In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
Complex analysis: Elliptic functions
This lecture is part of an online undergraduate course on complex analysis. We start the study of elliptic (doubly periodic) functions by constructing some examples, and finding some conditions that their poles and zeros must satisfy. For the other lectures in the course see https://www
From playlist Complex analysis
Complex analysis: Classification of elliptic functions
This lecture is part of an online undergraduate course on complex analysis. We give 3 description of elliptic functions: as rational functions of P and its derivative, or in terms of their zeros and poles, or in terms of their singularities. We end by giving a brief description of the a
From playlist Complex analysis
Elliptic Curves - Lecture 6a - Ramification (continued)
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Elliptic curves: point at infinity in the projective plane
This video depicts point addition and doubling on elliptic curve in simple Weierstrass form in the projective plane depicted using stereographic projection where the point at infinity can actually be seen. Explanation is in the accompanying article https://trustica.cz/2018/04/05/elliptic-
From playlist Elliptic Curves - Number Theory and Applications
Elliptic Curves - Lecture 5a - Order of vanishing
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Elliptic Curves - Lecture 4a - Varieties, function fields, dimension
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Elliptic Curves - Lecture 8b - The (geometric) group law
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Complex Numbers for ODEs (1 of 4)
ODEs: We define and present basic properties of the complex numbers. This part includes addition, subtraction, scalar multiplication, complex conjugate and modulus.
From playlist Differential Equations
Elliptic Curves - Lecture 14b - Elliptic curves over the complex numbers
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
"From Diophantus to Bitcoin: Why Are Elliptic Curves Everywhere?" by Alvaro Lozano-Robledo
This talk was organized by the Number Theory Unit of the Center for Advanced Mathematical Sciences at the American University of Beirut, on November 1st, 2022. Abstract: Elliptic curves are ubiquitous in number theory, algebraic geometry, complex analysis, cryptography, physics, and beyo
From playlist Math Talks
The (Coarse) Moduli Space of (Complex) Elliptic Curves | The Geometry of SL(2,Z), Section 1.3
We discuss complex elliptic curves, and describe their moduli space. Richard Borcherd's videos: Riemann-Roch Introduction: https://www.youtube.com/watch?v=uRfbnJ2a-Bs&ab_channel=RichardE.BORCHERDS Genus 1 Curves: https://www.youtube.com/watch?v=NDy4J_noKi8&ab_channel=RichardE.BORCHERDS
From playlist The Geometry of SL(2,Z)
Introduction to Elliptic Curves 2 by Anupam Saikia
PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA
From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)
Happy Pi Day! A curious fact about Pi related to elliptic curves
This is an "extra" lecture on my grad course on elliptic curves about a curious fact about Pi that has an interesting explanation via the theory of elliptic curves.
From playlist An Introduction to the Arithmetic of Elliptic Curves
Motivic correlators and locally symmetric spaces IV - Alexander Goncharov
Locally Symmetric Spaces Seminar Topic: Motivic correlators and locally symmetric spaces IV Speaker: Alexander Goncharov Affiliation: Yale University; Member, School of Mathematics and Natural Sciences Date: December 5, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Introduction to Elliptic Curves 3 by Anupam Saikia
PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA
From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)
Introduction to elliptic curves and BSD Conjecture by Sujatha Ramadorai
12 December 2016 to 22 December 2016 VENUE Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution. An
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
CTNT 2020 - CM Points on Modular Curves: Volcanoes and Reality - Pete Clark
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Conference Videos
Elliptic Curves - Lecture 27b - Selmer and Sha (definitions)
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves