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Equations for stability
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Title  Equations for stability 
Title of Series  Conférence en l'honneur de JeanPierre Bourguignon 
Number of Parts  6 
Author 
Kontsevich, Maxim

Contributors 
Gromov, Mikhael (Organization)

License 
CC Attribution 3.0 Unported: 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  10.5446/16447 
Publisher  Institut des Hautes Études Scientifiques (IHÉS) 
Release Date  2013 
Language  English 
Content Metadata
Subject Area  Mathematics 
Series
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Transcript
00:02
around we and the the view of race for the 1st in the world this is called the the interior of the
00:31
universe congregated around due to to strong regional and branch for
00:40
quite some time Goldman along with thousands constantly this and it's very mysterious subject which can dismiss artists and local glass or ample class in the fall over the general framework of crimerelated caterers and it's also has served in various properties this makeup to construct and explains it's a best score police differential geometry aeration principal convexity and all all this sources subject postal from pure heart Marcelo Sosa definition set me it's kind of simple but uh of footrest for adjustment would have dreamt littered caterers example fruit introduces something which the technical consider that the bondage computer shifts on some homes algebraic varieties and consider complexes of juice that is misconduct support no bonded it means that they're going to call ozone and fine India Greece and complicate supported Cornwall Drucker finishes in his kind of support "quotation mark consider model for some algebra and consider complexes of models the coexisting get translated category at the gate receipts and to just say What is it stability condition you need to think the 1st in it's some kind of terror blasts for each of the 4 cricketers should define several America environs and also it just supposed to get a map to the Home Office and proof of funds entrenched rebellion broke some quick fusion saw some couples of Chen class and then it the 3 once for oil and isn't there something that you can change it to conflicted killer glass 1st to get him ever want to see and see suits eventually UC broke from the group and blasts of what stable objects stable object every slope the 2
02:55
it's just collection of isomorphism plus afforded as a was stable and cities rule number and then visit falling coowners of several properties he
03:06
forget stable object sorry sir Q the president not to announce that the used US lecture classes here now yeah you you just consider it in this that you want to play you could hear issued by another ship at City Index Texas Air but considered metal sulfides and agent the Gopen below torsion testifying stable object that is there Bloomberg if he applied to this is me champ Blassingame placed the baguette complex number should be nonzero number and this is our moment equal to the center and then some you you should buy wants argument to be shifted blame by and then any object of your pedigree should be decomposing simple in the stable of simple object any of the ever Subaru integrating by 1 and then assistant Plus will change my mind was "quotation mark miners as number and they are going to have could as a friend the duties that local configuration the region struggling to get here justice seekers of morphisms anymore hasn't consensus among offices said it considered questions and pulled you but still belongs to C S C and I wouldn't say I degrees Inc In is the end of the day before his death very complicated to introduce quickly shifted it's extremely good cotton highdimensional spoke of such an example cited assets its service slightly related to get to the positivity but it's very delicate story people constructed here in dimensions recently but record traffic and the mission for its vary from copper constructs such as and there are many nice things about the stability conditions of the minister of regional if not not problemfree finish assumptions if you were a little bit the subtle changes a uniquely Barack stability can so a form of complex manifold in form of complex manifold from any category and manifold this kind of battle space structure it's it's Coleman at the space center suits has many wonderful properties but as those who have talked to construct them docile and Sir Alex Fagan of to frameworks merit can hold construct them and so the 1st framework is something easy situation when I can construct a distributed think it's kind of cleverer like situation where there is a certain North traveled to Rome makes a stability condition it is it is following what will be possible to get some algebra social fiber kosovo in a and ended up Anderson it's true finitely generated and assumes that is the sole director of collection of projectors commuting project the Soviets critical I thought appears to want to be a producer could resume full time yes it's enshrined and er considers a cleaver because 1 can and he felt was funded and directed this can make 2 generators and other rolled a pass of clearer and clearer may mean modifying it many relations but assistant curator late label .period councils have said such algebra but celebrates the murder and assault which should began Newfoundland has found you a hero some differential rate algebra and I assume that all cohomology Alderson critical a 0 words so admits some kind of resolution at some seconddegree minus 1 minor storm Song now so I have algebra and that 1 immediately constructed category and plaintiffs stability conditions what will be the category for the business case for the plan what is the catering category will be incensed modules for the localized policies and G Altera responded dimensional ,comma total :colon In this format some of them will each get a grip on the game brought in a few years Citigroup off this category sees it the same as did the group of category of finding dimensional in models so this giddy because some schools him to cart which is ability continued his representation of this other and mission of school is the end because of consider any representation because MEPs dimension for dimensional so should goods has just collection from fundamental spaces and lukewarm I was a little dimensions as mention Solomon negative proof few consider orbit representation of this algebra and no no juice arbitrary In America Saturday's victory somebody I was a major part disposal which just speak arbitrary number sign up land again ,comma refusal and then all the time we got beaten category will be was defining combination of some numbers not of plans alive in there spaces and define what a stable object orbiting don't have some to his largest thus immediately get them facing contested issues associated cold it's a mislabeled doesn't get worked up a couple too far and that was in the face of the beaches of skin
10:39
and Jennifer they also get to because the main and in 1 can also unless with the call tilting were very often 1 can make another algebra in which goes into jobs or that can make another jobs studded with this category and reduce the category seems to children as the still will be according to Category Cesar discovered the same catering different overrate race and this is basis that conditions the store pull kind of in products of Opel half claims will be attached to each houses have common longer 2nd formed to another it get different a description but you continue to those of brick manifold and go Oh What a Beautiful tilting the kind of left and right tilting the formal like this the sum was judges it's kind of get dedicated refiner to many objects this summer just different it comports with calls from different portraits of its on the and I suppose you choose some generators June generators which are of all juridical maybe I II and from some election generators and assumes that the we and so it was physical to some rejected for some IG into Pinnacle unfair and assume that you get some object you choose place 0 centered there is a small generators the small the generators on the island which is equal to a 0 0 at a 0 so slowly that verdicts a 0 In this case 1 can make new collection of DGA models you just find to visible equal to the Eiffel I'm identical place Europe and here's your children be kind of a twostep complex support yeah yeah 0 group plus 1 and you take that some all what the and all finally could delay 0 and all barrels from idly 0 in insecure and then consider universal map the islands and very easy check shows that because it and morphism also the some you take children it's just some again Dingell called molding in in positive degree of guys again vanish and then again continues game that's also some kind of world the natural game of golf 1 entrepreneurs eligible for the central related category and stabilities are continued openness OK so that what text it's pure algebra but already want to stop the sum differential geometry and now the differential geometry should go to the arbitrary filled with Sevilla school complex numbers and then 1 can describe what a stable just in completely different ways result is going to have semantics and so on what makes extent but not stable ordered political appointees stable objects
14:21
which underwrote some of stable object to is the same slope also and as the description it's because of falling it's considered it'll be unitary classes all the plaintiff representations of the representation of the falling think you say considered more In the BIA it consider positionally altering dimensional he space the presentation all the same algebra you no vision of other teams funding dimension he was space this was called and me said it preserves each projectors orthogonal .period some and then the vote the following conditions hold that I remember adjustment generators at consider some of commentators kept him gets himself greater and then should be equal to a major part on minus clearing mines on the the i.e. the eyes is the I'm mazes complex number Best Products big some more on 1 1 and that so that's equation action as a scientist I think it is far too many years ago at the end of the conference come from a relation is dramatic invariants serious as a stable this exactly the same stable symptoms of served damage in and is amended to Hamilton and reduction and didn't think and this is actually very beautiful all the infected toolbar coconuts analytical were algebraic may be similar the space of such rigorous classes the costs more space and between descriptions kind of Joseph for commission Georgia and you'll get a certain gala magic and if you if you choose different generator that different diplomatic on the same manifold castles the stress of generators canvas sort Jozef noncompetitive calamity could use a :colon magical all model based simultaneously and guys it's very interesting question here is that there is a sinker consulted officer representation of some star algebra considered "quotation mark formerly comprised Commission contradict variables and this is absurd differences there also was a full due to your associative algebra and the canvassing representations at the Kansas styles were made of the fundamentals of the issue but it's not sensible compression should be clued into wee remains to have canonical sister alter Brussels of social faltering public debate on think endusers of that we get some kind of differential geometry Waukee that's 1 thing gets it but that's it British symbols story applied to the rural entered through a far from into situated in a situation of interest like cooking shows and so on infected it has something to do with finishes In we loss kind of remark I explained everything about finding a misrepresentation but 1 credit due in threedimensional presentation let's think of religious that's it but analysts and In the variables and move was made to his home on the the island in the eyes and some for infidels who can get the same description of his knowledge consider all dropped but animals and it will be a port deal funded In a functions mentioned some of the priest at some point which is not reprimand bookish if the claimant can write this equation in circumstances you your projector will be only 1 the US the absolute conformity writer sinks and a recognition of the generators the extent at AIG will be genitals sovereignty and into the right conditions to get some unwanted berated him with space any this equation is equal to I would say that he I'll find that uses the life of the infinite dimensional knows lagged that of medical imaging kind of a accompanied this space a function this coral spawn mines Guerrero is it considered like entire functions on his appropriate grows and to take them subdued into did you write this equation there and it has some solution from the portable to 1 or a case of honorable the inconsistency the roses just blown over rebel just little by bonds you want to sleep and then again and Inc elation croatian operator was converted to Islam yes it's considered and Square will be invoked Victoria and that's a multiplication backs and adjourned to get the exact opposite is of reputed you'll be exactly 1 and that 1 can ask the Commission cultural arise at infinity this is it would be keratin thing to such as commentator of expected and will be endangered if greater plus some kind of small countries want place plus all of their considered subsequent future looks like advantages and then a toothless nicotine across a full invented to seek support than gets a goal as it is the conjectures that you considered a from chief of ideals of vitamin E . 2 stable object because of frequent the bundles should have canonical breaker appear prohibit structure and get this equation institutions and never studied it's very difficult questions and it's and that if can go to some limited pulled from borrowed constant fear and will to the limit them to get to the limit to get a young Mills secretion of low commissioning the suppression of Donaldson but that knowledge have adventures it's gross for "quotation mark finish it's not for vector bundles and assets should be right of view relation this conundrum all cases said so will 1 worked and but those us physics suggest that suggests that something completely different the oldest the ExIm article Britain come from there Mike Douglas center from your signature but it physics at completely different lots of examples of this reverse but let me say that there should be more so you don't have be adjusted I but that what is
22:19
the 2nd framework from the halls of it's a vote and give brands so it's stopped CalabiYau Laredo it has said that its of arbiter dimension of test get forum and has but agreed it called for a formal answer to sink its could be not compact at the end of the category which yourself to it is a truce is it's getting operable compressed numbers but formal posts used in 1 room bearable and it's getting married to depends on parameter on concentrates what 1 category and and assist called for for packaging no I just consist of someone Rongen all objects are medals you just as definition we'll see what his much a sort of what was it would totally stable objects and the conjecture In central contention the subject of this category has very canonical stability conditions of the main source of stability condition from them Saskatchewan to see his canonical stability conditions that is the object of this category it's it's very complicated things Ivanchuk .period structures here because that's the kind of limiting called a contiguous this is 0 premium limits as the most was of stable objects are the following creatures just explained this is uncertain was full of objects it's it's a apparent that wrong but it is a political oriented shuffled situation and what say that it's at a stable it's oriented block Rongen some were right here in the states of mindful that sexual could be seen this simple directors and could I mentioned tho and this has accessibility as exorcists impolitic mindful that the physicality of the discipline acclaimed for its Peru object at the end of the game has to do with you can let them of that nobody knows but I expect its outputs of some kind in the nation nearly I'm where is the physical the monarchy it's absolutely essential to have similar schedule for special Candia oneonone not not being a finger here have at home I think you actually don't have to specify the IOC I didn't finish to description that so there are several things here 1st 1st full suspects that is compact here that is special both slope the what does it mean that visitors can exist due 0 form who else yep liberated here to kind of any minor singularities positive singularities Arizona as it is until be belongs to gain argument of the seems to be Hey he's finally get the things that are part of stability and themselves some positive things wanted the International Monetary it's going to be Brazil is actually marginal Marsalis's series are always that could emission at least a year yes yes yes would be about the other system British can appear for the single Russians it has a special summit differently and ease inadmissible representations the fundamental rubles minor singularities for somewhere didn't sink the local system that said determinant of this is the case belongs to you 1 and so the last thing features very mysterious at speed riches come from where there was some creation of Torrington beating for placated and but I think it's actually means it should have some Dierker due British should play some role but nobody knows what do it and that is the right political molded glass affectionate holds about glassencased you because it's been and is the author and will be will be er rankles local seasonal multiplied by interval of this did you form should be this is only the 3rd player they said of top of the agenda of the members of hockey but those of the category will be 0 now know the claims of this the former exactly the list of stable objects the people that I will yet and if if we really from the Centers for cricket is equal to or cooking should some other writers that abuse of Zacatecas rudimentary Wilson's and the ladies of the differently that's so that's on the other hand the reason his release last month of golf course it's that it should be the kind of the only feasible way to construct a be conditional on the skater replica ships here than those of the the habit here of course we that the Schuylerville here I think this CalabiYau it's still strong and the rigid conditions what 1 really need 1 8 2 0 1 1 4 4 awful cricket agreed differently but again 0 1 can plays by context amended gloss and
29:33
form goes deformed Of the degree is summoned India's condition should begin if not should not mention all it really province of space and service of conditions which will it former skunk excluded the court decision that's will yeah I shouldn't have a complex structures that's that's be used to because the picture that upon should can of minimize some but in a report on the same conditions from officers complex formed just forget about remaining matches on the loneliness of 1 or not is that this think it's equal to a 3rd of the deviation from his days in honor not another star evocative is still the same story because 1 can always seem to agree on of Urbino metrics so the matter consists displaced it too but you get formal it's difficult on spot and it can also integrate absent when a former governor mindful that into cold area and this AD minimizing could special Lagrangian just recalls as if it to become effective some of complex numbers different slopes and but wrangling quality assets augmented but Rincon also right to convey a functional and minimizing insisting will be minimizing the city functional for the this is in something the hidden in the hold of the advice is :colon was the only if you if you start with remain Mexico but if you measure the area on sinks but some different means not by remaining magic but some signals with the assistance of the noting that the finish of consent form which not to mention call any us that we would have lost here in the heart of the heart of the life of a visible part that was the functions which also is essential like it applies to the use of the land because of his race on half of just variety tomorrow at the beginning of the year he said he was going levels all the usual habit don't have to foot the desert but that is the claim that this is the spirit of explicit representative it's not iterative like like telematics you can change for a new geometry is accused since this stable bundles like its land for purists and different equations gives the same solutions and here should be the same pictures that he changed little bit Omega good different equations his living on the limited are not not not nights it did questions of standards 0 it's completely the group was responsible for the life of a monopoly milk liberated for 11 it has ended 0 as a result falling because if you have a Russian manifold and now deformities is exempt from the tournament transformation so deformed that ended last Groff of differential some function but such would consider consider functions from a model of constant will be the defamation space and what you see is what you can you get in their argument of the scenes and I are going to should the constant argument is a function again with beverage medical 2 0 so get to map for space 1 dimension to the suspicions saying the mission shipped in did 0 as this aggression for being liberated if you consider the formation in and you only get Baluch feminist because the consume only if it's not 1 connected and consider 1st golden consider nonexempt information so that modest basis of such things happened and it's very important to pull the school a local system and it said altogether the modest specialist maybe would not reducible point to direct some of reducible of such that that this is a glance that some of the special session to become part the wrote all wet hair like an image of something and compartments for minimal manifolds but no what about local system local system can depend to infinity but in fact secretive that local systems group and all of them because of the could have ,comma humor harmonic on the system the canonical supposes Columbia the committment and some of them harmonic Maddox venue local systems boasting features a harmonica worry very fast and get kind of real Higgs field the event our world was definitely you get real fix Hill and which can be sought as a .period Classic at the of commuting Commission operators and the spectral we'll be a Michigan interpreters can Multivalued you get an of spectral for you not to manage real harmonic 1 form on Sicily metaphor of Oregon representational seeded meant to win from conform this motivated calmly ,comma will be the formation has especially resonant to villages and multiple cover all the success of limit of representational beacon for the limits of what that means that his unit of multiple cars from other Saturn's it's the have no boundaries the yet so that's a thing for a bigger picture isn't the committee I'm not on a list so you can't really judge hold ,comma this is it but it's there looks to Detroit that now have kind of 2 different situations and and what else can happen in fact I want to say that this could be the stability of mischievous dissertations on just who has arisen from the of falling in general kerfuffle soon predicts used to have them in category and stability but no geometry just category instabilities that because was moved from minister of kerfuffle services and who and to have a Jimeta description should go to some limit and if you will to some limit to get some targets space but from the moment the multiple targets this summer some proper Phuket is series will be the genesis of songs says the montages ahead and or office speaking can think like you have CalabiYau manifold black we just fiber at was some in manifold or small dimensions and small small fibers and that our and and actors just getting mindful to consider such conflicted really reparations and on the cases surfaced digital projector Flanders the small leap to curse and if you want to discover what is forecast to grow on the way you can check to see what is called a stable of what a special arrangements for them to get something to kind of the the following situation which In the next edition of falling it at least some examples
