Add to Watchlist
Symplectic field theory and its applications
46 views
Citation of segment
Embed Code
Formal Metadata
Title  Symplectic field theory and its applications 
Title of Series  International Congress of Mathematicians, Madrid 2006 
Number of Parts  33 
Author 
Eliashberg, Yakov

License 
CC Attribution 3.0 Germany: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  10.5446/15951 
Publisher  Instituto de Ciencias Matemáticas (ICMAT) 
Release Date  2006 
Language  English 
Content Metadata
Subject Area  Mathematics 
Abstract  Symplectic field theory (SFT) attempts to approach the theory of holomorphic curves in symplectic manifolds (also called GromovWitten theory) in the spirit of a topological field theory. This naturally leads to new algebraic structures which seems to have interesting applications and connections not only in symplectic geometry but also in other areas of mathematics, e.g. topology and integrable PDE. In this talk we sketch out the formal algebraic structure of SFT and discuss some current work towards its applications. 
Keywords 
symplectic and contact manifolds J holomorphic curves GromovWitten invariants symplectic field theory 
Series
Annotations
Transcript
00:00
Ladies and gentlemen it is my honor and my great pleasure to introduce decor forget their very generous with completion national treasure got his Ph.D. 1972 remain grad nasty bidders will begin under the supervision of Let me retire told of his dissertation woes singularities of mapping Nash a took kit
00:26
Officer position at 6 feet being there Camira public after a difficult period from months summer tonight to 1987 It was allowed 3 rate from the USSR a United States of America in 1987 visited mother was Sciences Research Institute Imus are in 1988 enjoying the mathematics department of Stanford University 1989 where he has been ever seen he now chairs the bottom of the present area researcher gesture Judge Merrick Victor topology the discipline that rule from the contested Deborah months ticket geometry underwent in the last 30 years
01:08
Under the influence of many people particularly Hyampom off but also Because of the Porsche from article physics Simplex job 3 really appeared As a geometry when your kind emit more clearly shows freed icon of aging all 18 on Nevada he assumed Among and then was fully established by Stern William Hamilton with Carnival contributions by dark winter could be in the 2nd part of the 19th century and the local content of the theory was completely uncovered the beauty of the series praised by Fiji's signed his introduction of real mathematics of the 19th century but . its usefulness the emergence of quantum mechanics in 1920 gave a major impetus for food developments of the theory and shoulders relevance for a wide area reputation The shift toward global subjecting geometry do some more time 1st major step was taken by Eugenio cannot be in the 1960 use but it is my Hyampom turned things around somewhat later by exhibiting completely new rigidity properties of automotive them simply manifold conjecture by got me back down over number fixed point of simply Dakota more reserves Also in Royal Dutch guess started to be interested in Greece Problems in 1979 and time Conley lanes and approved solved most conjecture posters further important evidence on due to the directed Andreas floor
02:44
Dutch I guess big started a very fruitful collaboration with for 1995 she presented a new version of the nominee mental series he developed for reasons 19 99 thousand abortion offer and given tough These lectures gosh I guess would pose where Subjected field interpretations stands today Yushan measure
03:08
So how
03:23
Of course it does what Doesn't work on so they team As Some have mentioned that some Prodi which initiated 2 years ago a a defender the poor and it's not You're 5 from being completed a lot of people contributed road just Building based in the occasion of the and this is of course not completely and that Below the people will look forward to working too simplistic conceded that can they created there were very relevant and I will not give their names because I definitely forget someone so what That is It is Some kind Being in press corps subjected to so complaints in Germany is Germany All not degenerate Keating had been biting him for like a kid in German German estimates for so Semitic for him at least 1 bears the signature but the kitchen at form with unique and the the differential form always candidate in this form And the old and the importance of distinctive about form is in the context of complex structure But if you think about it Even the event of space and convicted territory only listening and dimensional space and think about the babies as A complex for for Senate to take it for granted My imaginative part of the standard permission from so Lickteig manifold is a manifold locally modeled on the air After this special form and because that would be the with fear that many of them not just on the genetic of differential before and very important again later is Based the consider making journal Former together this complex that And in this case On the almost home extracted man complex expected on engine by the surface and that this is a compatible Simply for what Relate to chat the same way is the standard make a performance standard on the structure Relate to each other again So It's important and the very crucial for them For Ford called a development that almost extracted you only get all the plan Compatible and this is Jane moral as this is the kind of convexity should adjacent contractable choice but uh On the other hand if you ever GAA Always was Find the combined elements warning that mice slurry or so A big seek manifold unlike the cause of the 1st glance look like peddled 3 Miami The medieval methods for more amenable but unlike you my Make it meant for a huge group of more than a call to let As well This is probably due to the fact that You who visited some semantic for together and then and left 1 over Do and that is pretty medical and and my 1 or both of the stipulation due Such a fugitive So the group In the 3 dimensional case and make a lot of sympathy for just performance and the German that's a German German area preserving sorry but I did mentioned this is radically different from the group of some of them for really brought by an amazing closed this year the Polar due to the continued of the group is Progress of Group of the group of William during of Spanish so as Aziz's again created fundamental TNT Open the and make things so Soviet city algebra 0 4 0 of group consists of simply declared the field and this is just a cruel this is vector field The shares this Rogers said If you contact later for closed form an especially you would like to have that they consider the case and that the dual for what is it that the end then this functionalist called Milt Diana responding that field called mobility and that our and will by the simplex gradient of each and AT going so in the bag book orders of course ever within all oldest analytical form for a From the rebellion backed the field And the burning patient differential for the floor of this form be don't mind Richard equal could go to the gym So for AT compatible woman candidates Victor gradient just uh They are Very important obstacles that elect Sanchez said This may have the on Danish and Matilde site dimension can be Just stop And and in the context that evicted tonight by the property of the new were multiply By J. that injured they become almost over so there a dentist who most important example of Lagrangian manifold money they could then Bonneville and put them bond lamented that the canonical eclectic extract
09:40
As well as differential is famous for being killed and Section or if you like and even on the course For this section particularly if you have a Differential functions in exact form is Drive you that I will be with function is Lagrangian and on the other hand if you consider simply manifold with them what was then a draft in the productivity they can make former former on 1 of my most of them the draft of the Lagrangian and its oldest and the important Victor German then When you have a 10 months before and then Lagrangian manifold looks like good out of the automation and another system of course they look like they're are beautiful from sold This is because of this huge group of more than it's very difficult to find to convey beyond some of course because but the what it's in there and then a class of compatible with that man and that the clause is Molitor glass Although eclectic form is also in it but it 1st forum for loser Beginning 80 if nothing else was long essentially what some minor things and this further The Ronald Reagan Introduced flew more thinker As the tool for finding more settled Recent lexicon that will discuss this today Subs Let me but is about the plume met with almost quantity When the Fed last weekend as easy to talk about The more met with was composed manifold as In this Citizens for in just a differential called in your map But this Unfortunately it if you if you load the dimensional source manifold failed to mention that it doesn't that this is a highly over 3rd and never having Solutions genetic look so it's at That the miracle of the Christian immigration in the Group bookcase encouraging mention solos but as well Band The then and by the way this is almost gone extracting coal on the England Argument is that they the same This he just come form that In this case you have a look at it as a system as the Edmonton at exactly the same degree of freedom of practical Norfolk may have entered bulky and they pulled what occurred this case also J. also Jake along what they want to develop and like should because it doesn't Take much sent Because you on the phone with injured title fight to the this end of terminal edition If a motor where he and the schools and is appropriate under conditions that it exist them and Its principal single the same as the of bar It does Ripken applies then the called CDA and understood that Besides I sound you define model is a civil war water could be fined but finite dimensional manifold Dorotea's or before And algebraic German text but gave visitors They just don't sell But a Aziz's again of course Saying thing but it is extremely serious so his physical coolant of a worldwide and introduction Almost all of the treacherous to both matches that like You get a much more freedom of acting says called end another big German onto debate genital it take that as to how we can achieve that but he added that hope that you can ever a Almost as The freedom of the topology is chairman of the Senate But unfortunately it's not who I think he is Almost but not quite and in some cases indeed you can achieve the society and just forget about the button that gave it to infect too and that the class of fuel in talking about somewhat generally accommodations and more perfectly but I will not rule this But that is a huge step a line of Michael berated him off qualifier and scores devoted a lot of Building appropriate foundation for this But it so Local As they said in the non general cases find But If you want to get global Adelphia need cover the back end He is a stand of 1 of the major result was ruined by nonprofit ruled that there full Uganda Through similar is out at the end of the famous Clothes and the amount of composed provoked vacation or Does the space of But there is a big deal Get on the end of the The new about them and stay difficult to control this so that the role of subjected format Come south of unity in this born so Let me get the call to think about the amount the case so according the lower implementation here you can't talk about the among such as this might want the same as that about 4 For this condition
15:59
It is the same as hyperbolic may take on on the surface This condition Saturday and the stability condition described a just ensure that have cut their voting on this thing and then So there a competitor against Amount of the stained by nodal surfaces and they looked like a union of toe cast in Reported interpretation and the division means thinking loaded it will so the stability condition that they have the justices fight forever to comport grow come back here with the same but the difference this stability conditions be acidified quantum competence of God which I Sometimes called Is the band of flight Modification of remove compact so this is that we make a this phenomenon bobbing 0 4 60 of that doesn't exist in this case and took about 3 months and That separated the role of Objective for Mr. area but the point is that this Compatible deal on that day the famous any meaning means that I'm just integral or simply for And because for of that depend only on the home allergic Alaska over the net of the and so the new Our considered more vicar Molitor class you don't have to be worried about control of the same rule in that his body weight problem is about Lagrangian manifold So what Of the findings that then will morph occurred here with the began April called extract compatible with the woman then Victim but defied Based on what they could do with GE if he wants class Can be viewed the cycle as a kind of similar Indiana each model is based on just more of which is kind of Much more much simpler object and it's the political And the compactness theorem into a more underclass Of this cycle remain unchanged than Mandla J. wild Keeping them by visitors today Therefore because old G8 and from what not again and we get A physical remorse Is just the latest let me give examples of that Application and this Area is and somewhat in the formative years and is so Let's Baker said called simply cannot problem it's from cold About so let that hinted that based in our 40 Corsican been would the kind mentioned by the 1st known to their 1st In a minute period dimension for consider ball and Copley is a small hole And that idea of this quality Smaller than that of the ball and the but that thank you thank don't 10 those to We to put this by saying they had thought it would be a bowl of this fall And this is a clear that it's not possible for revises forcible so what to bar that in this set as the End Then what At because old called extracts Here the following property the ball is just who for a standard wanted it and PET spent an author near Our her near the value of the remaining part of Factory Lane stand by And because this is power All the context there should be because It is comic book gold to sets can easily poke prescribe almost compote structure you on someplace and just continue to extend elsewhere The condition that it compatible with They did for So what do not make a Lagrangian cylinder in this place just 1 like attendance even seem to get this End of the that Model is based Diaz is 1 my point Is not not so received before the war of course This led leg cylinder with deal by led Lagrangian and you get this kind of our room of conveyance this site has onedimensional family of this Lagrangian and this cycle black Then the need for Don't expect for a GATT have such removal of and This family together they form some kind of 1st stage this Lagrangian Lagrangian and when the bull by passing through the called it some woman has In the exists and moving war and so that for and some are meant to have a is being run again and its center said it on 1 of the flag and all of this will and then this month we can look at them The area on Monday can begin Computer
21:40
At the intersection of the feasible of more Inside ideas in because These will watching these abound like engine manifold and therefore It Keep it just as they said If that The band simply invented the depends on the regulars A Lagrangian it's difficult awhile or by and was end I can consider this area Looking at the wall itself and the ball The book this And the extraction society ever cooked passing the template of the center and at what was then that the perimeter iniquity over this Should be bigger than about where to get it Growth but then so is this Not only do they regulating mitigated by he the bank of break information contained in girls and saw that the could this summer Let's consider those subjected combative from the start I think people who the let's think about this problem the glasses some differential for on moment and then this can physically motivated not the defines that could relate that just pulling back these the model is based on what they got their wish The 1st might 2nd at center and integrating over or around so Uh soon forget I just said before the vote him but is 0 this is it And then we would like some kind generating function for older could relate to It takes basis and the call Molitor and not just to talk about Who Molitor thinks the bases with J and And then they did it defy any any home Molitor class can be expanded as bases this confusion Monday and called us Geibig and just do not distinguish between deed And this Mojica so this valuable forms All of this For the basis for knowledge and uses the broke even but then shall function for call for all could relate to that exist formally committed it's important that day that he has agreed Both the same grade followed better bridging could keep that then we get this thinkers and each competence even greater than the semantic expressions of and If you look back expansion in the variable get all clearly for the meaning of related as the very simple did just that if you consider more Do The political Molitor class then It is It was explained Don't often legal yesterday would be counting accounted allomorphic fur coat Sound Subject of it in the list Conditional offer that is taking some might want to 3rd don't cycles So also again a bit further including socalled descendant the variable If you don't No we probably will not be able to learn from my talks not just what I just want to say that You go further and the The but Incident In indecent more because Imposing some restriction on jets sophomore guard his and it said Traditionally that The way and But the important thing is that you will you did this to grow them but then began the depend indicating they instead of trying a visual dimension of so June hero But All of this Expansion with called pressure over most of the attention And foreign For the case of seek don't let's take just stand the basis of a pool of this wine and the twodimensional formal for the radical world class To Just projected flat the stand in the way of the Cold and consider this function would 1st Variable could of the theater wanted to heal and only things a lot this month we the ball and and so on
26:19
They gave and have very simple enumerated meaning that it wasn't yes The dog is number of rational got home given greedy and in the competent in the projected played by Kate Once the general It have standard number references to go through The boys get by 1 lands at the end Biogen was because the relation between a number of points the good he did not define Anthony End What I would do little to discourage some kind of Jimmy data generated by That filthy rich in explains that talk computing fucked This is a Today A name that means they couldn't procedure that From Kuhn said For computing this number bye I will some another 1 This Others also infect clause toward a queen of impotence and thereby prevent them from running biking so that the following consider this is a dimensional space over there should beware of formal 4 years you just can't think about this as a formal hoops in Space of and Accordance I to the and the bed just 28 confusion on expenditure Subs Notice that not constant and so that it considers them eclectic form the face of this eclectic form Richelle focused on the bottom bracket B and But I get to them while Is it will book to Emma Because of filter candidate contender in this form to think about this Bless back is a stands on foot or just defined on quote that That and collect the South be viewed as this saying that possible because that Senator DeWine basis for don't want she might him Anyway so this issue pretty famous which appeared in May A team of intangibles depends and the Hamiltonian signed on on this space We don't want functional on this you'll so let's take this month and in defiance of the Floyd to register with the Commission get these situations And this isn't there without beard dispassionate tho they could not continue Don't ladies and it Maybe that is 1 way to it just The 2nd order differential equation and I was told by the growing Knowing about stood before dog cellblock So they do that now the following the following a construction Let's see Big 0 section in the in this space Section in this phase attend space to or is equipped with you so you can think about is if you think about them free expansion and they just take 40 expensive it's only for the provision and and More days Reflection on the outcome of the so there will be some wounding Lagrangian manifold and not and against manifold building there have all or some of the with functions of the genetic by But some functions he said But the area in the world of formal power series of graphical and so can were fined dysfunction duty and finally a Bluray this function as this Particularly for And this is a sad day all function f expansion this function is is this inhuman number of debris so and it's important that Wheaton Potentially the sector can withdraw written and depends on the Omega So while woman explicitly does not participate in in the never nevertheless Sitting Just keep this bank bigger around and entering role so how the computer room and So it's a it's is is the favorite to take Beijing model is based but nobody ever Show Any kind of Not to little divided Commission explicitly And suggested was the only way to do it is that you've got a deformity of some kind of sued deforming G8 that gave the sound situation very can understand and that Because of the variant of the same as before and money with the just before went on to break situation and another way of doing this is to the genetic instantly feeding the 1 way the and don't Germanton that fellow But we don't know The manifold and the peace talks If you have a the real Cyprus in almost complex manifold began 10 that will stage that they say is engaged just in Insert Deegan and legal tender These were the Almost That Independent from the vertical court and they really meant you have mania for visiting Show this is impossible to do in there In the vote is extremely restrictive but none remove We do that and insect Lyndonville gays and initial portable but much modesty As Bundesliga but given little more good than we do this they also speak up since But would make that a full wanted more delays There's a Vermont Then need So you you you observe the code which looks like a lengthy upper part of some piece of growth in La hot got some support in all of you can get a bunch of civilian parts and there piece of guards bags it all together There's a major babe And they keep that Judge regional curvature have regional so To this End brings The studying these 2 objects this Look on the winner of the manifold which I than cylinder almost all extracted is invariant respect the translation and this is the end of the season But the board later than also made this city because this not Almost complete manifold We outside of the home but presented which appeared as a result of such So let's get more than ever Answered a tragic and vector field danger tormented life isn't G8 and 18 they bird sees the vertical court so this again the same Of the reverse printing procedure Which brings out of the manifold a cynical structure is determined by What is called In the incompetence of the gaps that if ever When our midfield You can In intended would dimensional manifold but it contained maximal won't accept of real good dimension what intersection that whichever distribution of extended the wife And And then you have the vector field I reaches the enemy Duet I didn't even see can always Of course defined some for Beach city by their mother with conditions of they go 1 on the back and on this on this and so do they think it will be be a orbit of the to garden accord with the important role in the story Item on the agenda and that that find that any of them we'll call this kid and Kansas natation for the space court so Carlos then youthful also to consider socalled what what case than a piece of periodic Corbett organized some kind of mania for printers like old ordered to I told you that begin the good thing is to almost complex manifold Unless give simply can control Show Meals and something place so you know I feel that this before makes similar ankle wide knowledge the wife dimensional so that makes rank of course before is due and 2 dimension What is 1 less and So we realize this For cited in the growth of eyes glowing in the field of this war and you end this house for now be preserved by the floor so The same is just say that are also the cardinal was formed Dealer for the better call bears a stable of fracture and that almost contract is called compatible with so There has to be important or from on insect I don't know I would not be like small modification this so the 1st is a floor case so in this case our main ethologist connecting door is not simply to command a and and then consider making of the victim or month let's support for instance that the victim or the isotopic identity originated by Taiwan depend dog in this case I Just before blast Simply in the fridge CD and department the same As In line on August 1 through 2 . of Geoghan letters of my beach and of course due to bad weather I go it as a present from injured 1 of his pictures What This is it kindred just chosen song So there's also Quantum and in the corner but If I want the that means that he is Madam Norman rebel Plainfield landed on Foreman only in this case artist called victory and another is lot of kids and that we get our manifold encircled by the 1st lady manifold and I did generators 1 and the space of Corbett adjust our regional so now we want to discuss Grove In this man they themselves have to be Kansas city Nikolay 1st talk about cylindrical so This means not just that they forget they can't stay over or forbidden to get there and get the whole motherfucker because GOD direction said Jay physical What God and therefore it would like to consider jet All what gesture but you could look like this Still I can't say but just as if is that and the 1st teammates because in instead fresco There's a safety the some kind of funds from the category which called Jimmy good at he old Japan will die activist compatible Jay and what the borders of ending Now Algebraic 50 borders 50 the old guard A differential algebra original discusses certain integral period line so invaded is good will leave Europe nations Because of the stature of the team might other and 1st of all it's not the 1 to Buddha but that 2 Gloria and 2nd that is much more But actually But There is a kind of national version of Stephen talking only about Jim you go out and then instead of this while algebra we get What's on algebra or simply manifold leg with this example and instead of fouryear period to get Lagrangian so by the Mexican border them take it manifold bond out to that and and for restricted to the boundaries This Omega pulasan Omega And I just want to say that you know that in the is there is a how composed Datacom borders and there is no logical was more but in this America will vote in favor Seek aboard the immediate past cylindrical and when they need to compose the borders and we just thank them 100 That just bizarre out things So let me now described 1st of all I need to say about this because it The South in Nunda general TSN district on Monday gays can be Although even depending on this but it don't want that kind of hyperbolic or roughly speaking so Let us As a shade and they vote or or I just sequence to infinite sequences of trade and I gave them face to grading said the same as I just got here even but there is a principle there the integer Beijing Muslim Condit's and this discussing so then I don't them in there End of 4 years so infected and things that we have at this big base where the like a dimension as a number of that got so and you can think that this collection although might just for kind of a collection of all of them is formal who would in the Since the 1st of and this is not just a reminder 1st commissioned as 50th Room Asian compatible Jade the Algebraical so I describe several rationalize and And full so Old international efforts to integrate what knowledgeable generated by this by this variable His accommodation relations at For some bracket physical and all others and this is the same As you can consider responding to that of former teachers just 1 2 and you go Element which it called milk Diana visited by the property was practice is itself so that may not this ages and all this old So this is what practical effect not necessarily is not viewed automated that warranty even In the fullest if he if given why allowed to bring the porcelain algebra surge ever Father business communication relations it said This was brackets figure 1 extra variable Look And kill another element in the monomers W. shows the sizes H promoted with its I would think which is exactly the same as the days go by age it is Europe because bought or sold It's important of course Old people who work in the Senate in order to swell argument can be presented the autumn of differential a period has violent patient which Ector this Both folks the space of functional to variable and And formal Our status in this age but variable And you will I but he sorry I forgot most important here Should be Yeah Then a by confused Not just deal you could get Solo What is Ireland is that more of injured his back just considered a national or international gave them more than in the towpath Found embrace Some functions The edge of the property Hummel Donny and vanishes on Lagrangian manifold Defined by this function to generate making you go that far considers make space there 1 the path of knowledge of discord and This is a priority told the form beachgoers And then In this summer the grace of God that Let the engine manifold beaches jet given by this function And you shut the door young victims field ever Given by function late last each month for the candy Last month called on hand and then it just means that you don't field standard of this so indicates that 1 of the good work aboard them to have addressed the manifold bonded by By made by just Kabul orders they won a run dimensional manifold Then better shape this Just Lagrangian Set based in this space and the bed is enough water them is a combination of Lagrangian Respondents as well I don't have time to explain but this operative For those Clegg engine for these shadow drafts of the martyrdom of this suggests a fistful of the composition of this So where the all this measure found out about relief Registered at the bottom of the model is is lot because the city legal and tidy built described team so this the physical appropriate compared to kitchen consist of socalled A lot of So this is the kind of typical building Similarly Story figure and wonderful motherfucker Neither the logic goes And you have a major they want on Each Begin each floor of this So The Guardian mentioned important things fourdimensional boundaries in the city in pickup game is with that Now what All None D Bill mirrors Not from This Notes that Copeland For a while For water 5 6 you have the 6 from 1 of the good of the bad that And Can't you will always have only 2 story building religion is a good you mentioned 1 that was about so In the case of a delay in the case of the manifold These cylindrical am They count of begin mentioned you only count as is known ghost Erratic cylindrical by at so So why this right because it While the Rays says the algebra beach discrediting who think or Fremont so look at this toast and The bus I would like to consider Or portable way of doing it For instance I agree with this And and Just extend this here Or I don't do it or I this month I rule these days and this is the largest and rule of law says and did exactly the same as I did As a state visit Each of the cell And the end of this And the list My right I'm sorry not possible to see in the picture but it's my by some of the easily I might These aren't but entered by 2 Lauer and that it is a lady says I muddled we get describe describe it And Asia and this is an a by the part of my interpreter So you get this month get Europe you want it to B cities A G not their 30 year due mindless wife Jane of mindless mindless Half of the covenant but figure but he he wanted to be seen End Bonds and you have to want to do While this is month and then you multiply them now while just in the terms both transport old people arrival Who does left or think about He is an 80 body 2 and could take a competitor of the parade and you presenting again this number of And not very efficient gate in this because of the case but because there are Kay Bruins multiple Thursday about 10 and Are going lose This way out of this So then again Also do a big The calls seated in the same way was Grown considered to be defined later and this is a really big fan talented Could seen in the end and it's a subject of Constantin Dundee have to remember what that cylindrical them by Mondello money don't last year And then I got 9 of them in the Related which now become element of this Brown on the And finally consider the June find All this age Agent bond A for this age And then from the floating band of must replaced Much as I didn't have the teacher Consist of the coolest former could trigger a 84 and then Turns out of the question of the following your recanted their age associated with this year's said of cheaper performance deceit that And then they get their share of the composition of them is a cloak these Made that polite Merit That s variable British want deformity available before But it will be difficult We that I Comport ages ago so this is They said it booked for visitors a they say these a our composition differential describes the boundary of the Mobile So that live inside It said in stocks I made some form over the barn and get this month and integrated formal Mayor again this it In many many interesting case you have A you you and this is differentiating stiffener differentiating They say they entered into very about you get the comedy data of AGI and G8 equal with you further HIJ individually and get Sequence Of commuting differential Moreover moreover we didn't get any the dissent variable so you get in Age depend in fainted may never evolve and and fans by this procedure to get is many commuting differential very scared the sign of some kind of 1 of integral system an Indian princess if you do it for the case a smile you get into sequence of commuting integral for the socalled grantback Berger had active this is not thing and you need to take account of quantum version of this replacing would you buy and then This will be commuting kingdom the and and if you do the same thing for for threedimensional sphere and send them to get a good Indigo for when days recalled the dissipation tho thereafter before now county who would go to fiddle So can't let us talk is The same still further Must equation H is for the euro again on while algebra the differing just accommodation and It property discredit across Europe and therefore again would meet Rabbi that with this many gave this far medic Friends inflow we get some tribal reasons in for would look forward which is not be explored the door there 10 without New algebraic structure and cooperation on On the plus bitch Not And the quantity Difficult On the Commodity each year extremely successful story in terms of finding conveyance Maine evolved and in fact dimensions theaters that and competing construction and then was fabricated but in fact mentioned is nice or said they but had mentioned Massingale is not so I don't give it 1 way violates to use age defined differential the face of functional 2 wonderful old folks space and then thought over this between change algebra Fracture on this basis and this A recent study by June bargain much solo So that Let's consider consider Madam The kids We have a and these bounded over aces Datacom borders and bounded by by Ryan White just aboard Monday Ireland explained that again associated with this Just got allomorphic covered the commodity missing Ricco and you get some Lagrangian but also we can get this Lagrangian manifold debate can do the same thing as visit but I'm including the foreign encouraging presided as was done the case of age and even ECB equal Goodyear other this naive is a variation on the 1st point granted manifold but these debate is not new but only if they don't the bond and then you get the falling following accommodation is A similar gene And given the lack of a case for war bounded by And They tend to get Senor infect get a soda Ms. Davis aggression And not just like to fear that have this they teach your if differentiated respected you get something DOGS Center claims it and And this is exactly cannot Corby commissioned for the evolution of this Is this Valdez But if you do this For keys All world See then again explicitly using a computer from diarrhea and then again this discretion But the flawed but used for immigration difficult but that in the final reminder suggest this debate To abilities But that they still think you want to do business can refer to clear his trader's some people working on this and on some things people not working yet but Francis said he litigated of applications the So cold logic good River applied for Dole who that managed but nobody ever seen any serious implications of Cold War across different from June of Britain's 0 2 But in a sense and do things this I'm sure you can do that can't generalize a Put the brokerage and more broadly Ginger's stalled so there this can of Relations this year wander system so as to keep you get This or dimensional manifold hooked on the structure and you'll always get some kind of infinite sequence of commuting differential appearing in additional 2 attributed his thinkers commuting dawn And more aware as is case evolution property allowed But I think Haitian sold them End Left hand side of this for the end the of the situation will become live said Mulino dribbled out at and the sale of generating system of integral but I want So when the algebra over whether they should be in What is it added more legit but of course there is Much more There's scant Komodo beat that while and that is much more structure and count Extract a chilled computable invented the problem so there is below the work now Getting the political and variant ideal a future for infants The idea that into The political manifold and do some kind of canonical data construction but engine bundle union potential bond or end And then he'll Stuyvesant take invariant variant of this and in many cases they turned out to be far from the political on the prince's citizen I just mentioned live and work On knowledge In their knowledge but that have a lot of work to do here So there is this And cat and more or them a constructing relative which is calf constructed more growth with not only 10 puncture but also his and They later listing the bulletin glass technology and that is what rule for plan After bar Lecture Cabinetlevel plaster mold you speak about this today And so there is A team There is a certain procedural coaching effective surgery It shows that later with serious data collection Spencer and not have to be able to compute plans 1 kind toe to developers isn't the sort of real shed light the series and there is a connection between the deposed from Over and over 50 years as a kind of some work Jim demand Warren here and a The revelations tropical German Businesses some of tropical German is that another very much related to the duration of the assisted euthanasia and notify
00:00
Computer animation
03:08
Computer animation
Meeting/Interview