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
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
For more cryptography, subscribe @JeffSuzukiPolymath
From playlist Elliptic Curves - Number Theory and Applications
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 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
Amit Acharya : An action functional for nonlinear dislocation dynamics
Dislocations are the physical defects whose motion and interaction are responsible for the plasticity of crystalline solids. The physics can be characterized by a system of nonlinear PDE which does not naturally emanate from a variational principle. We describe the development of a family
From playlist "SPP meets TP": Variational methods for complex phenomena in solids
Elliptic Curves - Lecture 15 - Introduction to the formal group of an elliptic curve
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
Richard Taylor "Reciprocity Laws" [2012]
Slides for this talk: https://drive.google.com/file/d/1cIDu5G8CTaEctU5qAKTYlEOIHztL1uzB/view?usp=sharing Richard Taylor "Reciprocity Laws" Abstract: Reciprocity laws provide a rule to count the number of solutions to a fixed polynomial equation, or system of polynomial equations, modu
From playlist Number Theory
Elliptic Curves - Lecture 8a - Weierstrass models, discriminant, and j-invariant
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
DDPS | Model reduction with adaptive enrichment for large scale PDE constrained optimization
Talk Abstract Projection based model order reduction has become a mature technique for simulation of large classes of parameterized systems. However, several challenges remain for problems where the solution manifold of the parameterized system cannot be well approximated by linear subspa
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
CTNT 2018 - "The Biggest Known Prime Number" by Keith Conrad
This is lecture on "The Biggest Known Prime Number", by Keith Conrad, 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 - Guest Lectures
Illegal Primes #MegaFavNumbers
Turns out I have several #MegaFavNumbers. Wikipedia article on illegal primes: https://en.wikipedia.org/wiki/Illegal_prime Phil Carmody's telling of the story: https://web.archive.org/web/20011212144451/http://fatphil.org/maths/illegal1.html The 1401 digit illegal prime: https://
From playlist MegaFavNumbers
Elliptic Curves - Lecture 22b - The maximal abelian extension of exponent m unramified outside S
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
The Biggest Known Prime Number - Keith Conrad [2018]
Slides for this talk: https://ctnt-summer.math.uconn.edu/wp-content/uploads/sites/1632/2018/05/mersennetalkCTNT.pdf May 29: Keith Conrad (UConn) Title: The Biggest Known Prime Number. Abstract: There are infinitely many primes, but at any moment there is a biggest known prime. Earlier t
From playlist Number Theory
Elliptic Curves - Lecture 19a - Elliptic curves over local fields (more on torsion points)
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
Andrew Sutherland: Computing the image of Galois representations attached to elliptic curves
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Number Theory
Igor Shparlinski: Group structures of elliptic curves #1
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Jean-Morlet Chair - Shparlinski/Kohel
Elliptic Curve Cryptography Tutorial - Understanding ECC through the Diffie-Hellman Key Exchange
Learn more advanced front-end and full-stack development at: https://www.fullstackacademy.com Elliptic Curve Cryptography (ECC) is a type of public key cryptography that relies on the math of both elliptic curves as well as number theory. This technique can be used to create smaller, fast
From playlist Elliptic Curves - Number Theory and Applications
Heegner Points 4 by Francesc Castella
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)