Maryna Viazovska (EPFL): Fourier interpolation
This lecture is about Fourier uniqueness and Fourier interpolation pairs. Suppose that we have two subsets X and Y of the Euclidean space. Can we reconstruct a function f from its restriction to the set X and the restriction of its Fourier transform to the set Y? We are interested in the p
From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"
The Vandermonde Matrix and Polynomial Interpolation
The Vandermonde matrix is a used in the calculation of interpolating polynomials but is more often encountered in the proof that such polynomial interpolates exist. It is also often encountered in the study of determinants since it has a really nice determinant formula. Chapters 0:00 - In
From playlist Interpolation
(PP 6.5) Affine property, Constructing Gaussians, and Sphering
Any affine transformation of a (multivariate) Gaussian random variable is (multivariate) Gaussian. How to construct any (multivariate) Gaussian using an affine transformation of standard normals. How to "sphere" a Gaussian, i.e. transform it into a vector of independent standard normals.
From playlist Probability Theory
A basic introduction to Lagrange Interpolation. Chapters 0:00 Introduction 01:07 Lagrange Polynomials 03:58 The Lagrange Interpolation formula 05:10 The Resulting Polynomials The product links below are Amazon affiliate links. If you buy certain products on Amazon soon after clicking th
From playlist Interpolation
Hermite interpolation. Numerical methods, chapter 2, additional video no 3. To be viewed after video Ch02n2. Wen Shen, Penn State University, 2018.
From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University
In this video I show you how to prove Cayley's theorem, which states that every group is isomorphic to a permutation group. This video is a bit long because I take the time to revisit all the concepts required in the proof. these include isomorphisms, injective, surjective, and bijective
From playlist Abstract algebra
Lagrange Interpolation Formula In this video, I present the extremely neat Lagrange Interpolation Formula, which gives a clean formula for a polynomial that goes through given points. And I do this purely using linear algebra techniques, which illustrates how powerful this subject actuall
From playlist Vector Spaces
Joe Neeman: Gaussian isoperimetry and related topics II
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
(PP 6.2) Multivariate Gaussian - examples and independence
Degenerate multivariate Gaussians. Some sketches of examples and non-examples of Gaussians. The components of a Gaussian are independent if and only if they are uncorrelated.
From playlist Probability Theory
The Runge Function, Polynomial Interpolation, and the Cauchy Residual Theorem
A tour of interpolation, starting with a simple example and ending with completely unexpected and beautiful convergence results. Skip to about 2:25 if you wish to avoid the gentle intro. Topics covered include: polynomial convergence examples, the Runge Function (not related to Runge-Kutta
From playlist Summer of Math Exposition Youtube Videos
Guido Kings: Motivic Eisenstein cohomology, p-adic interpolation and applications
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Guido Kings: Motivic Eisenstein cohomology, p-adic interpolation and applications Abstract: Motivic Eisenstein classes have been defined in various situations, for example for G =
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
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
Stephan Garcia - LatMath 2022 - IPAM's Latinx in the Mathematical Sciences Conference
Recorded 09 July 2022. Stephan Garcia presents at IPAM's Latinx in the Mathematical Sciences Conference. Learn more online at: http://www.ipam.ucla.edu/programs/special-events-and-conferences/latinx-in-the-mathematical-sciences-conference-2022/
From playlist LatMath 2022 - IPAM's Latinx in the Mathematical Sciences Conference
CMPSC/Math 451--Jan 28, 2015. Nested form. Error Theorem for polynomial interpolation. Wen Shen
Wen Shen, Penn State University. Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I
From playlist Numerical Computation spring 2015. Wen Shen. Penn State University.
p-adic Artin L-function over a CM-field by Tadashi Ochiai
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Maryna Viazovska - 2/6 Automorphic Forms and Optimization in Euclidean Space
Hadamard Lectures 2019 The goal of this lecture course, “Automorphic Forms and Optimization in Euclidean Space”, is to prove the universal optimality of the E8 and Leech lattices. This theorem is the main result of a recent preprint “Universal Optimality of the E8 and Leech Lattices and I
From playlist Hadamard Lectures 2019 - Maryna Viazovska - Automorphic Forms and Optimization in Euclidean Space
ch2 6: polynomial interpolation, existence and uniqueness Theorem. Wen Shen
Wen Shen, Penn State University. Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I
From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University
You might find that for certain groups, the commutative property hold. In this video we will assume the existence of such a group and prove a few properties that it may have, by way of some example problems.
From playlist Abstract algebra
The 3-point spectral Pick interpolation problem by Vikramjeet Singh Chandel
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019