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
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
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
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Trigonometry X: the Law of Cotangents (and another lovely relation involving cotangents!)
Boy, oh boy this is a longish one. I prove the Law of Cotangents using the incenter of the triangle, after motivating the path with another way one might seek to prove the Law of Sines using the circumcenter of the triangle. After that, I demonstrate an equally lovely relationship betwee
From playlist Trigonometry
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
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
Homotopy elements in the homotopy group π₂(S²) ≅ ℤ. Roman Gassmann and Tabea Méndez suggested some improvements to my original ideas.
From playlist Algebraic Topology
Algebraic Topology - 11.3 - Homotopy Equivalence
We sketch why that the homotopy category is a category.
From playlist Algebraic Topology
Duality for Rabinowitz-Floer homology - Alex Oancea
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Duality for Rabinowitz-Floer homology Speaker: Alex Oancea Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche Date: May 27, 2020 For more video please visit http://video.ias.edu
From playlist PU/IAS Symplectic Geometry Seminar
Irving Dai - Homology cobordism and local equivalence between plumbed manifolds
June 22, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry Recently constructed by Hendricks and Manolescu, involutive Heegaard Floer homology provides several new tools for studying the three-dimensional homol
From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry I
Contact non-squeezing via selective symplectic homology - Igor Uljarević
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Contact non-squeezing via selective symplectic homology Speaker: Igor Uljarević Affiliation: University of Belgrade Date: October 14, 2022 I will introduce a new version of symplectic homology that resembles
From playlist Mathematics
Anthony Henderson: Hilbert Schemes Lecture 9
SMRI Seminar Series: 'Hilbert Schemes' Lecture 9 Correspondences in homology Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students intereste
From playlist SMRI Course: Hilbert Schemes
Homology cobordism and triangulations – Ciprian Manolescu – ICM2018
Geometry | Topology Invited Lecture 5.5 | 6.1 Homology cobordism and triangulations Ciprian Manolescu Abstract: The study of triangulations on manifolds is closely related to understanding the three-dimensional homology cobordism group. We review here what is known about this group, with
From playlist Geometry
Classification of n-component links with Khovanov homology of rank 2^n - Boyu Zhang
Symplectic Dynamics/Geometry Seminar Topic: Classification of n-component links with Khovanov homology of rank 2^n Speaker: Boyu Zhang Affiliation: Princeton University Date: February 24, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Introduction to Khovanov Homology by Jozef H. Przytycki
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
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
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
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
Poincare duality for loop spaces - Kai Cieliebak
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Poincare duality for loop spaces Speaker: Kai Cieliebak Affiliation: Augsburg University; Member, School of Mathematics Date: February 07, 2022
From playlist Mathematics