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
Homotopy Group - (1)Dan Licata, (2)Guillaume Brunerie, (3)Peter Lumsdaine
(1)Carnegie Mellon Univ.; Member, School of Math, (2)School of Math., IAS, (3)Dalhousie Univ.; Member, School of Math April 11, 2013 In this general survey talk, we will describe an approach to doing homotopy theory within Univalent Foundations. Whereas classical homotopy theory may be des
From playlist Mathematics
Cylindrical contact homology as a well-defined homology? - Joanna Nelson
Joanna Nelson Institute for Advanced Study; Member, School of Mathematics February 7, 2014 In this talk I will explain how the heuristic arguments sketched in literature since 1999 fail to define a homology theory. These issues will be made clear with concrete examples and we will explore
From playlist Mathematics
Stable Homotopy Seminar, 2: Fiber and Cofiber Sequences
We review some unstable homotopy theory, especially the construction of fiber and cofiber sequences of spaces, and how they induce long exact sequences on homotopy and homology/cohomology. (There's a mistake pointed out by Jeff Carlson: when I take a CW-approximation at one point, I have
From playlist Stable Homotopy Seminar
Ling Zhou (1/21/22): Persistent homotopy groups of metric spaces
In this talk, I will quickly overview previous work on discrete homotopy groups by Plaut et al. and Barcelo et al., and work blending homotopy groups with persistence, including those by Frosini and Mulazzani, Letscher, Jardine, Blumberg and Lesnick, and by Bantan et al. By capturing both
From playlist Vietoris-Rips 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
ITHT: Part 12- Model Structure on Topological Spaces
Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#TheClassicalModelStructureOfTopologicalSpaces Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtub...
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
Invariant homotopy theory in the univalent foundations - Guillaume Brunerie
Topic: Invariant homotopy theory in the univalent foundations Speaker: Guillaume Brunerie, Member, School of Mathematics Time/Room: 4:00pm - 4:15pm/S-101 More videos on http://video.ias.edu
From playlist Mathematics
Mather-Thurston’s theory, non abelian Poincare duality and diffeomorphism groups - Sam Nariman
Workshop on the h-principle and beyond Topic: Mather-Thurston’s theory, non abelian Poincare duality and diffeomorphism groups Speaker: Sam Nariman Affiliation: Purdue University Date: November 1, 2021 Abstract: I will discuss a remarkable generalization of Mather’s theorem by Thurston
From playlist Mathematics
Extension by zero, compactly supported cohomology, beginning of proper base change
From playlist Étale cohomology and the Weil conjectures
Homological generalizations of trace - Dmitry Vaintrob
Topic: Homological generalizations of trace Speaker: Dmitry Vaintrob, Member, School of Mathematics Time/Room: 4:15pm - 4:30pm/S-101 More videos on http://video.ias.edu
From playlist Mathematics
Wiesława Nizioł - Duality for p-adic pro-étale cohomology of analytic curves
I will discuss duality theorems, both arithmetic and geometric, for p-adic pro-étale cohomology of rigid analytic curves. This is joint work with Pierre Colmez and Sally Gilles. Wiesława Nizioł (CNRS & Sorbonne Université)
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
The Spectral Diameter of a Liouville Domains and its Applications - Pierre-Alexandre Mailhot
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: The Spectral Diameter of a Liouville Domains and its Applications Speaker: Pierre-Alexandre Mailhot Affiliation: Université de Montréal Date: October 28, 2022 The spectral norm provides a lower bound to the
From playlist Mathematics
Ana Caraiani: Vanishing theorems for Shimura varieties at infinite level
Recording during the thematic meeting "Cohomology of Algebraic Varieties" the October 18, 2018 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisu
From playlist Algebraic and Complex Geometry
Perfect complexes, Lefschetz trace formula with torsion coefficients, intro to the main lemma
From playlist Étale cohomology and the Weil conjectures
Homological mirror symmetry and symplectic mapping class groups - Nicholas Sheridan
Members' Seminar Topic: Homological mirror symmetry and symplectic mapping class groups Speaker: Nicholas Sheridan Affiliation: Princeton University; Member, School of Mathematics For more videos, visit http://video.ias.edu
From playlist Mathematics
Proper base change continued, compactly supported cohomology, cohomology with supports, Gysin sequences and purity
From playlist Étale cohomology and the Weil conjectures
Proof of the MAIN LEMMA, cohomology of Lefschetz pencils
From playlist Étale cohomology and the Weil conjectures
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