Who Gives a Sheaf? Part 1: A First Example
We take a first look at (pre-)sheaves, as being inspired from first year calculus.
From playlist Who Gives a Sheaf?
Who Gives a Sheaf? Part 3: Mighty Morph'n Morphisms
In this video we discuss the definition of a morphism of sheaves.
From playlist Who Gives a Sheaf?
Spectrum of Hg Lamp / amazing science experiment
Identify the spectral lines of Hg lamp Enjoy the amazing colors! Music: https://www.bensound.com/
From playlist Optics
In this video, we introduce and discuss spectra (in the sense of homotopy theory). We explain how they generalise abelian groups. 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 informa
From playlist Higher Algebra
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In it we explain why the obvious definition of an epimorphism of sheaves is wrong, and construct the etale space of a presheaf as preparation for giving the c
From playlist Algebraic geometry II: Schemes
Who Gives a Sheaf? Part 2: A non-example
In this video we compare two pre-sheaves, one which is a sheaf, and one which is not.
From playlist Who Gives a Sheaf?
Sequential Spectra- PART 2: Preliminary Definitions
We cover one definition of sequential spectra, establish the smash tensoring and powering operations, as well as some adjunctions. Credits: nLab: https://ncatlab.org/nlab/show/Introdu... Animation library: https://github.com/3b1b/manim Music: ► Artist Attribution • Music By: "KaizanBlu"
From playlist Sequential Spectra
Marc Levine: The rational motivic sphere spectrum and motivic Serre finiteness
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.
Charles Weibel: K-theory of line bundles and smooth varieties
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. We give a K-theoretic criterion for a quasi-projective variety to be smooth, generalizing the proof of Vorst's conjecture for affine varieties. If L is a line bundle corresponding to
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
CDH methods in K-theory and Hochschild homology - Charles Weibel
Charles Weibel Rutgers University; Member, School of Mathematics November 11, 2013 This is intended to be a survey talk, accessible to a general mathematical audience. The cdh topology was created by Voevodsky to extend motivic cohomology from smooth varieties to singular varieties, assumi
From playlist Mathematics
Identify the spectral lines of Mercury light by a coarse diffraction grating
Enjoy! Music: https://www.bensound.com/royalty-free-music
From playlist Optics
Sequential Spectra- Part 4: Omega spectra
I decided to split up the nLab section "Omega spectra" into two parts. This one covers some initial intuition/motivation along with the definition. Credits: nLab: https://ncatlab.org/nlab/show/Introdu... Animation library: https://github.com/3b1b/manim Music: ► Artist Attribution • Mu
From playlist Sequential Spectra
From Cohomology to Derived Functors by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Connections between classical and motivic stable homotopy theory - Marc Levine
Marc Levine March 13, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu
From playlist Mathematics
Alexander Soibelman - Quantizations of Complex Lagrangian Fibrations, Normal Forms, and Spectra
Under certain conditions, it is possible to compute the spectrum of a polynomial differential operator via its Birkhoff normal form. In this talk, I will explain a geometric approach for obtaining the Birkhoff normal form of a quantized Hamiltonian using the variation of Hodge structure fo
From playlist Workshop on Quantum Geometry
Marc Levine: Refined enumerative geometry (Lecture 2)
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Lecture 2: Euler classes, Euler characteristics and Riemann-Hurwicz formulas The Euler class of a vector bundle is defined in the twisted Chow-Witt ring and gives rise to an Euler ch
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Duality in Algebraic Geometry by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Stable Homotopy Seminar, 14: The stable infinity-category of spectra
I give a brief introduction to infinity-categories, including their models as simplicially enriched categories and as quasi-categories, and some categorical constructions that also make sense for infinity-categories. I then describe what it means for an infinity-category to be stable and h
From playlist Stable Homotopy Seminar
Takeshi Saito - 1/3 On the characteristic cycle of an ℓ-adic sheaf
The analogy between the wild ramification of an ℓ-adic sheaf on a smooth scheme over a perfect field of characteristic 𝑝 greater than or equal 0 and the irregular singularity of a 𝒟 -module on a complex manifold suggests that the characteristic cycle of an ℓ-adic sheaf be defined as a cycl
From playlist Journées de géométrie arithmétique de l'IHÉS
Michael Groechenig - Complex K-theory of Dual Hitchin Systems
Let G and G’ be Langlands dual reductive groups (e.g. SL(n) and PGL(n)). According to a theorem by Donagi-Pantev, the generic fibres of the moduli spaces of G-Higgs bundles and G’-Higgs bundles are dual abelian varieties and are therefore derived-equivalent. It is an interesting open probl
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory