Terence Tao - From Rotating Needles to Stability of Waves: Local Smoothing... (November 29, 2023)
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- เผยแพร่เมื่อ 21 ก.ย. 2024
- Solutions to the wave equation preserve energy, and so, in some sense, they maintain their regularity over time. Nevertheless, there is a paradoxical local smoothing phenomenon: When measured in certain aspects, waves can become significantly smoother in a given region of space and time, particularly if one is willing to work “on average” by ignoring some outlier times. Quantifying this phenomenon has been important in applications related to partial differential equations and mathematical physics and has surprising connections to incidence geometry, combinatorics and even number theory. For instance, there is an unexpected connection to the Kakeya needle problem concerning the smallest area needed to rotate a unit line segment (or needle) 180 degrees on a plane.
In this Presidential Lecture, Terence Tao will survey recent and not-so-recent developments in this subject. More details: www.simonsfoun...
This was more physics than math. It gladdens my heart to see Terence Tao putting some of his attention to physics and other applications of math.
The pure math vs applied math distinction can be a limiting view.
we need pure math like water......and we need more pure math not reduce to applied math, but bring applied methods up to meet pure math, and then re-applied........@@hybmnzz2658 cheers
I think he's been interested in Navier-Stokes for a while so he does both number theory and physics related math.
Real genius cares aboutt the beauty of nature, not just complicated math but the best of it and that is its aplications
People who only care about "pure math" are like religious zealots.
He makes a good point. To make progress you learn incrementally.
Brilliant talk! Thanks for Dr. Terence Tao for illuminating this topic... He gave a very intuitive explanation for Noether's theorem
Organizers, please, do not set strict time limit for super interesting speakers like Terence Tao.
Great talk! Terry is still so active in math research and keeping pushing the boundary for human beings to understand math! Kudos to Terry!
" Great, TALK?" That was mumbling. What sort of xlown is this guy to get up in front of adults and mumble.
@@gregorybrennan8539 ???????
Thanks
Dear Prof Terry, an additional talk Part 2 would be super awesome.
What a great talk.
Thank you for this !!!
Time limiting Terence Tao to 45 measly minutes should be crime against humanity
Reminds me of my postgraduate PDE course, thanks for this presentation
PDE’s were so hard for me. My professor was kind of checked out
Great mathematical topic
The i-reflection of relative-timing decay sequences is the interference patterning of metastable temporal superposition substantiation, "You just look at it and you notice.." because you are in metastable resonance with log-antilog prime-cofactor condensation modulation wave-packaging, aka Singularity-point positioning in/of holographic nucleation inside-outside an absolute projection-drawing Aether of Absolute Zero-infinity reference-framing containment here-now-forever in Logarithmic Time Superspin Superposition-point Singularity Perspective Principle, ie the prime-cofactor number sequences condensation-> WYSIWYG wave-packaging.
Bro what
Awful explanation.
😂
16:05 "stationary point of the LAGRANGIAN" - this is wrong, it should be the "stationary point of the ACTION". The title of the slide refers to L(u) as the "action" which is correct, but he refers to L here and later (e.g. 16:59) as the Lagrangian. He probably got confused, and the notation ("L") probably doesn't help.
A freudian slip, happens to even the best of us
Not nearly as translucent as earlier, rather suggestive and ominous. If you lit a candle (point source) in the middle of a circle (generally, S^n) the light rays will come back to you trivially. If, instead of a candle, all you have are small balls, then how can you throw more than one at a time? Anyway, you can not throw more than one in one chosen direction until the first one returns.
Let us stay within the discrete setup and consider elliptic stadium. How many balls and of what diameter can you throw from one focus to arrive simultaneously at the other... There are plenty of variations on the theme, caustics, catastrophe theory.
Take your meds
I am no mathematician but small balls probably equal small dick
no shit
🌊 a new wave is starting
based !!
I didn’t realize mathematicians just normalize out the scalars and set them to 1. That makes sense
A needle floating on a water surface due to surface tension.....how should the water surface wobble so the needle starts rotating...what are relevant equations
We physicians use to define fysical functions by requiring that they are / can be in a Hilbert space and integrable by Lebesgue's method. It' was proven in 1978 ( if I remember) among other thing that fourier transforms Laplace transforms etc could be applied to these functions. Why use another requirement? What is the advantage?
........thank you TT ...great presentation....very refreshing indeed.....excellent compacted brief wave function overview......indeed near perfect timing, in this period of physic's in near crises .
..........you make me think the following
.............may i humbly state in the following brief comment
...........it seems...the universal action of gravity forces what looks like....a Fourier decoherence effect on the bounded in-phase superposition of '2^N' surface area waves , all waving areas share the same total conserved energy Hamiltonian H = PE + KE maximum energy amount H and differential dH = 0 always satisfied.
