Legendre's conjecture

Legendre Polynomials

An introduction to Legendre Polynomials and the Legendre-Fourier Series.

From playlist Mathematical Physics II Uploads

Legendre Series Example

An example of expanding a function in a Legendre-Fourier Series.

From playlist Mathematical Physics II Uploads

Legendre Polynomial Series

In this video I derive three series representations for Legendre Polynomials. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F

From playlist Fourier

Intro to Legendre Polynomials

In this video I briefly introduce Legendre Polynomials via the Rodrigues formula. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F

From playlist Fourier

Theory of numbers: Jacobi symbol

This lecture is part of an online undergraduate course on the theory of numbers. We define the Jacobi symbol as an extension of the Legendre symbol, and show how to use it to calculate the Legendre symbol fast. We also briefly mention the Kronecker symbol. For the other lectures in t

From playlist Theory of numbers

Viviani's Theorem: "Proof" Without Words

Link: https://www.geogebra.org/m/BXUrfwxj

From playlist Geometry: Challenge Problems

Legendre's Formula and prove that the product of n consecutive integers is divisible by n factorial

We prove a common fact in number theory: the product of n consecutive integers is divisible by n factorial Reference: 1. p-adic valuation https://en.wikipedia.org/wiki/P-adic_valuation 2. Legendre Formula for p-adic valuation for n factorial: https://en.wikipedia.org/wiki/Legendre%27s_f

From playlist Elementary Number Theory

Theory of numbers: Gauss's lemma

This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di

From playlist Theory of numbers

Recent developments in knot contact homology - Lenny Ng

Princeton/IAS Symplectic Geometry Seminar Topic: Recent developments in knot contact homology Speaker: Lenny Ng, Duke University Date: December 11, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Twisted generating functions and the nearby Lagrangian conjecture - Sylvain Courte

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Twisted generating functions and the nearby Lagrangian conjecture Speaker: Sylvain Courte Affiliation: Université Grenoble Alpes Date: February 26, 2021 For more video please visit http://video.ias.edu Courte-2021-02

From playlist Mathematics

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar 5/27/22

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Three 20-minute research talks Speaker: Daniel Rudolf (Ruhr-Universität Bochum): Viterbo‘s conjecture for Lagrangian products in ℝ4 We show that Viterbo‘s conjecture (for the EHZ-capacity) for convex Lagrangian pro

From playlist Mathematics

"How to Verify the Riemann Hypothesis for the First 1,000 Zeta Zeros" by Ghaith Hiary

An overview of algorithms and methods that mathematicians in the 19th century and the first half of the 20th century used to verify the Riemann hypothesis. The resulting numerical computations, which used hand calculations and mechanical calculators, include those by Gram, Lindelöf, Backlu

From playlist Number Theory Research Unit at CAMS - AUB

[ANT11] Quadratic Gauss sums

Last video, we used the fact that √2 = ζ + ζ⁻¹, for ζ an 8th root of unity, to tell us about the decomposition of rational primes in Z[√2]. In this video, we see that it is also possible to write √q as a sum of roots of unity for all *odd* primes q: in fact, we write down an explicit eleme

From playlist [ANT] An unorthodox introduction to algebraic number theory

What is the Riemann Hypothesis?

This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation

From playlist Mathematics

Estimating Reeb chords using microlocal sheaf theory - Wenyuan Li

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Estimating Reeb chords using microlocal sheaf theory SpeakerL: Wenyuan Li Affiliation: Northwestern Date: December 17, 2021 We show that, for closed Legendrians in 1-jet bundles, when there is a sheaf with s

From playlist Mathematics

Representations are sheaves' for Legendrian 2-weaves - Kevin Sackel

Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Representations are sheaves' for Legendrian 2-weaves Speaker: Kevin Sackel Affiliation: Stony Brook University Date: March 21, 2022 Given a trivalent plane graph embedded in the Euclidean plane (up to isotopy), Treumann an

From playlist Mathematics

C0 contact geometry of isotropic submanifolds - Maksim Stokić

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Three 20-minute research talks Topic: C0 contact geometry of isotropic submanifolds Speaker: Maksim Stokić Affiliation: Tel Aviv University Date: May 27, 2022  Homeomorphism is called contact if it can be written a

From playlist Mathematics

Augmentations, generating families and micro local sheaves by Michael G Sullivan

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

Introduction to number theory lecture 32. Calculation of the Legendre symbol

This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We use Gauss's lemma to find out when -2, 3, 5, are quadratic residues of a prime and give

From playlist Introduction to number theory (Berkeley Math 115)

Lars Martin Sektnan: Extremal Poincaré type metrics and stability of pairs on Hirzebruch surfaces

Abstract: In this talk I will discuss the existence of complete extremal metrics on the complement of simple normal crossings divisors in compact Kähler manifolds, and stability of pairs, in the toric case. Using constructions of Legendre and Apostolov-Calderbank-Gauduchon, we completely c

From playlist Analysis and its Applications