General discussion

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General discussion
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With Olivia Caramello, André Joyal, Laurent Lafforgue et Alain Connes
Point (geometry) Geometry Confidence interval Student's t-test Mereology Power (physics) Mathematics Lecture/Conference Different (Kate Ryan album) Ideal (ethics) Mathematician Series (mathematics) Posterior probability Area Forcing (mathematics) Reflection (mathematics) Model theory Content (media) Mathematical analysis Lattice (order) Numerical analysis Connected space Category of being Arithmetic mean Computer animation Logic Network topology Spacetime
Point (geometry) Dynamical system Presentation of a group Group action Greatest element Divisor Decision theory Multiplication sign Neue Mathematik Event horizon Rule of inference Food energy Theory Group representation Frequency Goodness of fit Mathematics Coefficient of determination Lecture/Conference Different (Kate Ryan album) Modulform Diagram Körper <Algebra> Amenable group Position operator Area Dissipation Haar measure Moment (mathematics) Content (media) Sampling (statistics) Division (mathematics) Volume (thermodynamics) Line (geometry) Vector potential Diameter Proof theory Thermal radiation Order (biology) Duality (mathematics) Normal (geometry) Musical ensemble Thermal conductivity Local ring Directed graph Maß <Mathematik>
Pulse (signal processing) Topological vector space Presentation of a group Cross section (physics) Group action Greatest element State of matter Multiplication sign 1 (number) Solid geometry Mereology Grothendieck topology Mathematics Sign (mathematics) Many-sorted logic Different (Kate Ryan album) Homotopie Analogy Conservation law Series (mathematics) Position operator Physical system Area Process (computing) Moment (mathematics) Sampling (statistics) Staff (military) Maxima and minima Price index Lattice (order) Measurement Connected space Fisher information Category of being Exterior algebra Duality (mathematics) Phase transition Spacetime Geometry Point (geometry) Classical physics Computer programming Observational study Student's t-test Surgery Theory Force Frequency Goodness of fit Thermodynamisches System Lecture/Conference Natural number Reduction of order Energy level Set theory Pairwise comparison Addition Forcing (mathematics) Prisoner's dilemma Physical law Diffuser (automotive) Content (media) Mathematical analysis Total S.A. Division (mathematics) Volume (thermodynamics) Limit (category theory) Numerical analysis Equivalence relation Formal power series Elementary arithmetic Logic Universe (mathematics) Musical ensemble Marginal distribution Maß <Mathematik>
Statistical hypothesis testing Group action State of matter Multiplication sign Modal logic Insertion loss Mereology Food energy Perspective (visual) Explosion Coefficient of determination Mathematics Many-sorted logic Meeting/Interview Homotopie Cuboid Circle Körper <Algebra> Series (mathematics) Fiber (mathematics) Logarithm Theory of relativity Sampling (statistics) Physicalism Infinity Fixed-point theorem Category of being Proof theory Sparse matrix Intuitionistische Logik Order (biology) Normal (geometry) Figurate number Relief Directed graph Point (geometry) Computer programming Observational study Civil engineering Theory Power (physics) Frequency Goodness of fit Centralizer and normalizer Lecture/Conference Simplicial complex Modulform Energy level Theorem Associative property Posterior probability Set theory Scaling (geometry) Forcing (mathematics) Model theory Commutator Morley's categoricity theorem Algebraic structure Incidence algebra Cohesion (computer science) Sphere Numerical analysis Logic Network topology Universe (mathematics) Homotopiegruppe Family Maß <Mathematik>
Statistical hypothesis testing Complex (psychology) Presentation of a group Group action Euler angles Correspondence (mathematics) Multiplication sign Equaliser (mathematics) Sheaf (mathematics) Survival analysis Function (mathematics) Food energy Meeting/Interview Cuboid Position operator Physical system Process (computing) Concentric Moment (mathematics) Infinity Flow separation Connected space Order (biology) Quantum Spacetime Point (geometry) Observational study Variety (linguistics) Rule of inference Hand fan Plateau's problem Theory Element (mathematics) Product (business) Goodness of fit Thermodynamisches System Lecture/Conference Energy level Condition number Weight Model theory Physical law Content (media) Line (geometry) Algebraic closure Universe (mathematics) Game theory Musical ensemble Collision Local ring Maß <Mathematik>
Geometry Category of being Group action Meeting/Interview Different (Kate Ryan album) Logic Game theory Distance Spectrum (functional analysis) Set theory Spacetime
Category of being Shooting method Process (computing) Observational study Meeting/Interview Universe (mathematics) Commutator Right angle Basis <Mathematik> Stability theory
Computer animation Newton's law of universal gravitation
as the and I think the and the urgency of few
words and totally unprepared who's to say something about what died like about the school Kilman is the connection between geometry and posterior and logic which what we can see in the talks and top that began in in the 1960 was the work of growth in the economy as students and it has a started a new way of looking at them in many subjects especially the connection between logic and topless and this is something which I believe will continue in the future as we can see we're tired Topol series and possibly I want to be tied to so I think that the future is it is very bright for topless steering OK so far and what I would like to say you know is a following is that a good and he gets a bit of a elite and inadequate surmise that the tradition of duodenal well somebody and a standard so as Albert we said Kennedy yet when we title when we began to organize and dedicated as organizers in all but lower than in mind is following without reminders that the what struck me during this conference was the fact that their hands people that normally would never meet and would never so the reason to talks of Gaza's did to come to visit and that the unifying their reason for that was exactly the ideals of the Bulls and there and I find this really amazing because of the very different arises from which the people were coming in and of course there is a to be silly and it's I mean when I was reading books in July Tubergen Sunday was stunned by the fact that people will not use integration of topless even tho if they had used in many many properties that they were dating which would have been far more conceptually understood that what they were doing so this is striking in its deep because feature which I cannot explain that I would ask you the questions which I cannot explain why it is as assists numbers which means that the people and like to use hole the worlds for pollution which already exist since final 55 years and Delaware instead of using the Web to oppose a professor to the 2 they'll know which end and that makes an increased I was this means not only in the eye by topology meaning many different topics I have witnessed this future and there and there but I have no explanation and I mean that it is the intent of 1st when we hardly you to organize this meeting is the intent was intent was to which attention as is away is a world the goal posts is is considered by the mathematical community we it's not that it's not done it's not finished it's far off home because of forces always expanding media that I forgot what it was citing wanted to write a paper about the boss and he was advised to instead the category of shoes because the word itself of top posts is bad and didn't make it he doesn't and I can't I can't tell you why I can't tell you why because I was on the other side for many years so in other words for many years when I was in danger work to post but will image that they out of the top post was a very strange to political space that I would never have to use and and you know and which had a I mean which didn't which was not part of the mathematics which I like very much richer of concrete where you OK you have a lot of problems analysis and for and it's only when I understood this is and the fact that smaller categories naturally give rise to a proposed that I said this is 1 of 4 so I mean that what I am saying is that they are among the most mathematicians those who don't except world tuples England's World 1st of all I wasn't known for many years and there and in the end the in life and is not only mathematics ignored this implies these days In because having no and they prefer to react to the notion by disobeying and by some kind of content because they don't want to make their faltering and that in in the poem Whitstable silly pulling is that it's not their fault which you can do easily when is defined for each mathematicians as it does on this model that we'll have survived all why don't you could be Sabado it could be fund or it could be the same but the better but whether I hope is that the disease confidence as executive these babies at each of you at some point as has been touched by all we know this is going to look at you and you have well of course stated that he shared the same view of things that can infect them with only inspired by you they're looking at what the goaltending keen sense of the wrote about the notion of topless text that good in Somalia which is a text of reflection both mathematical and and philosophical on sense silver over the course of that the growth in the Kennedy introduced and developed in writing his Canadian and saying that the core of what those with the strikes said and about to the Stacy's their insistence on their own the unifying the power of the notion of Topol said demand in many polling said he knew to be today than top Aziz unifying the better the can they can allow them them to embrace it and ball for the continues entities created to unify different areas of mathematics and so
I think that now we have Maine a situation where I had to pursue reasonable certainty sufficiently in Maturin from many technical viewpoint tool HUD and the analyzer decent dream although unifying the different branches of mathematics that and I think that I think that the notion of classifying the doubles which was 1st introduced in the seventies is particularly suitable for formalizing this idea of unification for formalizing their had been the phenomenon that there are 2 completely different looking to mathematical theories that might actually had the same in the content orders directly related mathematical content and so on and so I have tried to to set to explaining 19 and my costs that taking this point of view of classifying the position seriously canner but he needed to to let a great amount of the a surprising insights across the different mathematical fields but not just because different theaters even if you want to study just a single mathematical fearing head and and the fact that the Furies assault over leaving Gordon even is not that bad things so he designates internal dynamics so basically this internal dynamics of the fury translates into the fact that the eats classifying Tobosa Denise these multiple representations and so am I. by yeah they plainly that you can really extracted a lot of information about your fear is that you will do not have the sea and Weaver uncertainty glasses let's say so there is this element of magic if you want of surprise that they're easy Dineen opposites and I'm sure that we are really had a very very beginning of exploring guided the potential impact of all of these soul in particular might my in my open use that a we've all the tools that we have had the air in the school locker room and asked whether he illustrated this wider-ranging the impacts of this notion and especially there and the potential that these are getting very far from being gay and exhausted but it's still life ideas for the moment the fight thank you the government customers Republican-sponsored upon school this fall said What's Eating radiation is there and we don't go in now going to have a certain another it is respect so-called outcome of of while still on the witness stand on the matter and the Federal Council must John carries on uncovered some hope Labrador Shashank it was still more than 3 years could cause and native son was closer stronger because you have a good young steadier and I'm gonna speak a couple non-aligned Dong people said the orchid was ordered to Bosnia to Brasilia and did you former rule 1 out in prosecute call sound much easier under the Jamaat miscarriage of Baker and a bomb on designated days and then the dissolution of induce good goaltending DZ helicopters and my Aunt Mabel while little posts Cecil often think it is a valuable commodity in Dundee suggests shoulder to bulldoze the all the naffness refusal by the 1 of the goodness of Annika movie a diagram of the locomotives existed you know 88 32 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he did a very good in the generic term authorities there also possible breaches of law the mall we bowl along laughter yeah yeah but are still get desire to explore at your command to sneak onto the category key developing 1 of the the 2 new deposit Montana but in the end of the contents of the simple to the national debt upon such only memory pulses in the sample examples I like to post at the end of the year distributed to the matter and the Student Conservation the a prosecutor differed sheltered officials Nokia person official keeping the cost of the proposed that a cross-sectional images total modafinil sort of promoting a Club my copies of the many computer scientists at the yellow development unless there is a limit appeal the tumor to pick the 2 people in the middle of Americans proposal forces in the fall maybe I could switch to English for while so now we see that there is something new happening the 1st hire proposed 1 that it is not the end but that's important 1 when the subject is not really productive there is no development there is no important development in it I mean the fact that post Teri has a given rise given rise because clearly but the people who were invented higher proposed to really went directly and spar by 2 so that the fact that was is involving it's a very good sign for the subject it shows that Tobosa is not only double Syria has dozens conceded but maybe the music wanted to have a higher proposed to me too but as you can see it in the of pursuing staff I mean clearly this is a dream of higher preposterous that he was not able to 2 to create for various reasons but is so a this fact on 1 side however compulsory which is very important for geometry I mean if you read the work of Fleury it's not easy and it's very extensive you can see that it's it's that Wednesday that extremely general and direct very important for geometry and there is a school of around Lurie and my Tompkins a lot of people is especially dangerous state developing on higher geometry and have a higher proposed to really and stable homotopy were also to be found stable communities accessorized of those on this idea and it's it's really this is just amazing and there are many things that I did not understood in the past for example the constructions of the time space and couple how can you I mean time because he was he at time when the 1st with and there are new ways of understanding this construction and for the 1st time when I saw that I was a paper bag and get now and others and forget the name but I'm sorry what working on OK so that 4 2 for 4 people and when you when you have this new approach and when I saw the definitions of 2 of the Times phase this it is so simple and it just capture everything this is something I waited for 50 years that is there now it is very very simple Seoul and under side you have the logical side which is also involved with the woman to beat the Turi I was never looked at that to read is maybe not yet I mean this is a program I would say eventually we can all that it will become user-friendly I mean something can you imagine city of on Europe desk and you open and you start doing some proving things using this formal system if it's user-friendly and powerful it will be a lot of emotion and that if there is no doubt it is it will be the I cannot imagine how big it will be hard because young people are going to use it to mean that forget old people can't like myself who can't learn this stuff but clearly young people are going to take it and proved things that the older people's can't prove 5th and then so early don't posturing is still the connected to look out Erie and the classical logic of geometric logic to testifying to posters it is also booming yes so I'm very optimistic about the future just a few words about the distinction between elementary and growth in the 2 because from the point of view of unifying different mathematical theories we've each other they said particularly important aspect of growth in the still possesses them as opposed to elementary top Aziz which the and I basically did the essential difference between the 2 is the fact that when you have growth indicator was is you have site's cites a correspond to presentations of the year so basically a In some sense then and you don't have that the floor inventory doubles has sowed the seeds that are very important the flora formalizing Geddie said duality between now and the way of describing the mathematical theory and the eats a mathematical content as incarnated by declassifying doubles the so I personally think that that be said duality between the sites and that the opposite or between back somatic presentation of series ended body and incarnations as provided by testifying that was disease of outermost importance and NBC's is also an aspect the director of course it could be
also generalize ideas that was the set I didn't at the time to go to those about that in my closet of uncertainty as said most of the essential features of and then 1 mission the was usually carry on at least there's some and at the we have dialogs of the notion of Scitex the uh the carry on that Liestal positions we can certainly expect a decent unifying techniques a tool to generalize that at the moment we don't yet there had been a former maxim that the care and definition of high yeah genetic logic but it will surely come in the next 3 years as you know we have a semantic understanding of them aah wed led the sees that the United We really want any new with me they furious years although analog of the international language so I yes yes I yet on the yells of site ordering them language about what we would like a unity it led idea genetic so these the Steelers lax but I'm sure it will done and there and so I think it's very important to work on between this Seagate I mean I'd like to encourage people to investigate their howled the was very thinking that audience expressing themselves different presentations of all the topless because that I mean on the city's formalizes the data feeling Golden looking at something from different points of view so it is very satisfactory to have died disposability over materialize engaging and precise mathematical objected he intuitive feeling that you might have so you might find yourself working in a certain situation and not the things certain vague analogies and there's some vague connections there and then and you wonder what is really behind all of that and there's what a with suggested linking them saying that this situation is to try to identify topless that captures that it would be a situation that you want investigated and then you will have a 1 was that that he presented 1 point of view and then you will add another doubles which represent another point of view and then he would try to compare the studio was overseas to see whether the equivalent of created in another way and a few of our lucky to find that the nature relationships you might extract that information from the comparison of discussed classifying double is which would the hardly be visible by using alternative viewpoints they I mean I like compare and that the wisteria beat that with genetics of mathematics in the sense that that that I mean when you although genetics for example genetics allows you to all of I expect the sunny formation about individuals for example biological information about things he does it to counter to see could make the eyes so you really have to make an analysis of the the of the DNA sold considers not as that something is intuitive as uh surgery or of traditional medicine so if you are in another uh situation back to the kind of these sites that unity ingrained there are harmony held attainable using different thicknesses of Aum leader was feared is a bit like that in the sense that the you you can really get that by studying the very body and send from the point of view of different presentation before sides you can really feel even aspects of the fear is that you would have never imagined at least at the city's said the then on the experience that idea of the maturity myself and we and 1 we don't have in hand mentions in Treasury debt issuers unplanned and don't get me on my PC young Soo monarch stuff also additional metallurgical Eastern don't all men that within cannot stand appears from 2 monitors specific perceived as an area to get 88 uh no committee John until they got in the car the Jets he could not see seemed take on it just gently good answer yet do show some bottles the prom have had the solid dated diesel deep intimate Dodger Nevada did Tudor this volume on the record number of times although the collusion denies ski breakdown of American Museum .period community consistently initials piece of East again insisted upon aspect a mail sent young notify spent a reduced number of donkey but as they all want of university not saying a new costly visits businessperson Dyson um is Feb . owned by former Bremen gotten the Council did that both of them adult pleasure no pool what did he leave this is faster more kills features on the addition of status is a by disaster lead exposes loathsome Anabel Becky from on measurements as you make it dilemmas ostensibly dough when there were present at the meeting could indicate the city did in the end of the day the others is sparse the body from he also didn't want vacancy from Darfur song of his own .period no decibel Mikey aptly summed got William about it the best as he Yum sedated remained the donors you don't 8 men the level of on bottom especially Indonesia is redundant so warm almost study you go into geographically limited genealogical speech aspires and for the public indeed it middle genocide did to this process of Filippo alternate jurors who had their share of the lead to assess does its best not to create a 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these are already there shows perspective you would he often don't follow Goss on the form he the top post developers on the Hill Sitaula Pocasset Tobosa a of under deposed pool Pavlos and 12 of his own tender pleas e of many of these calls it don't go over there In these orders reported last year in that possibility there are brought immediate not there are calls don't do this at acidic smell also long gone nowhere in don't go on good consulted Idaho that deleted the person above an also overcome congressional steel was a little boy good monitor the until leadership dead Gouzy of this mayor of that day the pussy believed they all got prolonged by the middle shows good key must have been a good and and the Dozier another partner you intermediate interfere also said good news amid the follows a might assume it looking Jimmy is a mistake if from this origin is a questionable you know me irony duties reduce your me because young bond is going to be deleted a bust as he jumped is from this sort of logic all ensures good physical Markleysburg approach Sigurd Laloo he kept it on hold public companies supra good a it is wrong on the menu special from the subprime operational Marquez is set down in Goma the norm among the global yes and no longer associated out there until we get a lot the Minnesota completed their leader demanded it because the continuing and was you know what IndyCar in Armendariz Ahmadinejad Finnegan deleted that they be action the new way a good dose of civil Monday's murder here has hit upon a general owner did tell the pilot and in the film study of see although of it you know senate he began to go them again although EPA deserves it normally now have seen until he did get to go again was yet but it did till the sold on Mars did give Soros said Adobe the continuing Dunnigan can on there we begin to go again was young men and an was possibility will be by Puyallup hour don't I think that they will be deleted the deposed as he jumped for proliferation of share them Our consisted of Nabokov Devdas as you might think the plan all that and Monday good was scarcely young Italia probably had the gun was effectively the goal not done until we get was used the technique most of that sample possible we get there many pleaded but average possibility of beyond .period until people when there will be no museveni of Exeter deleted the was because he killed that they could told me ontology now having good only the stadium was evident in Memphis will on Monday he's smart people permitted to get done however the jubilant view a lot of energy source in shows until Sonoma memo busker Paul Molitor that is due I'm a delight and under space CVC did this put your on In the assumed he meant was amendment by some that I do it he did on Alonso dog sees as you do or you don't was of the sort of Moffett opposite you was young it don't sent me whether that's your local so that what was all this you already there it poll mustard and kissed you impose a but while there disputed you have yourself a lot it looks younger bluesy a delay born on a scale as it gives you he .period press those on Doublemint amid deep although he founded by lock up really instead the older would lose the ceremony in upbeat on Sunday it will not move was out of the start of the cool relief but that last BC CC did you know the better misappropriated property could yet export unit the deleted long runs In this before services are equal access to imported from futures also concluded were Minnesota something that is the microphone but you don't use it but many I would just like to come to amplify something that Andreas said that some minutes ago under recalled I think if I answer correctly the origins of categorical logic and Bross intuitionistic mathematics also mentioned brought impact on topology brought fixed point theorem and then went on to say that it's a rather remarkable that the listeria gave rise to both hired the posteriors with too well it and there's also this relation to homotopytypetheory where people do not keep saying that it's
expected that a lot of Atlanta is supposed to be then turning language of these Infiniti proposal would just like to amplify this point may be the same person who has been pushing the unification of all 4 of these points the most in the last years for just might Schulman who has been doing some contesting were consideration Europeans forces people like to speak about having this 1 model for more to be done through simplicial sets and I think it's worth their while to recognize that Mike is merely produced to infinite families of models of appreciative infinity balls 1 of which is that is the 1 of the current homotopy theory which goes into a quite some research level of modern research level territory where actual water be serious I think I'm more likely to pay attention and then just to close the circle of ideas that starts abroad just in his latest I he considers cohesive for what retired theory and gives a formal proof in there In intrusion which abroad 6 . theorems to inquiries about what had theory if possible to actually speak about the continuous circle its with its genetic structure as well as of the it's somewhat B type is you know Casey 1 and put these things together and using the profitability only of homotopy groups of spheres he can actually Reto Braun fixed point theorem in intuitionistic but now on what the authorities but the thing that is a beautiful unification of the 2 this kind of history of but posterior that has been happening just like advertisers figures is a beautiful article that and I think unifies many of the states that have been mentioned in this year's conference called something cohesive from what we theory and brought 6 . that's what I wanted to say thanks 4 and I think all these seminars has convinced In case the need to be convinced of the importance of .period series Seoul I know the country but they want to Phil and Lil Bit old number 10 all of my program there not because it is my program but because it's for me philosophically very important number 10 it is what they called the police for the language I'm not meaning the language of losses and meaning the human language which is the greatest achievement of humanity which has taken thousands of years to build I think that so In mathematics has benefited from the physics from my astronomy from the trade Central that may be there is a possibility by looking at the language 2 defined important structures not necessarily publishers I want to give just 1 example apart from the thing which I saved which are very elementary namely the notional which is in the language of the notion of small which has a very big contend is quite bold some smiles that may arise or that will certainly arise at the notion of small To take all its full power need the notional fiber category and some deep consideration on fiber categories which are not necessary publishers or fiber categories over topples the camera and they couldn't talk about this notion here because it's much much longer it would be much stronger them the things which I say and yet all right this is the mathematical development comes from better understanding just a better understanding of etc a better understanding of small and forces you 2 studies some structures in fiber categories would take I don't know the only so the language provided you don't violate just as I said the view you violated the the notion of etc. If you look at it and said sets that a week necessary force you to invent New In interesting and important structures that's what I mean by before the language not the language of Bhopal worry although the internal language of the language human language it is the most fabulous creation of humanity and maybe it's time now we didn't have the tools but categories or generalize categories all its addressed central might benefit From a study of foam fragments of the language if you have something to say it's time now he military officials and all she doesn't know Nunavut India but over 70 on the Hill through the 1st half of this this was the 1 that has only a screw industry controls don't but ultimately foundation repulsed "quotation mark put their family to to oppose the a & Sons tourist facilities there don't put on that others wonder the report was on the course of all this to your own stuff to do reduce your digital laptops that to be the top pulls the doorstep considerably by the time of the incident use to fall the stitches to close the ,comma may pretenses at national conventions used to you look as you all know will travel the comes hours assistant chief costs to consider become the longest that Kewell versatility and Ct more protective of companies owned by the media pursued many users post for while was concerned we understand the problem there's this girl that hindered the Schabowski execute on our own dolls do do Quoc group should give a man that would give usually take care needed to
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think exactly attendant opposes this what goes into the Quander exercise works inconsiderate has been amplifying for many years now is that 1 version of speaking about 1 commuted his stance quantum spaces as regarding them as multiple bosses in was beset it but a stable infinity getting worse or if you if you wish essentially trying she's doing this so but this is passages here could these things are connected via the proposed to the stable infinity carries the weight of the box and condoms has been considering as long as the president will which is what we assume there are sheaves of spectra so they do sit inside the tent the possible corresponding sheaves of Infinity's 6 and is in this way note on the art of conversation while you know what a beautiful it's kind of try to explain audible from the Prix quantum version while the tension proposes to the consumer so suggested discussion
with Telmex in a couple of weeks ago you said something about not None community and not geometry effect that some of the men effective came from different cultures from you can pop was said at the Bruce etc. to kill from a distance it don't to about stable categories isn't too cerebral to pop assisted upset all calling it's infinitely innocence on but the can afford to be different game and to parents and enrich different food that use lots of small but spaces but spectrum into it's just that and also in the plenary Bhopal sociable and thinks about props and I think it's good and doesn't knock Mitchell polluted rhetorical sets but said CSO it's me and which you know
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