Modular Forms | Modular Forms; Section 1 2
We define modular forms, and borrow an idea from representation theory to construct some examples. My Twitter: https://twitter.com/KristapsBalodi3 Fourier Theory (0:00) Definition of Modular Forms (8:02) In Search of Modularity (11:38) The Eisenstein Series (18:25)
From playlist Modular Forms
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
ComplexMultiplication 1/3 - i/3
From playlist Complex Multiplication
This lecture is part of an online graduate course on modular forms. We introduce modular forms, and give several examples of how they were used to solve problems in apparently unrelated areas of mathematics. I will not be following any particular book, but if anyone wants a suggestion
From playlist Modular forms
Jon Keating: Random matrices, integrability, and number theory - Lecture 3
Abstract: I will give an overview of connections between Random Matrix Theory and Number Theory, in particular connections with the theory of the Riemann zeta-function and zeta functions defined in function fields. I will then discuss recent developments in which integrability plays an imp
From playlist Analysis and its Applications
23C3: How to implement bignum arithmetic
Speaker: Felix von Leitner A short look at my pet project implementation Assembly language skills are a bonus, but not strictly required. This lecture will explain how software like OpenSSL and GnuPG do their arithmetic on 1024 bit numbers. This is not about how RSA works, or about how
From playlist 23C3: Who can you trust
Number Theory | Modular Inverses: Example
We give an example of calculating inverses modulo n using two separate strategies.
From playlist Modular Arithmetic and Linear Congruences
Discrete Math - 4.1.2 Modular Arithmetic
Introduction to modular arithmetic including several proofs of theorems along with some computation. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz
From playlist Discrete Math I (Entire Course)
Broadcasted live on Twitch -- Watch live at https://www.twitch.tv/simuleios
From playlist Misc
The Wreck of the S.S. Richard Montgomery
The History Guy remembers why we should not forget the wreck of one of the last Liberty Ships, the S.S. Richard Montgomery. The question of what to do about it, and its load of explosives, remains today. This episode was made for educational purposes. The events are portrayed within the c
From playlist US History
Jon Keating: Random matrices, integrability, and number theory - Lecture 2
Abstract: I will give an overview of connections between Random Matrix Theory and Number Theory, in particular connections with the theory of the Riemann zeta-function and zeta functions defined in function fields. I will then discuss recent developments in which integrability plays an imp
From playlist Analysis and its Applications
CTNT 2018 - "Elliptic curves over finite fields" (Lecture 4) by Erik Wallace
This is lecture 4 of a mini-course on "Elliptic curves over finite fields", taught by Erik Wallace, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2018 - "Elliptic Curves over Finite Fields" by Erik Wallace
Random Matrix Theory and Zeta Functions - Peter Sarnak
Random Matrix Theory and Zeta Functions - Peter Sarnak Peter Sarnak Institute for Advanced Study; Faculty, School of Mathematics February 4, 2014 We review some of the connections, established and expected between random matrix theory and Zeta functions. We also discuss briefly some recen
From playlist Mathematics
Peter Sarnak - Zeta and L-functions [ICM 1998]
ICM Berlin Videos 27.08.1998 Zeta and L-functions Peter Sarnak Princeton University, USA: Number Theory Thu 27-Aug-98 · 11:45-12:45 h Abstract: The theory of zeta and L-functions is at the center of a number of recent developments in number theory. We will review some of these developm
From playlist Number Theory
Geodesic Random Line Processes and the Roots of Quadratic Congruences by Jens Marklof
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
14B Complex Number Multiplication
The multiplication of scalar numbers.
From playlist Linear Algebra
Lattice Multiplication - Whole Number Multiplication
This video explains how to use the method of lattice multiplication to multiply whole numbers. Library: http://www.mathispower4u.com Search: http://www.mathispower4u.wordpress.com
From playlist Multiplication and Division of Whole Numbers
Kiran Kedlaya, The Sato-Tate conjecture and its generalizations
VaNTAGe seminar on March 24, 2020 License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
This lecture is part of an online graduate course on modular forms. We first show that the number of zeros of a (level 1 holomorphic) modular form in a fundamental domain is weight/12, and use this to show that the graded ring of modular forms is the ring of polynomials in E4 and E6. Fo
From playlist Modular forms