Diophantine geometry | Unsolved problems in number theory | Topological methods of algebraic geometry | Conjectures
In number theory and algebraic geometry, the Tate conjecture is a 1963 conjecture of John Tate that would describe the algebraic cycles on a variety in terms of a more computable invariant, the Galois representation on étale cohomology. The conjecture is a central problem in the theory of algebraic cycles. It can be considered an arithmetic analog of the Hodge conjecture. (Wikipedia).
Matthew Morrow - A crystalline variational Tate conjecture
I will discuss the formulation of a variational Tate conjecture for smooth, proper families of varieties in characteristic p in terms of crystalline cycle classes, and explain the proof of the conjecture for line bundles. A key new tool is a recent continuity theorem in topological cyclic
From playlist Journées de géométrie arithmétique de l'IHÉS
On integral aspects of the Tate conjecture - Alena Pirutka
Alena Pirutka March 13, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu
From playlist Mathematics
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
David Zywina, Computing Sato-Tate and monodromy groups.
VaNTAGe seminar on May 5, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Geometers Abandoned 2,000 Year-Old Math. This Million-Dollar Problem was Born - Hodge Conjecture
The Hodge Conjecture is one of the deepest problems in analytic geometry and one of the seven Millennium Prize Problems worth a million dollars, offered by the Clay Mathematical Institute in 2000. It consists of drawing shapes known topological cycles on special surfaces called projective
From playlist Math
Francesc Fité: The generalized Sato-Tate conjecture
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
Marcus du Sautoy on John Tates' work
Marcus Peter Francis du Sautoy is a British mathematician, author, and populariser of science and mathematics. You can view more content of Marcus du Sautoy here: https://www.youtube.com/channel/UCYF21Xc9fSdqVWRxpBAOleQ/featured This video is a clip from the Abel Prize Announcement 2009
From playlist Popular presentations
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
Francesc Fité: Sato-Tate axioms
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
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
Kiran Kedlaya, The Sato-Tate conjecture and its generalizations
VaNTAGe seminar on March 24, 2020 License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Christelle Vincent, Exploring angle rank using the LMFDB
VaNTAGe Seminar, February 15, 2022 License: CC-NC-BY-SA Links to some of the papers mentioned in the talk: Dupuy, Kedlaya, Roe, Vincent: https://arxiv.org/abs/2003.05380 Dupuy, Kedlaya, Zureick-Brown: https://arxiv.org/abs/2112.02455 Zarhin 1979: https://link.springer.com/article/10.100
From playlist Curves and abelian varieties over finite fields
John Tate - The Abel Prize interview 2010
0:00 Glimpses of the Abel Prize ceremony [In Norwegian] 0:23 Speech by Nils Christian Stenseth, President of the Norwegian Academy of Science and Letters [In Norwegian] 1:15 Tate Receives the Abel Prize from His Majesty King Harald V of Norway 1:41 Interview start [English]. Your father wa
From playlist John T. Tate
Moduli spaces of shtukas over function fields - Jared Weinstein
Joint IAS/Princeton University Number Theory Seminar Topic: Moduli spaces of shtukas over function fields Speaker: Jared Weinstein Affiliation: Boston University Date: February 13, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
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
Knots, three-manifolds and instantons – Peter Kronheimer & Tomasz Mrowka – ICM2018
Plenary Lecture 11 Knots, three-manifolds and instantons Peter Kronheimer & Tomasz Mrowka Abstract: Over the past four decades, input from geometry and analysis has been central to progress in the field of low-dimensional topology. This talk will focus on one aspect of these developments
From playlist Plenary Lectures
ABC Intro - part 1 - What is the ABC conjecture?
This videos gives the basic statement of the ABC conjecture. It also gives some of the consequences.
From playlist ABC Conjecture Introduction