The statement that K is a ball can also be proven completely elementary. Here is a sketch. Assume h=p on S^{n-1}. First, consider any two points x,y on S^{n-1} with scalar product (x,y)>0, i.e. the angle(x,y)=2, one has \phi/N
@randomzhjioewmx
2 ай бұрын
Moreover, in your approach via Blaschke-Santanalo inequality you only get that K is an ellipsoid. This is weaker than K is a ball, for it might be some affine image of a ball that is not a ball itself.. And Blaschke-Santanalo inequality has (I think) one more requirement, namely that K be symmetric around 0.
@jonahhenwood8432
2 ай бұрын
Please dont stop with these videos. Even from a someone who doesn't really understand the math content these are very fun to watch!!
@harelkariv1477
2 ай бұрын
Hi, You can find a fourier-analytic proof (in English :)) of the blaschke-santalo inequality on arxiv, the paper is titled "The Blaschke-Santalo Inequality", by Gabriele Bianchi and Michael Kelly. The paper is very well written, and the proof is relatively pretty and neat from the parts that I understood (I am by no means fluent in fourier analysis). This inequality rekindled my interest in fourier analysis and convex geometry, so thank you for the motivation to go learn more :)
@aua6330
2 ай бұрын
That was nice.
@Devesteter252101
2 ай бұрын
yayyyy
@Frank-lk8ox
2 ай бұрын
You should make a video series on Fourier analysis.
@notrealjohnny5399
2 ай бұрын
Thinking about the guitar part, it reminds me of myself. I love mathematics, and before my biggest fear was messing up on something while trying to teach someone; like, come on, I do this all the time why I messed up on a simple trig simplification. It is worse when I do it back-to-back.
@masonholcombe3327
2 ай бұрын
As a graduating math major this was a sick proof
@vokoaxecer
2 ай бұрын
Can't you use Claude or ChatGPT to Convert it from Spanish to English?
@RandomGameClips27
2 ай бұрын
i understand why youre only uploading here since im a student since September too. But damn, i miss your vids on your primary channel :(
@p4rityy
2 ай бұрын
What's the primary channel?
@OOobstkuchenOO
2 ай бұрын
Oof, looking things up the original proofs seem to use affine isoperimetric inequalities (with the equality case actually only having been settled in the mid 80s), are you sure you want to read and present a paper in a different field for homework credit? That sounds like a bunch of work. On an unrelated note: Are you looking for an elementary proof? Don't want to backseat your math homework but lmk if you'd like some pointers
@tianrungou6486
2 ай бұрын
Dude are you doing research in Convex Geometry? Your last video on Functional Analysis kinda hints at this area.
@saidanilogblogspotg
2 ай бұрын
I have a question : why do not take notes in digital notebook like remarkable 2 ?
@diffusegd
2 ай бұрын
I have a functional analysis exam next week loam
@jennifertate4397
2 ай бұрын
Cool vid. Thanks. But as for some of the expressions that you closely pointed out, how do you know that they're mathematical "guys" and not "gals"? 🤣🤣🤣
@Vengeqnce
2 ай бұрын
Hey , Ik it’s off topic but do you sometimes struggle to understand something so you take it for granted as a fact and just move on to catch up your lectures and don’t fall behind ?
@KurtGodel-po3zl
2 ай бұрын
In high level maths it's increasingly difficult to have this approach, since the point is the understanding
@soyoltoi
2 ай бұрын
You can sometimes get away with this, but you should actually go back and understand it, or formulate a precise question to ask an expert. However, in some areas, this is a common practice known as "blackboxing" when there is simply too much to absorb so you pretend it's similar to something you already understand and use it as such until something breaks (eg. Arithmetic geometry).
@Vengeqnce
2 ай бұрын
@@KurtGodel-po3zl thank you, but what is your approach in this kinda situation ? What do you recommend me doing
@PhDVlog777
2 ай бұрын
It depends upon the situation, but if we are talking class notes, I will usually consult textbooks and try and find different explanations that make more sense to me than what we covered in class. If the topic is way above me, then I will go to office hours and discuss the material with the instructor. When it comes to research and reading papers, then it is much more arduous since these papers are hyper-focused on one topic. So you just have to go through it slowly and discuss it with your advisor if you get stuck.
@latdoom4989
2 ай бұрын
By the way, the paper is in Spanish
@voidzennullspace
2 ай бұрын
How much clarity are instructors expecting at the PhD level? You mention all of these theorems, and obviously the instructor probably knows every result you're citing, but I was always taught to cite the result that I employ and also explain why I can utilize it. This was especially true in my Complex Analysis course as there are so many ways to solve contour integrals, and if I don't explain why I can use one of the 20+ results and actually cite them then it shows that my reasoning isn't as solid as it probably should be. I guess I'm just shocked at the idea that I might've been taught to do all of these things because "that's what mathematicians do" and come to find out the proofs don't need to be as fleshed out as my instructors are making it out to be. Is it just because at your level they know that research is taking priority over class work? Do they not care about citing results because it is obvious to them what result you're using?
@PhDVlog777
2 ай бұрын
It depends upon the instructor. Some instructors want every detailed spelled out whereas others just want you to get the idea. I think the philosophy is that they want you to experience what it is like to do research via the homework.
@voidzennullspace
2 ай бұрын
@@PhDVlog777 I see. Thank you for your reply!
@thawfeeqjamaal1777
2 ай бұрын
Be so good they can't ignore you.
@ericksonlk
2 ай бұрын
It's not even Portuguese... it's Spanish. But it's the same thing, mostly.
Пікірлер: 31