Diophantine geometry | Unsolved problems in number theory | Conjectures
In mathematics, the Manin conjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function. It was proposed by Yuri I. Manin and his collaborators in 1989 when they initiated a program with the aim of describing the distribution of rational points on suitable algebraic varieties. (Wikipedia).
Factorial Sums #wordlesswednesday (visual proof)
This is a short, animated visual proof demonstrating a finite sum involving products of factorials. #mathshorts #mathvideo #math #numbertheory #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #factorial #squares #factoradic #discretemath
From playlist Finite Sums
Will Sawin, The freeness alternative to thin sets in Manin's conjecture
VaNTAGe seminar, May 4, 2021 License: CC-BY-NC-SA
From playlist Manin conjectures and rational points
Sum of Squares I (visual proof)
This is a short, animated visual proof of the formula that computes that sum of the first n squares using 3 copies of the sum of squares to build a rectangle . #mathshorts #mathvideo #math #sumofsquares #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proo
From playlist Finite Sums
Sine of a Sum I (visual proof; trigonometry)
This is a short, animated visual proof of the sum formula for the sine function using the Side-Angle-Side triangle area formula. This theorem relates the sine of a sum to the sum of products of sines and cosines. #mathshorts #mathvideo #math #trigonometry #sine #sinofsum #triangle #manim
From playlist Trigonometry
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Marta Pieropan, The split torsor method for Manin’s conjecture
See https://tinyurl.com/y98dn349 for an updated version of the slides with minor corrections. VaNTAGe seminar 20 April 2021
From playlist Manin conjectures and rational points
Francesca Balestrieri, The arithmetic of zero-cycles on products of K3 surfaces and Kummer varieties
VaNTAGe seminar, March 9, 2021
From playlist Arithmetic of K3 Surfaces
Holly Krieger, Equidistribution and unlikely intersections in arithmetic dynamics
VaNTAGe seminar on May 26, 2020. License: CC-BY-NC-SA. Closed captions provided by Marley Young.
From playlist Arithmetic dynamics
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From playlist Shorts
Complex Numbers Explained | An Introduction to Complex Numbers
In this video, we look at an introduction to complex numbers. We show why it is necessary to consider i = sqrt(-1) and complex numbers, based on Gauss' fundamental theorem of algebra. We work through examples of adding complex numbers, multiplying complex numbers, dividing complex numbers,
From playlist Complex Numbers
Galileo's Odd Ratios #wordlesswednesday (visual proof)
This is a short, animated visual proof demonstrating the ratio of the sum of the first n positive odd integers to the sum of the next n positive odd integers is always exactly 1/3. #mathshorts #mathvideo #math #numbertheory #mtbos #manim #animation #theorem #pww #proofwithoutwords
From playlist Finite Sums
Yuri Tschinkel, Height zeta functions
VaNTAGe seminar May 11, 2021 License: CC-BY-NC-SA
From playlist Manin conjectures and rational points
Mertens Conjecture Disproof and the Riemann Hypothesis | MegaFavNumbers
#MegaFavNumbers The Mertens conjecture is a conjecture is a conjecture about the distribution of the prime numbers. It can be seen as a stronger version of the Riemann hypothesis. It says that the Mertens function is bounded by sqrt(n). The Riemann hypothesis on the other hand only require
From playlist MegaFavNumbers
On Sharifi’s Conjectures and Generalizations by Emmanuel Lecouturier
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
Bianca Viray, The Brauer group and the Brauer-Manin obstruction on K3 surfaces
VaNTAGe seminar, February 23, 2021
From playlist Arithmetic of K3 Surfaces
Persistence of the Brauer-Manin obstruction under field extension - Viray - Workshop 2 - CEB T2 2019
Bianca Viray (University of Washington) / 27.06.2019 Persistence of the Brauer-Manin obstruction under field extension. We consider the question of when an empty Brauer set over the ground field gives rise to an empty Brauer set over an extension. We first consider the case of quartic d
From playlist 2019 - T2 - Reinventing rational points
Descent obstructions on constant curves over global (...) - Creutz - Workshop 2 - CEB T2 2019
Brendan Creutz (University of Canterbury) / 26.06.2019 Descent obstructions on constant curves over global function fields Let C and D be proper geometrically integral curves over a finite field and let K be the function field of D. I will discuss descent obstructions to the existence o
From playlist 2019 - T2 - Reinventing rational points
A (compelling?) reason for the Riemann Hypothesis to be true #SOME2
A visual walkthrough of the Riemann Zeta function and a claim of a good reason for the truth of the Riemann Hypothesis. This is not a formal proof but I believe the line of argument could lead to a formal proof.
From playlist Summer of Math Exposition 2 videos
Eisenstein Ideals: A Link Between Geometry and Arithmetic - Emmanuel Lecouturier
Short Talks by Postdoctoral Members Topic: Eisenstein Ideals: A Link Between Geometry and Arithmetic Speaker: Emmanuel Lecouturier Affiliation: Member, School of Mathematics Date: September 25, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics