Hedetniemi's conjecture

A Breakthrough in Graph Theory - Numberphile

A counterexample to Hedetniemi's conjecture - featuring Erica Klarreich. Get 3 months of Audible for just $6.95 a month. Visit https://www.audible.com/numberphile or text "numberphile" to 500 500 More links & stuff in full description below ↓↓↓ Read Erica Klarreich's Quanta article on th

From playlist Graph Theory on Numberphile

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

Heine Borel Theorem

Here I prove the Heine-Borel Theorem, one of the most fundamental theorems in analysis. It says that in R^n, all boxes must be compact. The proof itself is very neat, and uses a bisection-type argument. Enjoy! Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHG

From playlist Topology

The Pattern to Prime Numbers?

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

The Euler Mascheroni Constant

I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is

From playlist Series

Function Space and series

In this video, I explain function space and how to change the basis vectors we use to describe function. This lead us to a different understanding of Taylor series, Fourier series and most series. I also explain the Heisenberg uncertainty principle using function space. Additionnal video

From playlist Summer of Math Exposition Youtube Videos

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

Sir Michael Atiyah | The Riemann Hypothesis | 2018

Slides for this talk: https://drive.google.com/file/d/1DNHG9TDXiVslO-oqDud9f-9JzaFCrHxl/view?usp=sharing Sir Michael Francis Atiyah: "The Riemann Hypothesis" Monday September 24, 2018 9:45 Abstract: The Riemann Hypothesis is a famous unsolved problem dating from 1859. I will present a

From playlist Number Theory

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

The Predictive Power Of Symmetry

From a bee’s hexagonal honeycomb to the elliptical paths of planets, symmetry has long been recognized as a vital quality of nature. Einstein saw symmetry hidden in the fabric of space and time. The brilliant Emmy Noether proved that symmetry is the mathematical flower of deeply rooted phy

From playlist Science Shorts and Explainers

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.

Uncertainty Principle - Klim Efremenko

Klim Efremenko Tel-Aviv University; Member, School of Mathematics April 23, 2013 Informally, uncertainty principle says that function and its Fourier transform can not be both concentrated. Uncertainty principle has a lot of applications in areas like compressed sensing, error correcting c

From playlist Mathematics

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