, and cyclic subgroups. We discuss an isomorphism from finite cyclic groups to the integers mod n, as well as an isomorphism from infinite cyclic groups to the integers. We establish a cyclic group of order n is isomorphic to Zn, and a
From playlist Abstract Algebra
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
Teena Gerhardt - 3/3 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
Masoud Khalkhali: Introduction to non commutative geometry 2
The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. 8.9.2014
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Henri Moscovici. Differentiable Characters and Hopf Cyclic Cohomology
Talk by Henri Moscovici in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/... on October 20, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Jonathan Belcher: Bridge cohomology-a generalization of Hochschild and cyclic cohomologies
Talk by Jonathan Belcher in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-... on August 12, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Teena Gerhardt - 2/3 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
Sheagan John: Secondary higher invariants, and cyclic cohomology for groups of polynomial growth
Talk by Sheagan John in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on December 2, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Michael Mandell: The strong Kunneth theorem for topological periodic cyclic homology
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Hesselholt has recently been advertising "topological periodic cyclic homology" (TP) as potentially filling some of the same roles for finite primes as periodic cyclic homology plays
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Lecture 10: The circle action on THH
In this video we construct an action of the circle group S^1 = U(1) on the spectrum THH(R). We will see how this is the homotopical generalisation of the Connes operator. The key tool will be Connes' cyclic category. The speaker is of course Achim Krause and not Thomas Nikolaus as falsely
From playlist Topological Cyclic Homology
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