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
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
Lion Gate, Mycenae, c. 1300-1250 B.C.E.
limestone, relief panel 9' 6" high Speakers: Dr. Steven Zucker and Dr. Beth Harris. Created by Beth Harris and Steven Zucker.
From playlist Art of the ancient Mediterranean | Art History | Khan Academy
Collatz Conjecture (extra footage) - Numberphile
Main video on Collatz Conjecture: https://youtu.be/5mFpVDpKX70 Riemann Hypothesis: https://youtu.be/d6c6uIyieoo Key to the Riemann Hypothesis: https://youtu.be/VTveQ1ndH1c Eisenbud 17-gon: https://youtu.be/87uo2TPrsl8 Fermat's Last Theorem: https://youtu.be/qiNcEguuFSA Bridges to Fermat (K
From playlist David Eisenbud on Numberphile
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
Watch our updated video here: https://youtu.be/jbn9_IKA3ow
https://youtu.be/jbn9_IKA3ow Sutton Hoo Ship Burial, c. 700 (British Museum, London) Multiple bronze, gold and silver objects of Anglo Saxon origin, found in Suffolk, England, including: a helmet, sceptre, sword, hanging bowl, bowls and spoons, shoulder clasps, a belt buckle, and purse li
From playlist Ancient and Medieval history | World History | Khan Academy
“Gauss sums and the Weil Conjectures,” by Bin Zhao (Part 7 of 8)
“Gauss sums and the Weil Conjectures,” by Bin Zhao. The topics include will Gauss sums, Jacobi sums, and Weil’s original argument for diagonal hypersurfaces when he raised his conjectures. Further developments towards the Langlands program and the modularity theorem will be mentioned at th
From playlist CTNT 2016 - ``Gauss sums and the Weil Conjectures" by Bin Zhao
Judith Leyster, Self-Portrait, c. 1633, oil on canvas, 74.6 x 65.1 cm / 29-3/8 x 25-5/8 inches (National Gallery of Art) Speakers: Dr. Beth Harris and Dr. Steven Zucker. Created by Steven Zucker and Beth Harris.
From playlist Baroque to Neoclassical art in Europe | Art History | Khan Academy
Peplos Kore from the Acropolis
Peplos Kore, c. 530 B.C.E., from the Acropolis, Athens, Greece (Acropolis Museum, Athens) Speakers: Dr. Steven Zucker & Dr. Beth Harris. Created by Steven Zucker and Beth Harris.
From playlist Art of the ancient Mediterranean | Art History | Khan Academy
In this video, we explore the "pattern" to prime numbers. I go over the Euler product formula, the prime number theorem and the connection between the Riemann zeta function and primes. Here's a video on a similar topic by Numberphile if you're interested: https://youtu.be/uvMGZb0Suyc The
From playlist Other Math Videos
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
Bushel with ibex motifs, 4200--3500 B.C.E., Susa I period, necropolis, acropolis mound, Susa, Iran, painted terra-cotta, 28.90 x 16.40 cm, excavations led by Jacques de Morgan, 1906-08 (Musée du Louvre, Paris) Speakers: Dr. Beth Harris and Dr. Steven Zucker. Created by Steven Zucker and B
From playlist Prehistoric art in Europe and West Asia | Art History | Khan Academy
Attic Red-Figure: Niobid Painter, "Niobid Krater"
Niobid Painter, "Niobid Krater," Attic red-figure calyx-krater, c. 460-50 B.C.E., 54 x 56 cm (Musée du Louvre) Speakers: Dr. Beth Harris and Dr. Steven Zucker. Created by Steven Zucker and Beth Harris.
From playlist Art of the ancient Mediterranean | Art History | Khan Academy
Techniques of constructions of variations of mixed Hodge structures by Hisashi Kasuya
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Arch of Constantine, 315 C.E., Rome Speakers: Dr. Beth Harris, Dr. Steven Zucker. Created by Beth Harris and Steven Zucker.
From playlist Art of the ancient Mediterranean | Art History | Khan Academy
Matthew Stover: Variations on an example of Hirzebruch
Abstract: In '84, Hirzebruch constructed a very explicit noncompact ball quotient manifold in the process of constructing smooth projective surfaces with Chern slope arbitrarily close to 3. I will discuss how this and some closely related ball quotients are useful in answering a variety of
From playlist Algebraic and Complex Geometry
“Gauss sums and the Weil Conjectures,” by Bin Zhao (Part 4 of 8)
“Gauss sums and the Weil Conjectures,” by Bin Zhao. The topics include will Gauss sums, Jacobi sums, and Weil’s original argument for diagonal hypersurfaces when he raised his conjectures. Further developments towards the Langlands program and the modularity theorem will be mentioned at th
From playlist CTNT 2016 - ``Gauss sums and the Weil Conjectures" by Bin Zhao
Weil conjectures 4 Fermat hypersurfaces
This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. T
From playlist Algebraic geometry: extra topics
Zagier's conjecture on zeta(F,4) - Alexander Goncharov
Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program Topic: Zagier's conjecture on zeta(F,4) Speaker: Alexander Goncharov Affiliation: Yale University; Member, School of Mathematics Date: November 10, 2017 For more videos, please visit http://video.ias.
From playlist Mathematics
Richard Hain - 4/4 Universal mixed elliptic motives
Prof. Richard HAIN (Duke University, Durham, USA) Universal mixed elliptic motives are certain local systems over a modular curve that are endowed with additional structure, such as that of a variation of mixed Hodge structure. They form a tannakian category. The coordinate ring of its fu
From playlist Richard Hain - Universal mixed elliptic motives