In mathematics, the gradient conjecture, due to René Thom (1989), was proved in 2000 by three Polish mathematicians, Krzysztof Kurdyka (University of Savoie, France), Tadeusz Mostowski (Warsaw University, Poland) and Adam Parusiński (University of Angers, France). The conjecture states that given a real-valued analytic function f defined on Rn and a trajectory x(t) of the gradient vector field of f having a limit point x0 ∈ Rn, where f has an isolated critical point at x0, there exists a limit (in the projective space PRn-1) for the secant lines from x(t) to x0, as t tends to zero. The proof depends on a theorem due to Stanisław Łojasiewicz. (Wikipedia).
Download the free PDF http://tinyurl.com/EngMathYT A basic tutorial on the gradient field of a function. We show how to compute the gradient; its geometric significance; and how it is used when computing the directional derivative. The gradient is a basic property of vector calculus. NOT
From playlist Engineering Mathematics
Example on gradient identities for functions of two variables.
From playlist Engineering Mathematics
Gradient theorem | Lecture 43 | Vector Calculus for Engineers
Derivation of the gradient theorem (or fundamental theorem of calculus for line integrals, or fundamental theorem of line integrals). The gradient theorem shows that the line integral of the gradient of a function is path independent, and only depends on the starting and ending points. J
From playlist Vector Calculus for Engineers
Introduction to the Gradient Theory and Formulas
Introduction to the Gradient Theory and Formulas If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Calculus 3
What Does the Gradient Vector Mean Intuitively?
What Does the Gradient Vector Mean Intuitively? If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Calculus 3
This video explains what information the gradient provides about a given function. http://mathispower4u.wordpress.com/
From playlist Functions of Several Variables - Calculus
What is Gradient, and Gradient Given Two Points
"Find the gradient of a line given two points."
From playlist Algebra: Straight Line Graphs
The gradient captures all the partial derivative information of a scalar-valued multivariable function.
From playlist Multivariable calculus
Mathematics for Machine Learning: What is Gradient?
In this video, we talk about gradients in machine learning, data science, and optimization. The generalization of the derivative to functions of several variables is the gradient. This tutorial is designed to be easy to understand with basic knowledge of Calculus 1. Finding gradients is im
From playlist Mathematics for Machine Learning - Dr. Data Science Series
Lillian Ratliff - Learning via Conjectural Variations - IPAM at UCLA
Recorded 15 February 2022. Lillian Ratliff of the University of Washington presents "Learning via Conjectural Variations" at IPAM's Mathematics of Collective Intelligence Workshop. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/mathematics-of-intelligences/?tab=schedule
From playlist Workshop: Mathematics of Collective Intelligence - Feb. 15 - 19, 2022.
2020.07.02 Ron Peled - Fluctuations of random surfaces and concentration inequalities
Random surfaces in statistical physics are commonly modeled by a real-valued function on a d-dimensional lattice, whose probability density penalizes nearest-neighbor fluctuations according to an interaction potential U. The case U(x)=x^2 is the well-studied lattice Gaussian free field, wh
From playlist One World Probability Seminar
Morrey's conjecture - László Székelyhidi
Members’ Colloquium Topic: Morrey's conjecture Speaker: László Székelyhidi Affiliation: University of Leipzig; Distinguished Visiting Professor, School of Mathematics Date: February 14, 2022 Morrey’s conjecture arose from a rather innocent looking question in 1952: is there a local condi
From playlist Mathematics
Marco Cirant: "Maximal regularity for stationary Hamilton-Jacobi equations"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop III: Mean Field Games and Applications "Maximal regularity for stationary Hamilton-Jacobi equations" Marco Cirant - Università di Padova Abstract: The study of gradient regularity of solutions to Hamilton-Jacobi equations is a crucial s
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Lagrangian Floer theory by Sushmita Venugopalan
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions (vt)
We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. Under a natural non-collapsing condition, this limiting flow is smooth on the complement of a sing
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions
We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. Under a natural non-collapsing condition, this limiting flow is smooth on the complement of a sing
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Talagrand's convolution conjecture and geometry via coupling - James Lee
James Lee University of Washington November 10, 2014 This is joint work with Ronen Eldan. More videos on http://video.ias.edu
From playlist Mathematics
Arnold Conjecture Over Integers - Shaoyun Bai
Topic: Arnold Conjecture Over Integers Speaker: Shaoyun Bai Affiliation: Stony Brook University Date: January 20, 2023 We show that for any closed symlectic manifold, the number of 1-periodic orbits of any non-degenerate Hamiltonian is bounded from below by a version of total Betti number
From playlist Mathematics
Piotr BIZON - Blowup for supercritical equivariant wave maps
We consider equivariant wave maps from R^{d+1} into S^d for d\geq 3. Using mixed analytic and numerical tools we describe the dynamics of generic blowup and the threshold for blowup. We hope that our plausibility arguments will stimulate rigorous studies of this
From playlist Trimestre "Ondes Non Linéaires" - May Conference
11_7_1 Potential Function of a Vector Field Part 1
The gradient of a function is a vector. n-Dimensional space can be filled up with countless vectors as values as inserted into a gradient function. This is then referred to as a vector field. Some vector fields have potential functions. In this video we start to look at how to calculat
From playlist Advanced Calculus / Multivariable Calculus