Arithmetic problems of plane geometry | Diophantine equations | Triangle geometry
Similar to a Pythagorean triple, an Eisenstein triple (named after Gotthold Eisenstein) is a set of integers which are the lengths of the sides of a triangle where one of the angles is 60 or 120 degrees. The relation of such triangles to the Eisenstein integers is analogous to the relation of Pythagorean triples to the Gaussian integers. (Wikipedia).
Modular forms: Eisenstein series
This lecture is part of an online graduate course on modular forms. We give two ways of looking at modular forms: as functions of lattices in C, or as invariant forms. We use this to give two different ways of constructing Eisenstein series. For the other lectures in the course see http
From playlist Modular forms
A11 Eigenvalues with complex numbers
Eigenvalues which contain complex numbers.
From playlist A Second Course in Differential Equations
The method of determining eigenvalues as part of calculating the sets of solutions to a linear system of ordinary first-order differential equations.
From playlist A Second Course in Differential Equations
10A An Introduction to Eigenvalues and Eigenvectors
A short description of eigenvalues and eigenvectors.
From playlist Linear Algebra
IWASAWA: Lecture 4 - Christopher Skinner
Christopher Skinner Princeton University; Member, School of Mathemtics February 23, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (5 of 35) What is an Eigenvector?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and show (in general) what is and how to find an eigenvector. Next video in this series can be seen at: https://youtu.be/SGJHiuRb4_s
From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS
Modular forms: Fourier coefficients of Eisenstein series
This lecture is part of an online graduate course on modular forms. We calculate the Fourier coefficients of the Eisenstein series introduced in the previous lecture, and use them to construct the elliptic modular function. (Minor typo: in the definition of E10 I wrote 262 instead of 26
From playlist Modular forms
Linear Algebra - Lecture 33 - Eigenvectors and Eigenvalues
In this lecture, we define eigenvectors and eigenvalues of a square matrix. We also prove a couple of useful theorems related to these concepts.
From playlist Linear Algebra Lectures
Pythagoras twisted squares: Why did they not teach you any of this in school?
A video on the iconic twisted squares diagram that just about anybody who knows anything about mathematics has been familiar with since primary school. Surprisingly, there is a LOT more to this diagram than even expert mathematicians are aware of. And lots of this LOT is really really beau
From playlist Recent videos
Summation formulae and speculations on period integrals attached to triples... - Jayce Getz
Joint IAS/Princeton University Number Theory Seminar Topic: Summation formulae and speculations on period integrals attached to triples of automorphic representations Speaker: Jayce Getz Affiliation: Date: March 27, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Chao Li - 2/2 Geometric and Arithmetic Theta Correspondences
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. I will give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also know
From playlist 2022 Summer School on the Langlands program
With the eigenvalues for the system known, we move on the the eigenvectors that form part of the set of solutions.
From playlist A Second Course in Differential Equations
On triple product L functions - Jayce Robert Getz
Joint IAS/Princeton University Number Theory Seminar Topic: On triple product L functions Speaker: Jayce Robert Getz Affiliation: Duke University Date: May 7, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Eisenstein series, p-adic deformations, Galois representations, and the group G_2 - Sam Mundy
Joint IAS/Princeton University Number Theory Seminar Topic: Eisenstein series, p-adic deformations, Galois representations, and the group G_2 Speaker: Sam Mundy Affiliation: Columbia University Date: April 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Francis Brown - 4/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)
In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of
From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)
Standard L-functions and theta correspondence by Shunsuke Yamana
PROGRAM : ALGEBRAIC AND ANALYTIC ASPECTS OF AUTOMORPHIC FORMS ORGANIZERS : Anilatmaja Aryasomayajula, Venketasubramanian C G, Jurg Kramer, Dipendra Prasad, Anandavardhanan U. K. and Anna von Pippich DATE & TIME : 25 February 2019 to 07 March 2019 VENUE : Madhava Lecture Hall, ICTS Banga
From playlist Algebraic and Analytic Aspects of Automorphic Forms 2019
New developments in the theory of modular forms... - 7 November 2018
http://crm.sns.it/event/416/ New developments in the theory of modular forms over function fields The theory of modular forms goes back to the 19th century, and has since become one of the cornerstones of modern number theory. Historically, modular forms were first defined and studied ov
From playlist Centro di Ricerca Matematica Ennio De Giorgi
Eulerianity of Fourier coefficients of automorphic forms - Henrik Gustafsson
Joint IAS/Princeton University Number Theory Seminar Topic: Eulerianity of Fourier coefficients of automorphic forms Speaker: Henrik Gustafsson Affiliation: Member, School of Mathematics Date: April 30, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Periods of Quaternionic Shimura Varieties - Kartik Prasanna
Kartik Prasanna University of Michigan, Ann Arbor March 3, 2011 In the early 80's, Shimura made a precise conjecture relating Petersson inner products of arithmetic automorphic forms on quaternion algebras over totally real fields, up to algebraic factors. This conjecture (which is a conse
From playlist Mathematics
Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (18 of 35) Checking Eigenvectors
Visit http://ilectureonline.com for more math and science lectures! In this video I will show an interesting property of multiplying the original matrix by its eigenvector, the resultant vector will be a multiple of the eigenvector. Next video in this series can be seen at: https://youtu
From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS