Firoozbakht's conjecture

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

The Collatz Conjecture: Easy Enough for a 3rd Grader, Hard Enough for Terry Tao

The Collatz Conjecture has been called the simplest math problem no one can prove. It has captivated mathematicians for two generations. In today's Math Minute (the fiftieth Math Minute!), I want to look at just what is so surprising about the Collatz Conjecture, and talk about a few ways

From playlist Math Minutes

Number Theory | A very special case of Fermat's Last Theorem

We prove a very simple case of Fermat's Last Theorem. Interestingly, this case is fairly easy to prove which highlights the allure of the theorem as a whole -- especially given the fact that much of modern number theory was developed as part of the program that ended in the full proof. ht

From playlist Number Theory

A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part4)

Let X be an algebraic curve of genus g⩾2 embedded in its Jacobian variety J. The Manin-Mumford conjecture (proved by Raynaud) asserts that X contains only finitely many points of finite order. When X is defined over a number field, Bogomolov conjectured a refinement of this statement, name

From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes

A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part3)

Let X be an algebraic curve of genus g⩾2 embedded in its Jacobian variety J. The Manin-Mumford conjecture (proved by Raynaud) asserts that X contains only finitely many points of finite order. When X is defined over a number field, Bogomolov conjectured a refinement of this statement, name

From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes

A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part2)

Let X be an algebraic curve of genus g⩾2 embedded in its Jacobian variety J. The Manin-Mumford conjecture (proved by Raynaud) asserts that X contains only finitely many points of finite order. When X is defined over a number field, Bogomolov conjectured a refinement of this statement, name

From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes

A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part1)

Let X be an algebraic curve of genus g⩾2 embedded in its Jacobian variety J. The Manin-Mumford conjecture (proved by Raynaud) asserts that X contains only finitely many points of finite order. When X is defined over a number field, Bogomolov conjectured a refinement of this statement, name

From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes

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

Fermat's Last Theorem for rational and irrational exponents

Fermat's Last Theorem states the equation x^n + y^n = z^n has no integer solutions for positive integer exponents greater than 2. However, Fermat's Last Theorem says nothing about exponents that are not positive integers. Note: x, y and z are meant to be positive integers, which I should

From playlist My Maths Videos

Recent developments in non-commutative Iwasawa theory I - David Burns

David Burns March 25, 2011 For more videos, visit http://video.ias.edu

From playlist Mathematics

Giles Gardam: Kaplansky's conjectures

Talk by Giles Gardam in the Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/3580/ on September 17, 2021.

From playlist Global Noncommutative Geometry Seminar (Americas)

Giles Gardam - Kaplansky's conjectures

Kaplansky made various related conjectures about group rings, especially for torsion-free groups. For example, the zero divisors conjecture predicts that if K is a field and G is a torsion-free group, then the group ring K[G] has no zero divisors. I will survey what is known about the conj

From playlist Talks of Mathematics Münster's reseachers

Gonçalo Tabuada - 1/3 Noncommutative Counterparts of Celebrated Conjectures

Some celebrated conjectures of Beilinson, Grothendieck, Kimura, Tate, Voevodsky, Weil, and others, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of (the majority of) these conjectures remains illusive. The aim

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Explicit formulae for Gross-Stark units and Hilbert’s 12th problem by Mahesh Kakde

PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath

From playlist Perfectoid Spaces 2019

Explicit formulae for Stark Units and Hilbert's 12th problem - Samit Dasgupta

Joint IAS/Princeton University Number Theory Seminar Topic: Explicit formulae for Stark Units and Hilbert's 12th problem Speaker: Samit Dasgupta Affiliation: Duke University Date: October 11, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

Gonçalo Tabuada - 3/3 Noncommutative Counterparts of Celebrated Conjectures

Some celebrated conjectures of Beilinson, Grothendieck, Kimura, Tate, Voevodsky, Weil, and others, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of (the majority of) these conjectures remains illusive. The aim

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Lillian Ratliff - Learning via Conjectural Variations - IPAM at UCLA

Recorded 15 February 2022. Lillian Ratliff of the University of Washington presents "Learning via Conjectural Variations" at IPAM's Mathematics of Collective Intelligence Workshop. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/mathematics-of-intelligences/?tab=schedule

From playlist Workshop: Mathematics of Collective Intelligence - Feb. 15 - 19, 2022.

Iwasawa theory of the fine Selmer groups of Galois representations by Sujatha Ramdorai

PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath

From playlist Perfectoid Spaces 2019

Jochen Koenigsmann : Galois codes for arithmetic and geometry via the power of valuation theory

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 Algebra

The Collatz Conjecture - summary of a proof

http://lesliegreen.byethost3.com/articles/neg_collatz.pdf http://lesliegreen.byethost3.com/articles/evidence.zip (now tested to *10 million digits*) The Collatz Conjecture is infamous for being easy to state but impossible to prove by standard methods. Clearly a non-standard approach is re

From playlist Covers