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
Periods of Quaternionic Shimura Varieties - Kartik Prasanna
Kartik Prasanna University of Michigan, Ann Arbor March 3, 2011 In the early 80's, Shimura made a precise conjecture relating Petersson inner products of arithmetic automorphic forms on quaternion algebras over totally real fields, up to algebraic factors. This conjecture (which is a conse
From playlist Mathematics
Héctor H. Pastén Vásquez: Shimura curves and bounds for the abc conjecture
Abstract: I will explain some new connections between the abc conjecture and modular forms. In particular, I will outline a proof of a new unconditional estimate for the abc conjecture, which lies beyond the existing techniques in this context. The proof involves a number of tools such as
From playlist Algebraic and Complex Geometry
Geometry of Shimura varieties - Rong Zhou
Short talks by postdoctoral members Topic: Geometry of Shimura varieties Speaker: Rong Zhou Affiliation: Member, School of Mathematics Date: October 6, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Fermat's Last Theorem - Numberphile
Simon Singh on Fermat's Last Theorem. Simpsons book: http://amzn.to/1fKe4Yo Fermat book: http://amzn.to/1jWqMTa More links & stuff in full description below ↓↓↓ EXTRA FOOTAGE: http://youtu.be/FXbsIbRVios FERMAT IN SIMPSONS: http://youtu.be/ReOQ300AcSU Interview with Ken Ribet, who played
From playlist Numberphile Videos
The Abel Prize announcement 2016 - Andrew Wiles
0:44 The Abel Prize announced by Ole M. Sejersted, President of The Norwegian Academy of Science and Letters 2:07 Citation by Hans Munthe-Kaas, Chair of the Abel committee 8:01 Popular presentation of the prize winners work by Alex Bellos, British writer, and science communicator 21:43 Pho
From playlist The Abel Prize announcements
Alex Bellos on Andrew Wiles and Fermat's last theorem
Popular presentation by Alex Bellos on Sir Andrew Wiles and on Fermat's last theorem. This clip is a part of the Abel Prize Announcement 2016. You can view Alex Bellos own YouTube channel here: https://www.youtube.com/user/AlexInNumberland
From playlist Popular presentations
On the Shioda Conjecture for Diagonal Protective Varieties over Finite Fields
Speakers Ben Church Chunying Huangdai Matthew Lerner-Brecher Navtej Singh Ming Jing Topics discussed Definitions and motivation, Examples over R, Examples, Uni-rationality and Rationality, The Zeta Function, The Weil Conjectures, Super-singularity, Shioda's Conjecture, Results, Code/Empi
From playlist 2018 Summer REU Presentations
The Biggest Project in Modern Mathematics
In a 1967 letter to the number theorist André Weil, a 30-year-old mathematician named Robert Langlands outlined striking conjectures that predicted a correspondence between two objects from completely different fields of math. The Langlands program was born. Today, it's one of the most amb
From playlist Explainers
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
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
Diophantine Geometry - Rafael von Kenel
Rafael von Kenel ETH Zurich; Institute for Advanced Study October 7, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Mark Kisin: Honda-Tate theory for Shimura varieties
Find 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, bibliographies,
From playlist Algebraic and Complex Geometry
The André-Oort conjecture follows from the Colmez conjecture - Jacob Tsimerman
Jacob Tsimerman University of Toronto April 9, 2015 The André-Oort conjecture says that any subvariety of a Shimura variety with a Zariski dense set of CM points must itself be a Shimura subvariety. In recent years, this has been the subject of much work. We explain how this conjecture fo
From playlist Mathematics
Andrew Wiles: Fermat's Last theorem: abelian and non-abelian approaches
The successful approach to solving Fermat's problem reflects a move in number theory from abelian to non-abelian arithmetic. This lecture was held by Abel Laurate Sir Andrew Wiles at The University of Oslo, May 25, 2016 and was part of the Abel Prize Lectures in connection with the Abel P
From playlist Sir Andrew J. Wiles
Ana Caraiani - 3/3 Shimura Varieties and Modularity
We discuss vanishing theorems for the cohomology of Shimura varieties with torsion coefficients, under a genericity condition at an auxiliary prime. We describe two complementary approaches to these results, due to Caraiani-Scholze and Koshikawa, both of which rely on the geometry of the H
From playlist 2022 Summer School on the Langlands program
Michael Harris "Shimura varieties and the search for a Langlands transform" [2012]
Michael Harris, Institut de mathématiques de Jussieu "Shimura varieties and the search for a Langlands transform" The Langlands reciprocity conjectures predict the existence of a correspondence between certain classes of representations of Galois groups of number fields and automorphic re
From playlist Number Theory
Andrew Wiles - The Abel Prize interview 2016
0:35 The history behind Wiles’ proof of Fermat’s last theorem 1:08 An historical account of Fermat’s last theorem by Dundas 2:40 Wiles takes us through the first attempts to solve the theorem 5:33 Kummer’s new number systems 8:30 Lamé, Kummer and Fermat’s theorem 9:10 Wiles tried to so
From playlist Sir Andrew J. Wiles
Special cycles on simple Shimura varieties - Wei Zhang
Workshop on Representation Theory and Analysis on Locally Symmetric Spaces Topic: Special cycles on simple Shimura varieties Speaker: Wei Zhang Affiliation: Massachusetts Institute of Technology Date: March 8, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics