Discussing h-vectors and the g-conjecture. Featuring June Huh from the Institute for Advanced Study at Princeton University.
More links & stuff in full description below ↓↓↓
A little extra bit from this interview:
Shapes in higher dimensions:
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15:36 familiar row
1
1 1
1 2 1
1 3 3 1 wow
1 4 6 4 1 amazing
June, huh?
you are nice and friendly guy ~
I stop introducing, i just go around and make friends 🤗
Never thought about zero dimensional sphere before. Amazing video.
Back then in school I didn't like this video much asking myself what have I learned exactly?
Now in university, having learned some algebraic topology, I really appreciate June Huh's simplified presentation here
Sometimes i get anxious watching old videos like this. Theres so many incredible advances that’s happened, if you want to be interdisciplinary, things like this could catch you off guard and cause you to reevaluate.
Triangulated sphere is a fancy way of saying triagons and Catalan numbers 😂
infinity
infinity
awesome
"you could certainly think of three-dimensional sphere instead of two-dimensional" – that was funny (especially becuase it wasn't intentional)
저는 수학을 좋아하는데 뭔가 릴렉스되요.
it fills me with great curiosity
Amazing..
For Euler's characteristics, why should I subtract right hand side to left hand side? Can I subtract reversly? The I could get x. 1-x. 1-(1-x)= x
I just realized from his definition of you think about a sphere is in different dimensions, that a 4d sphere, at least moving through 3d space would be a small sphere that grows to a maximum and shrinks again. For some reason I thought it would be the same size throughout but that would be more of a 4d spherical cylinder which is fun to think about on its own.
epcot ball
If we include f[-1] (= 1, for the null space) and f[n] (= 1, for the full shape), the alternating sum would always equal 0.
If the substraction started from the left hand side. the result would be the binomial coefficient if the triangle is rotated.
1
1 5
1 4 10
1 3 6 10
1 2 3 4 5
1 1 1 1 1
—rotate->
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Looks like any polynomial can be turned into a triangulated sphere.
Perfect explanation. Goes inexorably to the point, you have no chances other than nod and agree.
옛날에 봤었구나…. 신기하네 ㅋㅋ
He looks so happy
His handwriting is better than almost all of the people that appeared in number theory. You can see the poetic power behind it
The absolute best math channel to ever exist.❤
Lucky guess.
now there's some serenity
gonjecture
SubStraction was a distraction.
허준이교수님이 여기에 !!
Nimberphile!
헐
Sacred geometry starts at @7:24
conplan 8888
12*12 + 6*6*6
144 + 216