Dennis Sullivan - The Abel Prize Interview 2022

1:44 Manifold explained
4:44 Space according to the prescription
5:26 What can be deformed and pushed, in homotopy theory, in the homotopy type as opposed to the actual manifold?
7:10 With the surgery exact sequence?
7:40 Milnors influence on the area - combinatorial manifold case
9:44 Hauptvermutung
11:45 Obstruction group in dimension four
12:32 Galois group and the study of manifolds
14:56 How can we view manifolds? As we would view algebraic varieties?
16:56 Poincaré moments
17:36 Fascinating experience during PHD oral exam
20:58 Have you had any similar insights in your other areas of study?
22:10 The Adams conjecture and the MIT notes
26:36 The rational homotopy theory
28:00 Cohomology determines the entire rational type, eg. Kähler manifolds
30:41 Dynamical systems and their importance in studying manifolds. Impact of Denjoy, Herman and Yoccoz
37:42 Influence of Feigenbaum
40:15 The non-wandering-domain theorem
41:40 Dictionary
47:44 Is there some type of mathematics that you don’t like?
48:10 You promised to replace Newton’s calculus by Poincaré’s combinatorial topology
54:50 Is Navier-Stokes problem one of the hardest Millennium Prize Problems?
56:51 Selberg said “I believe that it is the simple things that will survive in mathematics.” Do you agree?
58:53 Sullivan comments on Abel's philosophy of mathematics
Abel Prize laureate 2022: Dennis Parnell Sullivan interviewed by mathematicians Christian Skau and Bjørn Ian Dundas.
Dennis Sullivan, Stony Brook University, USA, and the Graduate School and University Center of the City University of New York, USA, was awarded the Abel Prize 2022 “for his groundbreaking contributions to topology in its broadest sense, and in particular its algebraic, geometric and dynamical aspects”.
Dennis Sullivan is interviewed by the two mathematicians Christian Skau and Bjørn Ian Dundas. Produced by Gyro for The Norwegian Academy of Science and Letters / Abel Prize © 2022

[@seantilson8728]

Great Interview. It makes me sad we don't have a similar one of quillen.

[@scottychen2397]

Well hold on, This is the bass drop: @27:27 ‘And then it did’ Boooommmmmm I mean…. Lets not act like anything else compares to that. It hits different when its not a donaldson-theorist at the drop Hits different

[@scottychen2397]

@28:12 ‘Khaler Manifold’ Is not 🕷️ the same thing as an algebraic variety….. Things here are not just some imprecise moldy collection of archaic terms. This suggests that ‘Manifold’ guy is truly more proper about what is actually True geometry…. True physics…. And the Feynman character here is being an IMO contestant relating to the techniques moreso than the meaning of the entities involved, making this problem or event a Problem or event that’s primarily about identifying the correct Algebraic variety: the full set of solutions of a number theory problem or otherwise as an object of topological formation. This is the guy saying you recieved a whopping ‘1/7’ on a question for finding one solution and not the entire set of solutions. In an advanced setting, this could be held in mind with the entire space that is the Khaler Manifold, however the thing of interest here is the question of Topological formation. Not necessarily the quantity of solutions…. All formations of variety are compared to that of the entire space. This is not a meaningless mold of vocabulary - this is serious use of vocabulary that a stupid person wouldn’t grasp.

[@davidfsnyder]

Great! Loved it.

[@scottychen2397]

I didnt love this part: @47:58 ‘No’ That ‘No’: he’s leaving out how immature his understanding his metaphysical understanding - Perhaps not his command, which is powerful - But his actual understanding of the metaphysical - let alone how that contributes to the formation of epistemological rigor: the thing he’s a professor of - distinctions between the various *Manifolds* that are existent. Its not literally just space…. LOL

[@1Darknews11]

Thanks

[@seantilson8728]

Björn Dundas ftw!

[@scottychen2397]

Hehe you jewish boyz @31:45 Now you boyss, I know youre beginers and of course there’s a multidimentionality to manifolds such as milk; that’s correct! But space-time as an object is a 4-dimensional manifold. If you have any alterior to the classical (Kant) ideas to the contrary: that can’t get taken too far. One shouldn’t stray too retardedly from excercising up to and including technical mastery of the Theory of 4-fold metrizablility over the reals… the algebraic closure that is the complex numbers being something of a tangential nature starting from the core of this theory. It starts with a relationship with Uryson’s metrization theorem Over 4-fold euclidean topology… Exercising the e.g. the normality of metric spaces would be a simple exercise and branching from there is where one finds a sense of creativity. However, if you can’t do basic technical things and have an attitude against the idea of spacetime being 4-dimensional, then no more number theory for you boys! Intuition has to be dealt with in a way that doesn’t kill its vitality: the Zariski topology you boys do your ‘type’ - work around isn’t hausdorff Who knows if a singleton can be called closed anymore? As a start

