Elliptic curve cryptography | Elliptic curves
In geometry, the Hessian curve is a plane curve similar to folium of Descartes. It is named after the German mathematician Otto Hesse.This curve was suggested for application in elliptic curve cryptography, because arithmetic in this curve representation is faster and needs less memory than arithmetic in standard Weierstrass form. (Wikipedia).
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
Minimal Discriminants and Minimal Weiestrass Forms For Elliptic Curves
This goes over the basic invariants I'm going to need for Elliptic curves for Szpiro's Conjecture.
From playlist ABC Conjecture Introduction
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 - 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
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 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
This talk is about the Riemann-Roch theorem for genus 3 curves. We show that any such curve is either hyperelliptic or a nonsingular plane quartic. We find the Weierstrass points and the holomorphic 1-forms and the canonical divisors of these curves. Finally we give a brief description of
From playlist Algebraic geometry: extra topics
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
Max Jensen: Convergent semi-Lagrangian methods for the Monge-Ampère equation on unstructured grids
The lecture was held within the framework of the Hausdorff Trimester Program Multiscale Problems: Workshop on Numerical Inverse and Stochastic Homogenization. (15.02.2017) In this presentation I will discuss a semi-Lagrangian discretisation of the Monge-Ampère operator on P1 finite elemen
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
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
Lecture 18: The Laplace Operator (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Wei Ho: Explicit models of genus one curves and related problems
CIRM HYBRID EVENT We discuss various explicit models of genus one curves, some classical and some a little less so, with an eye towards applications in number theory and arithmetic geometry. In particular, we will talk about how understanding such models has shed light on many kinds of pro
From playlist Algebraic and Complex Geometry
V. Tosatti - $C^{1,1}$ estimates for complex Monge-Ampère equations
I will discuss a method that we recently introduced in collaboration with Chu and Weinkove which gives interior C1,1 estimates for the non-degenerate complex Monge-Ampère equation on compact Kähler manifolds (possibly with boundary). The method is sufficiently robust to also give C1,1 regu
From playlist Complex analytic and differential geometry - a conference in honor of Jean-Pierre Demailly - 6-9 juin 2017
Billiards in quadrilaterals, Hurwitz spaces, and real multiplication of Hecke type - Alex Wright
Members' Seminar Topic: Billiards in quadrilaterals, Hurwitz spaces, and real multiplication of Hecke type Speaker: Alexander Wright Affiliation: Stanford University; Member, School of Mathematics Monday, November 30 Video Link: https://video.ias.edu/membsem/2015/1130-Wright After a brief
From playlist Mathematics
Félix Otto: The matching problem
The optimal transport between a random atomic measure described by the Poisson point process and the Lebesgue measure in d-dimensional space has received attention in diverse communities. Heuristics suggest that on large scales, the displacement potential, which is a solution of the highly
From playlist Probability and Statistics
Ben Andrews: Limiting shapes of fully nonlinear flows of convex hypersurfaces
Abstract: I will discuss some questions about the long-time behaviour of hypersurfaces evolving by functions of curvature which are homogeneous of degree greater than 1. ------------------------------------------------------------------------------------------------------------------------
From playlist MATRIX-SMRI Symposium: Singularities in Geometric Flows
On minimizers and critical points for anisotropic isoperimetric problems - Robin Neumayer
Variational Methods in Geometry Seminar Topic: On minimizers and critical points for anisotropic isoperimetric problems Speaker: Robin Neumayer Affiliation: Member, School of Mathematics Date: February 19, 2019 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Elliptic Curves - Lecture 4b - Singularities, morphisms
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
Morse-Bott theory on singular analytic spaces and applications to the topology of… - Paul Feehan
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Morse-Bott theory on singular analytic spaces and applications to the topology of symplectic four-manifolds Speaker: Paul Feehan Affiliation: Rutgers University Date: November 29, 2021 We describe two extensions, called th
From playlist Mathematics