Yiannis Sakellaridis: Plancherel formula, intersection complexes, and local L-functions
In the theory of automorphic forms, L-functions (and their special values) are usually realized by various types of period integrals. It is now understood that the local L-factors associated to a period represent a Plancherel density for a homogeneous space. I will start by reviewing the c
From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
The Plancherel formula for L^2(GL_n(F)\GL_n(E)) and applications… - Raphael Beuzart-Plessis
Workshop on Representation Theory and Analysis on Locally Symmetric Spaces Topic: The Plancherel formula for L^2(GL_n(F)\GL_n(E)) and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups Speaker: Raphael Beuzart-Plessis Affiliation: CNRS Date: March 6, 2018 Fo
From playlist Mathematics
Completeness and Orthogonality
A discussion of the properties of Completeness and Orthogonality of special functions, such as Legendre Polynomials and Bessel functions.
From playlist Mathematical Physics II Uploads
Cauchy-Riemann Equations: Proving a Function is Nowhere Differentiable 1
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Using the Cauchy-Riemann Equations to prove that the function f(z) = conjugate(z) is nowhere differentiable. This is a straightforward application of the C.R. equations.
From playlist Complex Analysis
Proving the Function f(z) = 3x + y + i(3y - x) is Entire using the Cauchy Riemann Equations
In this video I prove that a function is entire using the Cauchy Riemann Equations. An entire function is one that is analytic on the entire complex plane. I hope this video helps someone out there!
From playlist Complex Analysis
Asymptotic invariants of locally symmetric spaces – Tsachik Gelander – ICM2018
Lie Theory and Generalizations Invited Lecture 7.4 Asymptotic invariants of locally symmetric spaces Tsachik Gelander Abstract: The complexity of a locally symmetric space M is controlled by its volume. This phenomena can be measured by studying the growth of topological, geometric, alge
From playlist Lie Theory and Generalizations
Alexander Bufetov: Determinantal point processes - Lecture 1
Abstract: Determinantal point processes arise in a wide range of problems in asymptotic combinatorics, representation theory and mathematical physics, especially the theory of random matrices. While our understanding of determinantal point processes has greatly advanced in the last 20 year
From playlist Probability and Statistics
Definition of spherical coordinates | Lecture 33 | Vector Calculus for Engineers
We define the relationship between Cartesian coordinates and spherical coordinates; the position vector in spherical coordinates; the volume element in spherical coordinates; the unit vectors; and how to differentiate the spherical coordinate unit vectors. Join me on Coursera: https://www
From playlist Vector Calculus for Engineers
Lec 9 | MIT 6.450 Principles of Digital Communications I, Fall 2006
Lecture 9: Discrete-time fourier transforms and sampling theorem View the complete course at: http://ocw.mit.edu/6-450F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.450 Principles of Digital Communications, I Fall 2006
Integral Transforms - Lecture 9: The Fourier Transform in Action. Oxford Maths 2nd Year Lecture
This short course from Sam Howison, all 9 lectures of which we are making available (this is lecture 9), introduces two vital ideas. First, we look at distributions (or generalised functions) and in particular the mathematical representation of a 'point mass' as the Dirac delta function.
From playlist Oxford Mathematics Student Lectures - Integral Transforms
Weil conjectures 5: Lefschetz trace formula
This talk explains the relation between the Lefschetz fixed point formula and the Weil conjectures. More precisely, the zeta function of a variety of a finite field can be written in terms of an action of the Frobenius group on the cohomology groups of the variety. The main problem is then
From playlist Algebraic geometry: extra topics
The Green - Tao Theorem (Lecture 3) by D. S. Ramana
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
How to find the position function given the acceleration function
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation
Parseval-Plancherel Identity | Normalization in Quantum Mechanics
In this video, we will investigate the Parseval-Plancherel identity, which is named after the French mathematician Marc-Antoine Parseval, and the Swiss mathematician Michel Plancherel. It states that the integral over the absolute square of a function does not change after a Fourier transf
From playlist Quantum Mechanics, Quantum Field Theory
Lec 11 | MIT 6.450 Principles of Digital Communications I, Fall 2006
Lecture 11: Signal space, projection theorem, and modulation View the complete course at: http://ocw.mit.edu/6-450F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.450 Principles of Digital Communications, I Fall 2006
Functional Analysis Lecture 07 2014 02 11 Riesz Interpolation Theorem, Part 2
Proof of theorem in case of general L^p functions. Using Riesz interpolation to extend Fourier transform. Rapidly decreasing functions; Schwartz class functions. Fourier transform of a Schwartz class function. Properties of Fourier transform (interaction with basic operations); Fourie
From playlist Course 9: Basic Functional and Harmonic Analysis
Jérémie Bouttier : Autour de la mesure de Plancherel sur les partitions d'entiers - Partie 1
Résumé : Le but de ce cours sera de présenter quelques techniques liées aux processus de Schur, dans le cadre le plus simple de la mesure de Plancherel sur les partitions d'entiers. La mesure de Plancherel est une mesure sur l'ensemble des partitions d'un entier n, où une partition donnée
From playlist Probability and Statistics
Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger
The other famous classical theorem about cyclic quadrilaterals is due to the great Greek astronomer and mathematician, Claudius Ptolemy. Adopting a rational point of view, we need to rethink this theorem to state it in a purely algebraic way, without resort to `distances' and the correspon
From playlist Math Foundations