37:10
with Getafe litigator manifold and then got constructed will shave off strangulated getting that means essentially conifer local system of Connecticut Christmas maybe there is some jobs here can think about getting rid of the because think up for cracked there before that of all the information is Jenny private CalabiYau in Foca categories of fiber and because it can cause doesn't change get local season for packaging cable fiber and there was a study in possession of each category will have stood the test of X which met from the Group of this category just as funny because his incidents to the fiber of canonical bundle .period Texas should the public agreed 12 times bundle when this socalled stability was not the complex numbers but onedimensional vector space ejection makes sense you can multiply stability by constant the changes In the end it complex line here and there should be Cullimore Freakley depended upon markedly dependent on land but what happens again in this bid example you integrate following a lot of rotten whose where varieties hybrid that would for homework will form the basis the pinnacle mysteries and a stable objects to the use of stable objects to the fulllength novel get single Lagrangian manifold the beaches on all have CBS is what I mention 1 animal and it's true it begets single accountant and X which is you know something in return and I when what sense especially as its refining on each Anita but you get but but a local constant fended off stable objects this category but now it is up like is the extra you need access to get there get homework 1 form near the and then the 6 should be of special this flops at the respect of this form of 4 fitness as argument this from be equal the they also get some bizarre equation and zealots and much good image Ronald Wilson said likes branches typically attempt each other and then should get here at this point except wrangle interim litigated richest Maine structure that's so that this makes things and you can imagine the fibers to grapple directly using purists and very simple game "quotation mark but then again this season in some and that was the 2nd of natural framework to define for Kankakee even tho this was not constitute a stupid it was responsible .period but any critic category and the causing serious leave together this is very simple example which is you should finish this exSoviet complex Scott and photo became too great now the categories where you consider some cyclicals print protect projective algebra associative is something can diagram and you have the arrows that some kind of arrows look like fools experience we can get some barrels and no arrows and some commentators but now I'm not competent to good will be equal to 0 you get this will be a relations itself rather than the double to makes star approved the question yesterday at this category must abilities very simple and stable object to respond to the following things stability despite the collection points in the complex plan and stable objects are possible intervals could commit to this thing and then 1 can make makes things together and get with something called spectacle networks this makes especially those that logic a very beautiful things which had discovered by so people injured also by going up to Monet's can it's a bit on complex got it considered Multivalued multivendor to call market ,comma fault that it's beginning with school spectral careful to at of conform this to this summer vacation and any consider another of the 3 wedding dresses for eager to get communities were to reduce was formed and other forms of argument over the phone by members G legal procedures and then you get into JK when they meet each other and with some kind of 3 women graphs associated not only me yet because Russian the gruff dimension and then you get some kind of mess conditions some bread plants and it just on the surface doesn't got bronze surface sunken wrote computer program and to see how the since this essential albeit in a very delicate be misses funk and and study a secretive secretions it's really beautiful dramatically then under this is some magic it was like all its 11 gradient is considered Oklahoma on form and to consider she retained by the angle sitting consider level set of real part the action now so that's beautiful objects it and this is stabled concerns threedimensional color Pittodrie there's some kind of highdimensional 16 gold simple language of think questions a version the but you have to be very useful to the look me it's Bridget the it's a bit strange name years it's Gulf stability said the condition he called for the Commission which is in the best condition and it's the condition is but the whole something substructure conditioner founded audio and video tensions analysts immediately yeah it's likely revision it sets out popularization the real value of some of the money will go to the this is
44:42
of course yeah but it to coffin since analysts of predict and local brewers but both academicians really hurt him this is not only in the history of the United it's weird police the suspect notices fact this stable mystical the category and the W
00:00
Computer animation
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00:39
Principal ideal
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03:04
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14:20
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29:31
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44:41
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