Brownian Castles and the Yang-Mills Millennium Problem with Martin Hairer (Fields Medal 2014)
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- Опубликовано: 20 окт 2024
- Martin Hairer (Fields Medal 2014) explains his current research on universality classes and how it links to the unsolved Millennium Problem on Yang-Mills and the Mass Gap Hypothesis.
Martin's work looks at interfaces generated through random processes - which can be modelled using the video game Tetris. We begin by discussing 'Ballistic Deposition' which belongs to the 'KPZ Universality Class', before moving on to 'Random Ballistic Deposition' which gives rise to a completely new universality class which Martin names the 'Brownian Castle'.
Finally, Martin explains how his research in stochastic processes has led him to the Yang-Mills Mass Gap Hypothesis - one of 7 Millennium Problems that has a $1-million prize...
Part 1 on the original 'Tetris Model' is here: • Playing Tetris with Ma...
Interview with Martin Hairer of Imperial College London. Recorded at the 2019 Heidelberg Laureate Forum.
Produced by Dr Tom Crawford at the University of Oxford.
Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: www.seh.ox.ac....
For more maths content check out Tom's website tomrocksmaths....
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
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Make sure you watch part 1 where Martin explains the 'Tetris Model' here: ruclips.net/video/Z6XP3n-Sjiw/видео.html
Dear friend,
I would like to have a little suggestion , why does not pro Martin Hairer cooperate with pro .Terence Tao to solve Yang Mills existence and mass gaps? Pro.Tao is an excellent expert in PDE , he has some works related to Yang -Mill problem.
Pro Tao's Yang -Mills work has led woman mathematician Karen Uhlenbeck to get Abel prize . Can you research more information about pro.Tao?
If a^x=a^y+2^z where a,x,y,z are positive integers. Find the sum of all possible values of ayz/(x-1)^2.
Can you solve this problem???
It's awesome
@@k.m.junayedahmed3748 ha ha I solved it when I was in 1st grade. 😎
This animation truly is mesmerizing. I watched this video for the first time years ago, and just now am taking a stochastic calculus class in which we talk about the KPZ equation, and still these animations were as vivid in my memory as the first time I watched them.
This is fascinating. And Martin seems like such a genial guy.
He really is!
Back in 2014 when he won the Fields medal, after his plenary lecture in Seoul, I was lucky to have had a conversation with him for about 20 minutes. I was in the first year of college which I believe it’s called high school in America, and gave me priceless advices on my career where I’m in the physics department now and plan on moving to mathematics. And hopefully keep striving for a PHD 😄
amazing, best of luck!
Mind blowing content as usual. Instagram sent me a notification the other day saying "You follow Tom Rocks Maths, maybe you'd be interested in Nobel Prize" do they know something we don't??
Haha if only...
Reminds me of how plants grow leaves horizontally to overshadow smaller, competing plants resulting in less diversity
Nice observation!
MORE VIDEOS WITH HAIRER PLEASE
I'll try my best! He is awesome.
I wish that I can sit for a hour with Martin Hairer and just talk with him about mathematics.
I can confirm this is indeed as fun as you think!
brownian castle is a great name 🍀nice video :)
What if the Tetris simulator thingy would be in 3D?
... then it would be SO much more difficult
@@TomRocksMaths Correct me if I am wrong but I think a 3D tetris simulator would not at all be any difficult/interesting from a 2D one as a 3D random tetris would be equivalent to 2 independent projections of 2D random tetris. Therefore the behaviour Martin studies will also tell us the behaviour of 3D tetris
Hello sir. This is very exciting but are we aiming the essay (for the competition for teddy rocks maths) at someone who has no clue about maths accept for basic counting or can we aim it towards someone who can at least do high school maths.
Edit: by high school I meant gcse maths. And also, you talked about high school students getting a student prize, was that meant to be the british version of high school (where we go until we are 16) or the american version (where they go up until they are 18)? This was the part that confused me a bit. Thank you.
The high school prize is for ages 18 and under. As or the content, it should ideally be able to be understood by someone who has completed high school maths (or GCSE as you say).
Why do the tools break down in 4 dimensions?
Can you pls give this Yang-Mills and mass gap in simple terms??
I have an article trying to explain it here: tomrocksmaths.com/2017/03/27/yang-mills-mass-gap/
Encountered 4 minus epsilon dimensions before and just nope....
We've all been there...
Great👏🔥
The answer is 6!
Tom rocks Millennium Problem
nice
@@TomRocksMaths Dr.Tom I think we should try rocking Riemann hypothesis , don't you ?
cool
Don't you fall him in the word!
Why these geniuses they don't explain me the pollain grain motion in terms of atomic physics (where it should come from that randomness !?). This not science anymore.
I watched you for the first time when u were checking one of the youtubers answers for their Oxford ug entrance test...i dont remember his name lol😂...but damn dude what i wanted to say is u look too cool to JUST study maths or science... do modelling omg
you're too kind
Hmm.. Machine Gun Kelly.
I'll take it :)
@@TomRocksMaths oh just kidding. we love you.
for me these things have nothing to do with physics , just worship of intellectual vanity. Also quantas are just macroscopic phenomena in an apparatus. There is nothing to quantize, rather we should describe how an apparatus (made of atoms) produces a classical outcome. Browniana Castel ;) , it neither exist a Brownian motion. None ever derived it and of course the pollain grain does not have that analytic properties of the Wiener process !
Mass !? Energy is equal mass, there is no mass gap. Rather one should on the right side of Einstein's equation is the question.
Wish you made sense … but you don’t .
it would be great that you let him talk, and not try to be so assertive
???