Relating Topology and Geometry - 2 Minute Math with Jacob Lurie

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Many believe the mathematical fields of Algebraic Topology and Algebraic Geometry are totally unrelated, but Harvard Professor Jacob Lurie delights in finding the connections. Hear about his work at the leading edge of mathematics.
Professor Jacob Lurie visited the Fields Institute for the Séminaire de mathématiques supérieures (SMS) 2018 from June 11 to June 15, 2018.
The Fields Institute is a centre for mathematical research activity - a place where mathematicians from Canada and abroad, from academia, business, industry and financial institutions, can come together to carry out research and formulate problems of mutual interest. Our mission is to provide a supportive and stimulating environment for mathematics innovation and education.
For more on the amazing mathematical research we support,
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Visit our website - www.fields.utoronto.ca/about
Music:
The Walk by Split Phase
Licensed under Creative Commons: By Attribution 3.0 License
creativecommons.org/licenses/b...

Опубликовано:

10 сен 2018

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Комментарии : 41

@Israel2.3.2 4 года назад

Weil Conjectures comprehension is certainly one of my goals prior to passing away.

@leif1075 3 года назад

Why if i may ask? Amd are yheu hard to understand ?

@josephhlavinka7732 3 года назад

@@leif1075 yea, the weil conjectures are mad intense; entire fields of research mathematics were revolutionized in the mid 20th century to actually get a proof of them (and Sid could be angling to comprehend them because the revolution really was explicitly driven by them, so they're mad important), and even now at best you're either gonna a) spend a whole graduate topics course actually building up the machinery to actually prove them or b) take (or self-learn) a couple semesters of graduate coursework that already assume a couple semesters of graduate coursework, after which you can begin attempting to slough through the proofs

@leif1075 3 года назад

@@josephhlavinka7732 Slough through..why do it then..sounds awful and not worth it...just curiosity..that doesn't seem like enough always..and I wonder what makes them so hard..

@kreitzerova2371 2 года назад

@@leif1075 They're very much worth working on precisely because proving them is so difficult, as the mathematical machinery that people invented to tackle that difficulty has really pushed the boundaries of mathematics. That machinery nowadays finds applications in many areas from machine learning to string theory to biochemistry

@leif1075 2 года назад

@@kreitzerova2371 well as long as it's mostly fun and and enjoyable though I hope?

@differentnamedchannel 2 месяца назад

Man "Higher Algebra" and "Higher Topos Theory" have been in my list of books to read once I'm in some kind of a long term comfort zone.

@rianakanthi6752 3 года назад

I love him

@Anican1008 4 года назад

I totally agree with you on the statement about college calculus. I'm lucky enough to have hanged onto math until probability, then my mind was blown.

@reimannx33 3 года назад

Yep , I see evidence that you are a captain bluto mind- pretzel.

@leif1075 3 года назад

@ Anican You mean you don'tlike calculus..which is what Lurie seems to imply he doesnt like it ejther..? And why and how was your mind blown by probability..I'm reslly curious..i find probability very unintuitive..

@jessewolf6806 2 года назад

Continuous Probability requires calculus as a pre-requisite

@leif1075 2 года назад

What about probability blew your mind??

@NoProbablyNot 9 месяцев назад

Omg speak on it. Idk how folks don't get this

@jessewolf6806 2 года назад

If the first college math course had been number theory instead of calculus I would not have pursued a math education.

@Ruktiet 8 месяцев назад

Fully agree. Let’s not forget that math is anthropocentric, and so every topic in math can be traced back to ideas arising from problems in our physical world. And in that sense, calculus is a lot closer to bed than number theory because it has a lot of familiar, intuitive geometric ways to reason about it and be applied to.

@gogigaga1677 Год назад

GREAT GUY

@reimannx33 8 месяцев назад

Stop going gaga for him upto a homotopy.

@leif1075 3 года назад

Who wrote the music in this?

@FieldsInstitute 3 года назад

The Walk by Split Phase (check out the full description under the video).

@leif1075 3 года назад

@@FieldsInstitute Oh thanks so much I didnt see it.

@shupingwang3392 4 месяца назад

Affected.

@bringiton5282 Год назад

He's so cute !

@erronblack5015 7 месяцев назад

He's a genius, he got perfect score in math Olympiad won gold in high school

@andrewkelley7062 2 года назад

I myself go for a concept over direction. I will give a example. I once thought of a situation of what would be the best sandwich, which through some harambie sort of events lead me to a equation that I can only describe as more beautiful than I thought possible. Then again there were several contributing factors. Do you see the edge of the null. Star trek deep space 9 the smart ones. Nope no engendering just ,random, beautiful,, right,, just for context. There solution. My brain just did that thing you know from when you learn something. like times tables. We all find those hard until our brain does that ting where we just know.... to time..and . perception then it well it went far enough where I know you will see this . Which is all I need to get my point across. I am just trying to help.... What would you like to know , what more would you have me do.. linch pin mostly instinctual. people ginuely like you when what you feel like you is you. I relate. There are things bigger than us. This is a approximation of what I got back from all of you that is why. At least I took the time to... To show you something beautiful. not you the hole. ya we will get there. give it time.

@andrewkelley7062 2 года назад

you don't get it duality is a mirror. ohoooooooo

@k.s.whitney8282 2 года назад

This 2-minute lecture took an abrupt right turn at Albuquerque at 1:20. It set you up for an example of algebraic topology then hit you with some non-sequitur gibberish. Guess I’m gonna have to drop the course. 😆

@ronaldandradetineo4391 Год назад

Is he high on something? He has a striaghtforward and calm way to presenting and debunking things.I have seen him on IAS.

@Kinghercules 3 года назад

I like that it starts with calculus..... because it weeds out the weak. 😁😁

@antoniostojanovski9008 3 года назад

I think it is a bad idea,the idea of the school system is to actually teach people something.That's why globally the math scores are failing.That's why a lot of people don't know math or use math.We need as a society to have more people to know math,not less.University should be less about choosing the ,, right people" for something there are no ,,right people" . The problem is with knowledge being associated with productivity and industry, that's why selection is made

@ryanchiang9587 5 лет назад

modern mathematics not so hard!

@rokujadotorupata4408 4 года назад

yeah, essentially it's just abstract and much more general, most people find it hard because they usually think of math being about computations and think focusing much on abstractness is philosophy, while really mathematics is a symbolic\diagramatic language where abstract objects are the words and abstract concepts are the sentences