In algebraic geometry, a morphism between schemes is said to be smooth if * (i) it is locally of finite presentation * (ii) it is flat, and * (iii) for every geometric point the fiber is regular. (iii) means that each geometric fiber of f is a nonsingular variety (if it is separated). Thus, intuitively speaking, a smooth morphism gives a flat family of nonsingular varieties. If S is the spectrum of an algebraically closed field and f is of finite type, then one recovers the definition of a nonsingular variety. (Wikipedia).
This came as a surprise. Although it looks like an example with smooth time-stepping, it is not. It is with original, simple time-stepping. I'm not exactly sure what this means. Maybe my smooth time-stepping method is superfluous.
From playlist SmoothLife
Smooth Transition Function in One Dimension | Smooth Transition Function Part 1
#SoME2 This video gives a detailed construction of transition function for various levels of smoothness. Sketch of proofs for 4 theorems regarding smoothness: https://kaba.hilvi.org/homepage/blog/differentiable.htm Faà di Bruno's formula: https://en.wikipedia.org/wiki/Fa%C3%A0_di_Bruno%2
From playlist Summer of Math Exposition 2 videos
algebraic geometry 25 Morphisms of varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of a morphism of varieties and compares algebraic varieties with other types of locally ringed spaces.
From playlist Algebraic geometry I: Varieties
David Ayala: Factorization homology (part 2)
The lecture was held within the framework of the Hausdorff Trimester Program: Homotopy theory, manifolds, and field theories and Introductory School (7.5.2015)
From playlist HIM Lectures 2015
Helmut Hofer Institute for Advanced Study April 5, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Michael Temkin - Logarithmic geometry and resolution of singularities
Correction: The affiliation of Lei Fu is Tsinghua University. I will tell about recent developments in resolution of singularities achieved in a series of works with Abramovich and Wlodarczyk – resolution of log varieties, resolution of morphisms and a no-history (or dream) algorithm for
From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021
Stefan Kebekus The geometry of singularities in the Minimal Model Program and applications to singul
This talk surveys recent results on the singularities of the Minimal Model Program and discusses applications to the study of varieties with trivial canonical class. The first part of the talk discusses an infinitesimal version of the classical decomposition theorem for varieties with vani
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Resolution of singularities of complex algebraic varieties – D. Abramovich – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.13 Resolution of singularities of complex algebraic varieties and their families Dan Abramovich Abstract: We discuss Hironaka’s theorem on resolution of singularities in charactetistic 0 as well as more recent progress, both on simplifying
From playlist Algebraic & Complex Geometry
Shane Kelly: Motives with modulus over a general base
27 September 2021 This is joint work with Hiroyasu Miyazaki. Motives with modulus, as developed by Kahn, Miyazaki, Saito, Yamazaki is an extension of Voevodsky's theory of motives with the aim of capturing non-A1-invariant phenomena that is inaccessible to Voevodsky's theory but still \mo
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Moduli Spaces of Principal 2-group Bundles and a Categorification of the Freed.. by Emily Cliff
Program Quantum Fields, Geometry and Representation Theory 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)