Eating Curves for Breakfast - Numberphile 

This is a continuation of a video with Isabel Vogt at: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-CcZf_7Fb4Us.html

What may not come across, because of Vogt's modesty, is how impressive this result is. A question this simple and natural is something one would expect to have been answered already in the 19th century. (Brill-Noether theory did indeed originate in the 19th century.) And if it wasn't answered in the 19th century, then one would expect that the enormous advances in algebraic geometry in the 20th century would have polished it off. The fact that the problem wasn't solved until the 21st century indicates that the problem is very hard. Many people tried to solve it and produced only partial results, until Larson and Vogt answered it completely. Regarding whether the theorem is beautiful in light of the finitely many exceptions, of course it is true that theorems without exceptions are prettier. However, the existence of finitely many exceptions is something that mathematicians have learned to expect, and to live with. Sometimes the finitely many exceptions have their own beauty. (The classification of finite simple groups has finitely many exceptions---the sporadic simple groups---which are very beautiful.) The existence of finitely many exceptions also usually makes the theorem harder to prove, because your argument has to take them into account somehow. Any argument that is too simple can't be correct because it won't explain the exceptions.

I'll never get tired of seeing professional mathematicians getting passionate about their own work! :)

This follow-up video begs for a video to be made on Brill-Noether curves and what differentiates them within the broader family of curves in general

Man as an amateur mathematician, and one who briefly pursued a degree in Mathematics, I'm so jealous, but also so very happy to see someone who has made it as a mathematician. Hopefully one day I'll appear in a Numberphile video for something I've found. If nothing else, that'll be a cool bucket list item to cross off.

I feel like the title of this video is going to be in a rap song some time in the future

I think what most mathematicians fail to grasp the profoundness of, is that with the infinitude of numbers, there are so few exceptions and they are of such extremely low values. The fact that we can prove these theorems (even with the restrictions) using such low value numbers is absolutely mind boggling.

Love her enthusiasm! Really fun videos!

Why is her enthusiasm so contagious?

Amazing work!

This is so cool and I would love for a deeper dive into this, maybe at main channel pace. Let’s have more Isabel!

we can agree Analysis has the best tricks in the book, but Algebra is the legit magic

Great explaination!

Beautiful, Beautiful result!!

Love her energy. :)

Great video on the general Vogt-Larson theorem. Any relation to Robbie Vogt?

"Do you wish it wasn't kind of a little bit ugly" is a great question about a piece of math :D

A brilliant individual

Very cool! Since two of the exceptions are (as I understand it) in 3-dimensional space, is there a way for us to kind of easily visualize those?

You are such a good interviewer

Is the Noether in Brill-Noether theory Emmy Noether?

Well Done!

This is so cool. So beautiful. Great job!

Hmmm I wonder if the same tuples appear in the tropical setting! Perhaps preserved under degeneration - but tropically I could believe more tuples show up because of tropical varieties that aren’t tropicalizations of regular curves… Unrelatedly, I’m also curious: in these exceptional cases, how else are they geometrically realized? Consider an exceptional case triple (d,g,r). Does this imply curves of of genus g embed into their W_d^r(C) in a special/unexpected way?

Congratulations :)

Funny enough, I did heard about this theorem from Larson himself in a seminar talk, but I didn't realize she is his collaborator until now.

This should have been part 1... (and with the duration of part 1)

whow! well done

The only name of the all the works of the persons that appeared on this channel that I will remember forever is the "Parker Square"

awesome mathematician

What a delightfully strange result!

so.. does this Vogt-Larson theorem have a wikipedia page yet?

I could tell in her eyes that she knew this theorem might be named after her, but mathematicians are generally a humble bunch, and as expected, she would never think of naming it that herself.

Brady man you called her achievement ugly 😂 she didn't lose her temper though good for her

great! The CRC16 is rediscovered!!!

A few questions for Vogt: You mentioned that the four exceptions are curves that live in a surfaces that do not pass through the right number of points. Is there anything in common between these four surfaces? Are they pretty? (Show us pictures! :D )

That’s so weird and cool. What is driving the exceptions!? Why is it finitely occurring and in the small numbers!? Those particular numbers

Larson and Vogt and married to each other, which is a fun detail.

Many of the mathematicians I know occasionally adorn themselves with some kind of mathematical object. Do Professor Vogt's earrings have such a story?

Obviously, this is the "Larson-Vogt" or "Vogt-Larson" Interpolation Theorem.

voght-larson interpolation theorem, obviously

Great at math, not so great at drawing circles ✍️

I love how excited she is to explain this all, she has a great vibe. Would enjoy a lot if she was my lecturer.

Sadly, I don't really get it. I'll have to take another run at it.

I'm guessing that r=1, which would cause problems given the r-1 denominator, makes no sense because you can not have an Horizon of dimension 0.

I need her to extrapolate more info about the exceptions.. ! #Numberphile3

4' 26'' 😂😂😂😂👍👍👌😉

Funny, I didn't understand anything about the theorem, except that It seems beautiful, and also she is a cutie pie.

Fields Medal contender?

What would make someone think fo complex numbers though..it could have all real solutions for all you know..

I've had to watch the pair of videos twice because i was too confused the first time by the four switches at the back of the book shelf. WTH a library has wiring behind wood in 2023.