.......Why not divide energy value H into 2^N different discreet plane bounded surface areas, each is plane area that is divided by the same maximum total bounded conserved energy dH = 0 value
.......Note.....a wave function surface areas are factorized by H's energy and its conserved dH = 0 energy amount
ha... ha...looks the pair of energy factorizations, both H = constant and dH = 0 universally entangles/factors the wave function by a total energy H = const and dH = 0 constraints
Note... the different Fourier surface area waves when/if factored by the same total maximum energy amount H, will each calculate/compute different local energy densities, that together add up, sum, or integrate to, a shared conserved in-phase coherent total energy 'H' value that can be imagined to translate a wave front with a surface energy tension that has a zero angle of parallelism edge.
.it seems....that the 'action' of gravity is to initiate a coherence to decoherence phase shift in a wave function's leading boundary edge ....
in effect you can say the .....non-zero GRAVITY causes DECOHERENCE.....just as the fabulous 'Roger Penrose' has past suggested.....
.
...imagine physic's testing the following... Decoherence conditional
......if........... a wave surface areas has '0' curvature (zero gravity)...
.....then...... the surface waves have '0' decoherence and translate 'no' out-phase energy packets
.... if..........a wave surface areas has '~0' curvature (~zero gravity
.......then .....the surface waves have '~0' decoherence and translate out-phase energy packet
...Tao and Penrose ....come together soon please...would be fabulous indeed
thanks
Intuition confirmation is only possible after the experience of the holistic AM-FM time-timing wave-packaging in the specific format, ie in Actuality of Euler's e-Pi-i sync-duration resonance shell-horizons continuous connection.., you cannot help noticing if you are shown the appropriate decay/regeneration sequential narrative of information In-form-ation narrative and balanced Equations. This is our sense-in-common memory modulo-geometrical modulation cause-effect mechanism in/of coherence-cohesion objectives in perspectives of logarithmic i-reflection coordination. Such is life.
Take a grammar class
Great physicists know a lot about mathematics but great mathematicians know almost nothing about physics.
The arrow(?), string-like Sublimation-Tunnelling jump /collapse of relative-timing i-reflection reverse process, in superposition at the cross-sectional interference location, 1-0-infinity instantaneous Entanglement nucleation..
A unidirectional vector-value?, a half-truth of delay-decay and not QM-TIME Completeness.
Entanglement = Renormalisation; interference = superposition, and "It's always NOW".., Absolute inherent "Mathematical" Disproof Methodology of superimposed Zero-infinity connection of nothing floating in No-thing, apparent.. Observable logic of QM-TIME reference-framing containment, and empirical generation of the 3 laws in 3D-T 3-ness Cavity of 2-ness logarithmic condensation properties of string-like 2-ness i-reflection at the vanishing-into-no-thing sequences of relative-timing ratio-rates Perspective.
And "smoothing" is the default mechanism for Fluxion-Integral frequency density-intensity alignment of condensation-coordination vanishing-into-no-thing resonance bonding proportioning chemistry.., math-music reciprocation-recirculation mathematical
I'm pretty sure I saw this on the bumper sticker of a car because they just couldn't get Keep On Truckin' to fit on it..
Bro you really need to work on your communication what an absolute rabble of unnecessary jargon.
Tao
So?
What are the number theory connections?
none here
Hiw am I supposed to care about this or anything else when most of the ppl Incare abit are desd and gone and soon all of nthem will be..then how am I tongo on...
Well, it's the same for everyone in this world. So always cherish the time you have now with your loved ones.
First comment
Princeton University
Is this the new math?
STEM == D : D== MATHEMATICS FIRST 21:40
10/DEC/2023
EPITHELIAL GROWTH UND EXISTING : SOLID AMBER : FRAGRANCE CONSUMABLE SEMISOLID 45:13
@@STEM671Seems like the wrong video man.
Bruce Lee
Who understands this guy??? They pay him to speak?? In money?
When you are as great a mathematician as Terry Tao, people want to listen to what you have to say about mathematical topics. It was not a made-for-youtube event. It was a lecture to an audience of interested persons - mathematicians and people interested in mathematics. If you didn't get anything from it, then it wasn't for you. Move along.
i would certainly pay him anytime
@Hiltok When people of this age mumble, any mental clinician will tell you it is a disrespect for the listener ." I'm so important you must work to listen to my god-like words."
@@Hiltok How is that string theory working out?
@@gregorybrennan8539 How is that divorce working out for you?
Very poor delivery
Why?
@@18890426he has a nervous sounding voice. It’s interesting that someone of his stature doesn’t sound confident, which is perhaps why people like how humble he seems