[@mikej3555]

44:50 45:48 47:13 48:35 57:37 The goal of math is to simplify everything ... 01:00:05

[@scottychen2397]

*first time stamp* @46:00 So let’s just clarify here: The ‘Manifold’ - guy knows that if the Data-Science features of SMOOTH manifold being the same is a suspicious event. He rudely, goes ‘no. No no. No no No’ Because this is actually hidden terrain of the thing he actually does. Because he doesn’t give flapping crap about the philosophy of manifolds… (in the beginning) The thing he actually does is (*) Dynamics Dealing with the objects: (*) von neumann algebras And so forth

[@scottychen2397]

@27:44 ‘Algebra does this part. Analysis and geometry does this part’ One must pay clear attention to what ‘Manifold’ guy is saying about the problem’s ‘Rational theory’ They’re talking about bringing a Galois action into a problem of differential geometry…. Meaning that this field of intellectual activity is circulating a picture that IS geometry. However, one is in a sincerely very mature way - an IMO contestant probably wouldn’t appreciate it like they do - taking care of the illusions of geometry here. Not ‘the folliage is located at a pure geometric point and therefore the probability of finding it at this point is 0’ Its: regarding the question of what kind of Analysis Or Algebra Is required to believe one is truly relating to and understanding the geometry. This is the first theoretical step in a realm of professional creativity: this is the sense in which I define the potentially ambiguous term ‘mature’ 🐍

[@scottychen2397]

Dennis, If you can’t appreciate the Euler Characterstic - in all its Grothendieckian abstraction - as a very very peculiarly impressively artful interpretation of the (nonmathematical) concept of ‘Compression’ In this, one could call, ‘combinatorial perturbation’ of ones familiar *desirable* (only certain geodesics and certain fundamental forms will be seen with fixation) differential geometry… Youre not solving little IMO ‘please classify me as special so my Daddy loves me’ number theory problems. So I agree with the ‘manifold’ - guy’s sentiment: why act like a Galois action is something that’s going to become a thing……? 🐍 You should not act like this long list of Witten invariants is going to be something that’s actually going to be appreciated before you can read about this *fantastically impressive* Data-science feeling Concept of compression in full exactness….. as Grothendieck approaches in finite word count regarding this concept that in fact has nothing to do with compression of density. Density *proper* So if you can’t just read , 200 pages of EGA or something then I don’t know exactly what you have going for you….. Witten is a gay pornographic actress in comparison to anything about Grothendieck…. There’s a *vocabulary* youre missing out on.. your feynman-ness then becomes something thats less of a virtue and more of An indian street vender thinking his motorbike is going to be a proper education on the forces of nature in all her majesty

[@supremespanker]

Anyone else had to google slinky?

[@scottychen2397]

Let me telll you, I mean Wow…. I mean a spanker…. That takes me back to the dirac deltas.. Let alone a slinky SPANKER

[@scottychen2397]

@28:07 Wow. They can’t handle the Dirac Deltas…. I did say ‘Dirac’, Im not like one of those… you ….know.. I mean this isn’t…. So ‘Manifold’ guy: This research for the Euler Characteristic with, you know, any combinatorial homology, cohomolgy; you know Anything we can get our hands on: ‘Determines the type’ Type of what.? You could do Homotopy type theory on Bourbaki Proofs. The proofs are paths, for sure. So lets continue being retarded about the cohomology. But type of what?

[@scottychen2397]

@27:23 ‘I didn’t know analysis or anything like that’ This is not what topology is for…… You know, like shooting up European theorems of set theory, completely having lost full consciousness of where this is going to go towards outside one’s hazy trip of formal logic - aesthetic though this may be. Analysis is the sunrise - of - or after a night in Göttingen. A platonic Göttingen, as it were. His ‘Archimedean place’

[@scottychen2397]

They should speak about the glass shape in relation to the Atiyahn ‘Fibre Bundle’ And this absurd behaviour on the part of AT&T and their peoples’ unwillingness to erase the possibility that they’re Just being a bunch of dogs installing some potentially crappy thing on our WIFI systems… Since they cant figure out how to respond to questions like a human.. If the maths involved in this kind of competitive technology is of a certain nature then my demandingness is in fact quite uncalled for. But one would have to see an explanation for this. The hot water in the house is unstable for example

[@massivememer7893]

what are you yappin about