Algebraic curves | Moduli theory
In algebraic geometry, a stable curve is an algebraic curve that is asymptotically stable in the sense of geometric invariant theory. This is equivalent to the condition that it is a complete connected curve whose only singularities are ordinary double points and whose automorphism group is finite. The condition that the automorphism group is finite can be replaced by the condition that it is not of arithmetic genus one and every non-singular rational component meets the other components in at least 3 points. A semi-stable curve is one satisfying similar conditions, except that the automorphism group is allowed to be reductive rather than finite (or equivalently its connected component may be a torus). Alternatively the condition that non-singular rational components meet the other components in at least three points is replaced by the condition that they meet in at least two points. Similarly a curve with a finite number of marked points is called stable if it is complete, connected, has only ordinary double points as singularities, and has finite automorphism group. For example, an elliptic curve (a non-singular genus 1 curve with 1 marked point) is stable. Over the complex numbers, a connected curve is stable if and only if, after removing all singular and marked points, the universal covers of all its components are isomorphic to the unit disk. (Wikipedia).
Stable Homotopy Seminar, 8: The Stable Model Category of Spectra
We discuss the enrichment of spectra over spaces, and the compatibility of this enrichment with the model structure. Then we define the stable model structure by adding extra cofibrations to the levelwise model category of spectra, and restricting the weak equivalences to those maps which
From playlist Stable Homotopy Seminar
Stable Homotopy Seminar, 7: Constructing Model Categories
A stroll through the recognition theorem for cofibrantly generated model categories, using it to construct (1) the Quillen/Serre model structure on topological spaces and (2) the levelwise model structure on spectra. The latter captures the idea that spectra are sequences of spaces, but no
From playlist Stable Homotopy Seminar
Stability Analysis, State Space - 3D visualization
Introduction to Stability and to State Space. Visualization of why real components of all eigenvalues must be negative for a system to be stable. My Patreon page is at https://www.patreon.com/EugeneK
From playlist Physics
Minimal Discriminants and Minimal Weiestrass Forms For Elliptic Curves
This goes over the basic invariants I'm going to need for Elliptic curves for Szpiro's Conjecture.
From playlist ABC Conjecture Introduction
Beginners Guide to Derivatives of Parametric Curves in Calculus - Chris Tisdell Live Stream
A beginner's guide to derivatives of parametric curves in calculus. Here we look at some basic examples..
From playlist Calculus for Beginners
In this video I take a look at the slope of a curve (that is not straight line).
From playlist Biomathematics
Fixed points and stability: one dimension
Shows how to determine the fixed points and their linear stability of a first-order nonlinear differential equation. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org
From playlist Differential Equations
#Cycloid: A curve traced by a point on a circle rolling in a straight line. (A preview of this Sunday's video.)
From playlist Miscellaneous
C67 The physics of simple harmonic motion
See how the graphs of simple harmonic motion changes with changes in mass, the spring constant and the values correlating to the initial conditions (amplitude)
From playlist Differential Equations
Richard Thomas - The Katz-Klemm-Vafa formula
Richard THOMAS (Imperial College London, UK)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
Recursive combinatorial aspects of compactified moduli spaces – Lucia Caporaso – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.3 Recursive combinatorial aspects of compactified moduli spaces Lucia Caporaso Abstract: In recent years an interesting connection has been established between some moduli spaces of algebro-geometric objects (e.g. algebraic stable curves)
From playlist Algebraic & Complex Geometry
Pierre Parent: Stable models for modular curves in prime level
Abstract: We describe stable models for modular curves associated with all maximal subgroups in prime level, including in particular the new case of non-split Cartan curves. Joint work with Bas Edixhoven. Recording during the meeting "Diophantine Geometry" the May 24, 2018 at the Centre
From playlist Algebraic and Complex Geometry
Rahul PANDHARIPANDE - Stable quotients and relations in the tautological ring
The topic concerns relations among the kappa classes in the tautological ring of the moduli space of genus g curves. After a discussion of classical constructions in Wick form, we derive an explicit set of relations obtained from the virtual geometry of the moduli space of stable quotients
From playlist École d’été 2011 - Modules de courbes et théorie de Gromov-Witten
A Semistable Model for the Tower of Modular Cures - Jared Weinstein
Jared Weinstein Institute for Advanced Study October 27, 2010 The usual Katz-Mazur model for the modular curve X(pn)X(pn) has horribly singular reduction. For large n there isn't any model of X(pn)X(pn) which has good reduction, but after extending the base one can at least find a semista
From playlist Mathematics
Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 4/5
The main topics will be the intersection theory of tautological classes on moduli space of curves, the enumeration of stable maps via Gromov-Witten theory, and the enumeration of sheaves via Donaldson-Thomas theory. I will cover a mix of classical and modern results. My goal will be, by th
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Perfectoid spaces (Lecture 5) by Kiran Kedlaya
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Joel Hass - Lecture 4 - Algorithms and complexity in the theory of knots and manifolds - 21/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Joel Hass (University of California at Davis, USA) Algorithms and complexity in the theory of knots and manifolds Abstract: These lectures will introduce algorithmic pro
From playlist Joel Hass - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
Finding rational curves by forgetful map - Runpu Zong
Runpu Zong Member, School of Mathematics October 1, 2014 More videos on http://video.ias.edu
From playlist Mathematics
Stability and Eigenvalues: What does it mean to be a "stable" eigenvalue?
This video clarifies what it means for a system of linear differential equations to be stable in terms of its eigenvalues. Specifically, we show that if all (potentially complex) eigenvalues have negative real part, then the system is stable. If even a single eigenvalue has positive real
From playlist Engineering Math: Differential Equations and Dynamical Systems
Davesh Maulik - Stable Pairs and Gopakumar-Vafa Invariants 5/5
In the first part of the course, I will give an overview of Donaldson-Thomas theory for Calabi-Yau threefold geometries, and its cohomological refinement. In the second part, I will explain a conjectural ansatz (from joint work with Y. Toda) for defining Gopakumar-Vafa invariants via modul
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory