The Hasse-Weil zeta functions of the intersection cohomology... - YihangZhu
Joint IAS/Princeton University Number Theory Seminar Topic: The Hasse-Weil zeta functions of the intersection cohomology of minimally compactified orthogonal Shimura varieties Speaker: Yihang Zhu Affiliation: Harvard University Date: Oct 20, 2016 For more videos, visit http://video.ias.e
From playlist Mathematics
Elliptic Curves - Lecture 14a - Elliptic curves over finite fields (an example)
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
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
Heuristics for the arithmetic of elliptic curves – Bjorn Poonen – ICM2018
Number Theory Invited Lecture 3.6 Heuristics for the arithmetic of elliptic curves Bjorn Poonen Abstract: This is an introduction to a probabilistic model for the arithmetic of elliptic curves, a model developed in a series of articles of the author with Bhargava, Kane, Lenstra, Park, Ra
From playlist Number Theory
Alex Mueller - Dwork's proof of the rationality of the Hasse-Weil zeta function I
Alex speaks on Dwork's computational intensive proof of the rationality of the Hasse-Weil zeta functions for smooth affine varieties, as given in Koblitz's book on p-adic analysis.
From playlist Alex Mueller giving Dwork's proof of rationality of zeta
Elliptic Curves: Good books to get started
A few books for getting started in the subject of Elliptic Curves, each with a different perspective. I give detailed overviews and my personal take on each book. 0:00 Intro 0:41 McKean and Moll, Elliptic Curves: Function Theory, Geometry, Arithmetic 10:14 Silverman, The Arithmetic of El
From playlist Math
Alex Mueller - Dwork's proof of the rationality of the Hasse-Weil zeta function V
Alex speaks on Dwork's computational intensive proof of the rationality of the Hasse-Weil zeta functions for smooth affine varieties, as given in Koblitz's book on p-adic analysis.
From playlist Alex Mueller giving Dwork's proof of rationality of zeta
Andrew Sutherland, Arithmetic L-functions and their Sato-Tate distributions
VaNTAGe seminar on April 28, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Elliptic Curves and Modular Forms | The Proof of Fermat’s Last Theorem
Elliptic curves, modular forms, and the Taniyama-Shimura Conjecture: the three ingredients to Andrew Wiles’ proof of Fermat’s Last Theorem. This is by far the hardest video I've ever had to make: both in terms of learning the content and explaining it. So there a few questions I don't hav
From playlist Famous Unsolved Problems
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
The Most Difficult Math Problem You've Never Heard Of - Birch and Swinnerton-Dyer Conjecture
The Birch and Swinnerton-Dyer Conjecture is a millennium prize problem, one of the famed seven placed by the Clay Mathematical Institute in the year 2000. As the only number-theoretic problem in the list apart from the Riemann Hypothesis, the BSD Conjecture has been haunting mathematicians
From playlist Math
Fred Diamond, Geometric Serre weight conjectures and theta operators
VaNTAGe Seminar, April 26, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in the talk: Ash-Sinott: https://arxiv.org/abs/math/9906216 Ash-Doud-Pollack: https://arxiv.org/abs/math/0102233 Buzzard-Diamond-Jarvis: https://www.ma.imperial.ac.uk/~buzzard/maths/research/paper
From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)
Acylindrically hyperbolic structures on groups - Balasubramanya
Women and Mathematics Title: Acylindrically hyperbolic structures on groups Speaker: Sahana Hassan Balasubramanya Affiliation: Vanderbilt University Date: May 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
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
Complex analysis: Weierstrass elliptic functions
This lecture is part of an online undergraduate course on complex analysis. We define the Weierstrass P and zeta functions and show they are elliptic. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj537_iYA5QrvwhvMlpkJ1yGN
From playlist Complex analysis
Wanlin Li, A generalization of Elkies' theorem on infinitely many supersingular primes
VaNTAGe seminar, November 9, 2021 License: CC-BY-NC-SA
From playlist Complex multiplication and reduction of curves and abelian varieties
Elliptic Curves - Lecture 13b - Elliptic curves over finite fields (Hasse's bound)
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
Edgar Costa, From counting points to rational curves on K3 surfaces
VaNTAGe Seminar, Jan 26, 2021
From playlist Arithmetic of K3 Surfaces
Algebraic geometry 45: Hurwitz curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It discusses Hurwitz curves and sketches a proof of Hurwitz's bound for the symmetry group of a complex curve.
From playlist Algebraic geometry I: Varieties
Francesc Fité, Sato-Tate groups of abelian varieties of dimension up to 3
VaNTAGe seminar on April 7, 2020 License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties