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Midsummer Bures Dreams

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In the past year around and I don't think
I ever gave me my life such as speculators talks as the sponsor of an infected intake the kind of I wanted to convene announces Title I hope to have more deals with consent from you have now the 2 of have some what the damage that has all but died there in some of the couple a couple years ago was a conference here and I was giving a talk about some kind of development and flexible side of scintillating topology and I kind of declared in the following up of humanistic principles of instant elected topology just that is beyond philosophy could there's not there is nothing but each principles like whatever whatever whatever is not a candidate for a restricted by Michael Moore because he had it isn't can be contracted them and it exists I kind of my took days and that it was bit in the similar speed when I was talking to them and then uh fork I wasn't Jorgensen and he asked me questions kind but can you just make some say statement but does that mean I still can make a precise statement but it can afford to let me can see a few more words the direction this last year or 2 so I have some kind of justification that they didn't have to be immune to the sun so taking and can affect my major general kind of direction is the following that the the infected apologies there methods coming from this cheerful watercolor for in different incarnations and there are some kind of results and a for 10 many wonderful results for approval in the direction especially this is the home of a curfew is powerful in dimension for for instance you mentioned Gromov proved too and that is unique extracted on on foreign kind of essential if idiosyncratic manifold which is a standard standards at infinity it will look like a forward in the ink is on a visit to the addition of new McDuff the result is that it's in fact these are for up to maybe blocked sir In high dimension kind of this whole Moffat covers the same sustained same tempers the ideas they give only the political itself and so there's is also a result by a floor among government felt that said and hiding mentioned if you have a using something just differential topology can prove that if the manifold the standard like impinges on the Standard provided the politically provided the princes and water because investment In but then this is kind of a completely different type of herself so on Lake In dimensions intervention for it will be in a similar way and that is a disaster proved testosterone which is that if you have a Lagrangian manifold enough for regions are at infinity to look like tools and this Lagrangian the manifold he's up to optimal doing this the book so inside dimensions you think all again powerful home off corner methods we have a lot of results about constraint Foreign Service known this manner for him to be honest with you these if properties and then but that is not known there is absolutely no I think called using this will morph to prove that its effect Hamilton his adopted some kind of version of the so-called nearby Lagrangian conjecture and my point is that probably because this is difficult because the kind of looking at this problem in the long run the main so that this is already a part to this type of results already belongs to each principle and and you need to prove that his age principle that state and that kind of weird talking something considered acceptable so let me on that 1st review just a few kind of the recent developments in this flexible sense of subjected the project so so there too Maine flexible object which you know injected apology and them going to world the Over .period manifold there a lot of Bloomberg News and continued to any what is and what is what is that going to manifold get it and maybe maybe not portend and precise definition that is that nowadays mainly in Kowloon definition of the word
instance what models definition is the following is a good taken but many of them in there that we use following finished up in mansion its most loyal mostly long enough and in dimensions he lives in a mansion the is just said there is a certain it is danger In the context the manifold beaches a danger along the boundary to and extraction and In high-dimensional you can say that kind of 1 of the crew definition which is in effect due to the presence of precise this is the same as the manifold authority that if it contains product all sides this added a large quantity ball part of the agree but that that that's the important thing is the contemplative alter the audience that even there is a a certain particularly contain certain practical wife for that this is some kind of embedding or something and that's something can be very small and accuse there and and somehow this kind of implementation of this virus made the whole thing so is the same in the same sense said that is an agenda and and this is not a motion the floor of the genre not is In the technical is it's an awesome in in the 1st is kind of introduces phrases notions of this context manifold meanings of this agenda not could complement of at least but then I don't that there is proof object is very similar property exists in high-dimensional Condit manifold and it ain't going to manifold in all dimensions regarded great cities and again does matter whether particle diffusion for instance there is a certain local local local construction called abbreviations which you can make this dish and it's not and you can define the agenda not the fool even isotopic customization from others again an agenda not can can be made to the some local local modification it again this is a symbol of the similar suggestion that as soon as have the smallest can lose virus than names that all the completed flicks so there is a on the 1st glance this kind of 2 different objects but their diet literally the solution and not an inch or that conduct manifold on the related to 4 I don't think that stage here I'm going to at least the same existence can prove that the world will house Over the serious problem but I'm sure that covers of which said the following the so give isn't giving any meaningful contact meaningful then Condit manifold you can make it's kind of of like didn't synthetic manifold that has this kind of standard construction of simplistic taking product of simplistic manifold is this meaningful the opposite complete extraction and the same you lose contact man for the day conduct manifold is simply bad that mean you multiplied by buying up forget this syntactic manifold and then you take this simplistic manifold this kind of life in that it is simply extension here and in this manifold have this product and have the diagonal and there is a diagonal elections here but you can cost portion by our action here and then you get a call on Commission and the diagonal now after the question so you don't you get new conduct manifold and you get this kind of again Lagrangian diagonal remaining and want to get out you get our diagonal as you 207 manifold in the this protocol and there can he and it should be the rule that this manifold deliberately that if and only if there is a diagonal for the 2nd so I think in direction that's pretty easy and this project because I I think proved is that it is if authorities that the loss but you know what additional insurance office from so also consider that there are many other kind of connection but the this and all these things for and supported however going to come in 4 and a half years and you can always have a construction of over a
given given lesions that manifold you can attach a title Lagrangian and the thought that simply to handle like thinking about this manifold is the boundary of the synthetic manifold of kind of part of its
computerization can at the that you attach a candle to this and this handled by itself is just good and bundled with score of n-dimensional and so can just a type in the boundary over the disk itself is agendas and many of the loans abound in Europe but also Of course you can you have this is going to have that he's got it can also kind of subtract him currently at that total to this man so you have also this construction and so forth forget to borders between Our regional context manifold and other Condit manifold negative side this month a if they need and not of more than there is out there already is simple pity so they said this was not an updated and what I'm kind of looking back in my dog I will be trying to explore this notion that the battle between the different versions of things statement about agenda not listen to and Quantic manifold "quotation mark another kind of let me know if you Morgan analogies between the 2 regions the situation and worked the court so so what Coleman feature that most because he had completely failed in both cases so if you if you have opportunistic Condit manifold or dimension greater than the dimensions of the again special situation because of all this and that ,comma from all Jenkins and stuff kind of related to gage here but inside if you can't that if you tried to define for instance according to algebra or any kind of invented based on because you can get there is this algebra is identical equal to you sir there that relative version of older insisted that invariant footage and and some manifold for instance you can define this vision and more job but also for those manifold and again if it's lost its identically this year and like those that serve no way of extracting any any variance Out of forgot and hence this was the motivation for me and for 1 for Murphy infects to prove think believes that the fact that I think and you can the result for hearing prove in gaze at a almost context extracted eased the uh whom 2 to genuine context or at least at current extraction and dormitories that Conde extracted using the Foreman who thought that they would begin to exactly the same result health in the world who called in the legendary so it can result which we have in Asia and the world is simply looking at the Lagrangian mindful of his agenda inbounded is that this and it is on the inbound use is on negative and so we consider this eclectic manifold this gone a negative quantum about that means that there is getting manifold and there is some type of surface human W because of the heat you have the Lagrangian Lagrangian submanifolds is bounded on 1 were on the scene and negative abounded in the sense that I simplistic form is the exact meaning that bounded it is a doll as a .period could increase pointed to the fact that field is considered postponing the vector field standards and that's the negative then when there is a genuine boundaries this it's very easy to construct a Lagrangian mania for views bond that any formal Lagrangian class is realized by the recession engine manifold and again you have complete page principal aim is to do such things performance hasn't opened their event as elegant Lagrangian isotope the Estonian isotopic even then good you glad about that I need to be alone to move so I'm slightly slightly lag because if this is to provided this is getting this is the and enduring the sizable appeared this Lagrangian maybe more mobile more Balkan I made maybe changes Lagrangian at some combo part but not that fee In other when you take it like this and then you kind of spoiled this Lagrangian his 1 single point again you can have the virus in in this Lagrangian manifold look like call over this this and this and this and that and not pitchers the site all is completely afflicted began militantly kicked the ball into again kind of like another feature of this it any homework man for sightseeing Q failed because some of it all disappearances home let's look at this as a syntactic simplistic counter 5 4 the 1st just 1 thing so that have now the national total total to fly fumes at the clinic and said that and not simply manifold so consider non-strategic manifold this is is negative content on the eve of the bond uses bond is over to then this object should become completely flat so like it should be easier to construct the eclectic structure on manifold is this kind of 1 single conical born then again I'm talking about manifold dimensions at least 6 dimensions for the this is a single conical Kabul and he's using single recording clinic point and Saturday at this point that our simplistic form look like simply dissertation look like some victimization or all summer authorities that Conte extraction roundabout some you can't unfortunately we should not proved this is enough for some results in this direction but unfortunately not quite this and I have atomized hold that this old In this form but let what do most of the full up to support you have started with the board that was the 1st time since the the beginning of this year and things that I don't use guns this just 1 we're committed to that the center the that but but there with how hard they get the basics right from synthetic minerals they can get this Lagrangian with help from the independent candidates inflicted meaningful it was the same in but you if you have a simplistic manifold and get Lagrangian but even if you can get a against the analysts and services to have the support of plus the fact that the some from school board said this fact Saturday from most borders if don't demand for G minor the blast well we want to make this a border them into the eclectic manifold it is called the bond so prescribed here some quantity structure and prescribe here some context project and we want all this to be a negative "quotation mark inbounded the ball is going to not fell through
1 because that simply manifold because it it's near the bond that look like simplification and negative and important simplification of crisp on the course when the mountain flew into concerned about have of course you need to to have almost complete structure in order to the the theory is full of them so that the animal welfare myself so in this situation again dimension dimension dimensions lesson on the mansion is at least 56 so far for then and you can always find some you need for land that that's a newly formed the blue reform 1 on W Saturday there Is this clampdown on Monday minus
W is defined defiance of the minus Lando dipped last month of the supply line of all owns boundary this against negative and impose reportable disease bonding provided provided this is the form that means that the land that the land synthetic this is elected compatible compatible with Jr but by then the following conditions that 1st of all this the mind of overtime that In In this context actually make a difference is the worth that and unfortunately I need the condition that the the responded by rounding up about that is not an issue so in this situation is thinking of this book is about the features nonempty began all this past election eclectic aboard them on think if this authority said using the city's out which I told you before that that uh the the surgery surgery on the and surgery on move the agenda nor is there Of all the agenda is over you can easier to prove the following results that you have always been dimension in dimensions uh agreed agrees is greater than for you can always find comportment between any conduct structure in order to use the structure for the isn't it they get manifold and multiplied manifold by buying federal then you can find on this manifold syntactic structure all always in dimension beginning not for but the thing is aimed plant extracts different ways that you can just kind of users facts and Elizabeth observation of customers Murphy and therefore the statement you can replace it by just assuming that both about overworked because political body plays any company founded by that using system for essentially the statement that you have to work conduct structure and correct any political cabanas impotence them almost complete you can make it simply and inside mansion this storing all dimensions including 4 but inside dimensions this isn't in addition implies that on the structure the positive bond could be stands in particle in particle much of the work would begin to get a sympathetic structure it and they get a but they get support both now see M 2 and if any clause in and then any global manifold and say that that support almost gone it's almost complex almost conflicts in the complement of 1 point so there so that complete almost complex structure in the complement of 1 and then you go 1st duty some small bowl of this and make this into some kind of Kabul organism which is look like standard Ottawa and conduct searches in gym and you're asking is it possible to construct Simplot extracted all the manifold this manifold manifold 1 wants anyone on the manifold minds .period construction collect extraction which is suspended and so the ceiling which I mentioned just at the beginning all of a flood among the government says that the this manifold apologies if he is simply extracted apologies from Vatican artistic essentially just have to be on the bottom if I allowed 1 single point and there is a single reported to be like cold were called for physical expression of fear that they can do it on the simplistic so I think particles in particle of it after the Commission which which I said it in the following ways that you they get a new manifold which you want to make a simple and then if you connect some is already enacted many of which simply think that this manifold always magnificent that extracted . com for what but all I I hope that in this situation much stronger for the beaches of Hall's 1st of all all the completed this would be unnecessary and moreover moral use of health care in parameter question of just simply picked apology on many of what should be a nonexistent let me know have moved to kind of felt that this was and still is not the image of itself except that this is only a a small piece of so let me have now moved to Baltimore to the yeah again yeah that's kind of right opposes analogy between the Lagrangian a relative cool situations so you so the file to think about this kind of simplistic caps Lagrangian kept thinking negative bound but of course it much more interested everything positive about suppose suppose have like mind staying so his band manifold sold you thinking about this is is we can think about that some simply accountable for started that his staff that is this a ball and the status of architecture and along the long 1st isotropic manifold and get some kind of meaningful features also critical and then you start to look at the handle along news and some manifold and you get In you Weinsteins handled want to
get the men forget the manifold the contact abound so this is kind of important class of manifold of course all stand manifold like this for all filed a brakeman for this it's important glass class class of of forces that the manifold and we would like to understand their simplicity porch some it was not since long time ago some -minus time manifold I'm not so interesting contends sense that if there there's not handle off index than this manifold is its objectives is determined by Q colleges and again it's manifested in some kind of homomorphic statement that the subjective so far this year the generalized by renowned bought a miscarriage back to some class which recalled flexible 1 so flexible stunned many folk it's 1st of all if object again or dimension greater than for sold starting from 6 and flexible Weinstein manifold this the handle border where all handles all critical handle attached along and internal or kind of more more precisely to say if you can find them simultaneously and they have to be passed along with the school loses and link that means at a very attached inclusion and year have to be losers complement of all of the songs for this movie lose 1 Wednesday thousand manifold lifetime handle boarded again have been using inflatable knowledge and again it is the approved it said said that satisfy kind of complete each principle in the sense that any any manifold Bishop potentially can be my stand manifold I mean uh looms of flexible Wednesday project in any to such structure are homotopic provided provided that therefore money in the same class the Commission so there is no so on 1st glance the it's kind of again known that a single object flexible won't stand for but not quite recall I but on the of the flexible manifold still have a very very material context character for instance on the tedium of of earlier class that if said that that if you have such manifold that context that even if you know that you have a contract meaningful and it's Kontic manifold but this flexible Weinstein men involved then the bond is it then the Concord bounded contexts such as the Member for instance homology homology of movement and infect infected said him some kind of work in progress In his letter for and not the kind of things that in fact much some more subtle topology remembered by but I can't expect it not completely all the benefits of glass because of course it's straightforward total because it someday tumor and then what is called unionized .period acknowledges that there has to be isomorphic store 2 for or what is called the stage blast simply to homology is determined by the boundary has to be to the manifold but this existing depends diffusion depends on station which depends on the future of the fact that the independence of the inconvenience of fat for any anyway so thoroughly saying that still abound that kind of interesting soldiered on so all the things he had it done out to be much more subtle than intended for the use of mystery barked at the beginning so there is additional work of the kind of legal and that in much the same the answer the following questions we asked this flexibility is invariant under 1 thousand book so support you can taken Weinstein's structure and the 4 others Weinstein's structure and a glass of wine and the question is should remain flexible and and kind of like critical question has the following the political some Weinstein's structure on flexible manifold and have some found sub levels is flexible has it also have to have the ophthalmology but turns out of there as examples and a sub level set of Weinstein's function can only flexible manifold forms kind of wrong 1 instance function can be more flexible so things that Peterkin subtle but it but let's let's move to listen small to at the end of this year so what is and work all flexible last time manifold in the Lagrangian agenda Inc the support you have now the Weinsteins windfall we have a the meaningful from the bondage and now they have Lagrangian Lagrangian some manifold this is not the Lagrangian particularly granted him Lagrangian some relief from the business agenda so I'm I'm talking about the Weinsteins manifold squandered boundary and correct the agenda and benefit is Lagrangian but thought it was just a majestic tools for you that there is in this In the class of Weinstein's manifold there exists a the glass with the school flexible Winston manifold whereas if have a
kind of Candlewood construction told dimensional Phoenix and handle attach a local news agenda and the soldiers have this kind of like completing the Baldrige this is my question and like all this the movement stalkers can to title to have this analytical all result analogous to result in the relative situation and the gold futures to support a Lagrangian now you have a good some and men condom like them in provisions sir I would like to took to call what does it mean that Ellis flick so far so some for example but what would you want to be flexible thought so this is it but I want them talking is again part of kind of something is discussing currently children at the end of the article as so so what all examples of his status as W and yet they can take the product of the number 10 in the simplex extraction and began his brother you have the Lagrangian but because the Lagrangian diagonal and this Lagrangian diagonal use and about I want this to be flexible if my W flexible this kind of money runs important example the 2nd 2nd example mission which moves afoot to support I can anyone standing for and now I suppose I'm expecting the handled along with vision in so losers and then not by by the the did not about the exact I want you to that exactly executive so they cannot buy aren't exactly 1 of the manifold because if they do that this would kind of cathartic and whom go prohibits now this like this can the jury rejected his call for home-office Rokocoko Lagrangian there is a bad patch this is of course you can convention course and I want the school quality and escape to be flexible 1 flexible Lagrangian so what is it that natural before the here a kind of conjectural definitions of what but flexible like the engine manifold so for this is the following so what is it that when and where many consider them front the considers this uh Panhandle kind of critical Weinstein's cannot the good bands and bundled off dimension and this this could this handout of course contain 2 Lagrangian use this as the jurisdiction and that the fiber but it also because they can go normal models because they can call normal bundle all over the world I think it is bundle addicted to it that they get is abandoned what was contained in his mind of all responses have just handle and not now I can take it now and I can take a good normal bundled all of some 7 views of smaller dimensions so if you take care if the sky is the goal and then this is now Korey keys coherent scope or about the old intermediate for a lot of this Lagrangian and what would want 1 when I do this my handle border In the latest at the provide money and that than they had ties to handle simultaneous simultaneously at the manifold and something that so another another rate like you if you talking if you don't think in terms of so you have this W L and here we have the more functions most functions on his back and I want the critical point I want this critical critical points Citigroup 1 of the restricted to I'm also a critical point critical born all all on the South so when I when I took each time I have the conduct manifold and my Lagrangian promises some I have attaching fear for the candle which is again redundant and this attaching the need to intersect my mine while that of my Lagrangian manifold what called cleanly as long as it's known does that but along some fear some Equatorial sphere of smaller dimensions and then when you are tied to the scandal yacht that's kind of smaller handle which is 1 of those ,comma normally to to Lagrangian so I always while this might critical points while is critical .period 1 might stand minister-level Phoenix and but 1 Lagrangian that can be of 1 2 3 in the 1st this that so I want for this is the speaks to me but I know what it's like to be a key condition of computer condition following that the the critical so critical points over all the index and so on and off in the case this is a list of the things that have different the condition of the I don't know if you can estimate that the crest Christians but you just show of support such thinking supposed such thinking this In addition I want the following conditions all right critical pawned off the or else on although the index led and so on my Lagrangian submanifolds I'm not allow critical point of doping in its presence this Lagrangian cannot be called it must feel about so I want so each
time when I have the here which in Investec my bounded off Lagrangian along for this is that some at attaching sphere the agenda and
and intersect this bounding along some Equatorial sphere I want this feel to be in the compliment compliment all this intersection for this kind of violence if someone has to be outside of the 6 4 the French Lagrangian is if you have people at flexible so if you can find all know manifold Wednesday and functions the you have this problem you can use the I can contact me conduct manifold you can call it that the fact that is I kind of building on they have already this my manifold and of a piece of flagrant and instrument in our touching and I am attaching handle along some and I do not think this past and the so this is that this is the boundaries of the flag around Jenin and this is a decision and the and the Long Beach the required to intercept these along some quite a few of the greatest benefits mountains that handled the Bulls of could this also have a very transparent interpretation in terms of this uh left handled would you became so so he could have lasted and so now is the oldest worker from beginning from donors and in the latest of a general pardon finally can take a last time manifold and you can kind of presented this fall so if there is left fibrillation over the years summer by critical this is fine and the fiber itself is manifold from all the other lectures presentations and number can prove this yet I think but certainly the withdrawal that there is this certain kind of that can be proven in the same period of boulders partners now that if you have a Lagrangian submanifolds in this Weinstein manifold that it can find this Livshits picture in such a way that this Lagrangian said many folks who projected to total according to about so this centuries of existence cloth case but that kind of should 2 old friends of relative of gays and that in this case so that the cell Lagrangian would pass through the bond bunch of this critical point all of this leftist probation and and like it will be precisely like I'm looking at the complex analytic
function and it on all Lagrangian manifold it's that they carry it's kind of real analytic complex analytic expansion of really function this is a peak so for them and that this kind of reserve hand of the West Bank cannot hear what exactly will be used as a symbol of all the political forces Cocoros for instance some anyway well the cycle see the flexibility in number in that suitcase in this picture so this is all this is I think it can like worry it will take part you can go in there hearing sojourns but I think that if you are thinking Gillett about this so uh but I still think it's understood what it should be an easy means in terms of left to speak but so I think 1 thing to I drills have good with questions of this that that I think what's your question some of the questions that I think for every Lagrangian manifold such presentation but there the flexible not flexible Griffiths could it was the Commission and flexible conditions later flexible that all this handles asia and in many of the definition of flexibility for a closed case that all decisions texture and he just 1 additional genes that there is a complement of all this so you now I want from 10 of the conjecture kind of 1 while the dozens of them the 1st I'm kind of British that this is ruined and the I'm almost 1 could prove be title what it 1st and for the 1st time I have seen the statement that it would give the statement in a closed case and I want to formulate them kind of their analog and so on the 1 statement in the court case is that when we have the aim 18 almost complex manifold if this kind of borders have homework to be done before of dimensional think that it means Western straps morally flexible instead of 4 I claim same came through here support but they can you take in Wednesday for and taking some any submitted for decades and any medicine men not just take it any any from submitting false vision formerly a Lagrangian which means that I can think it like mind-bending and I can kind of forms 2 0 2 2 Lagrangian engine plane and also agenda about the former it looked like this thing it is either topic to delay granted some manifold is too flexible like so any any submanifolds Ugandan allies as a flexible like that manifold if the that you anyone OK so that was kind of 1 thing the 2nd thing that the flexible seeing him all then the 2nd thing that this flexible objects have not sympathetic topology namely again if you have to such objects so here have this kind of L 1 and L tool so you can
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Formale Metadaten

Titel Midsummer Bures Dreams
Serientitel 2015 Summer School on Moduli Problems in Symplectic Geometry
Anzahl der Teile 36
Autor Eliashberg, Yakov
Lizenz CC-Namensnennung 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/16321
Herausgeber Institut des Hautes Études Scientifiques (IHÉS)
Erscheinungsjahr 2015
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik
Abstract I will discuss some questions and conjectures concerning symplectic topology of Weinstein manifolds.

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