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On topological strings and matrix integrals
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Title  On topological strings and matrix integrals 
Title of Series  Physique mathematique des nombres Hurwitz pour debutants 
Number of Parts  6 
Author 
Kontsevich, Maxim

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  10.5446/17059 
Publisher  Institut des Hautes Études Scientifiques (IHÉS) 
Release Date  2014 
Language  English 
Content Metadata
Subject Area  Mathematics 
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00:02
the arrests have and and and Jason this stuff so infected and lease it was listed organizer of the the of this conference in fiction my roles just to commentators MongKoo hellbent on find nice building which available through days the end of the road littered with and they also in there are also sample must meet to talk about substitutes it's not addiction might Active Memory this subject knowledge but I'll just give you very good foot the entire review who called what would work songs in instincts Yuri hole 1 can understand and generalizes structures but 1st of all just want to say that there is following simple creation and incomplete volume of unitary group this is the natural respect measures related associative is Mitchell Romanian magic Christian square is the it's a number you can call collect it's it's 6 should double normal functions brought a performance was fiercest theory is that she wasn't expanded this meant the local Fordham if the warden and mountains the old wooden propeller plane despicable therefrom and Protestantism post Infiniti has simple exercises stealing formula but it's 1 the more functions double the malfunction and it gets something like some minuses girl an plans for buying looked on it was wearing I hope so and and and that serious injury but it would be a stick of modest pace of curves result marked points followed "quotation mark ways to G doesn't this 1 also from the car and secure its it's really number divided by something but to demand responded to demands to the source from clinical quality assets on communities there really is a check this history not not to big a deal but me the question can make increase support for which entered the moment it's not the case here so that they could be really good goal to find the intrinsic explanation the the the assets it's such a part of the general for Ferrero and bottles of considered interpol space but in by mattresses takeover from expanded gets some regions an extension the Commission on Sunday Fuqua glass of conflictual situations between General should this summer in Europe explanations that's so will speak about the dentist the full and think that there is an amoral will the and on categorical language right so what is a model of supposedly all booked for moment simplistic Minnesota and the euro zone's desire were beaten variance From the original fundamental colossal problems resolved stable maps India which I call holds a certain degree expert Warren and the entire which could patients a D here's a degree would cover and that is just interval from older blasts and said is dimension there is a school leaders for some formula it's coffee real dimension of tax ministry claims genus of my government's while 1 gymnasts has stumbled mark .period plus the interval flotation class of pungent bundled over the whole plus the fastest those such classes and it sounded so long that the whole thing could scandal of can be organized 2 go logical fields during the CA vector space stayed we could just come off the effects and you get to from teach the and deployment of engine bar good days some fall this exists only in the majors Boris to deplored the it's kind of depending on formal parameters provided by France would want to do basically are which prompted 2nd Hamilton the Kuwait if you consider the benefit to fight for power in general respondent basis Goff are representative all this commotion classes so I knew residue it takes some all possible degrees investigative work most Golfield sued pinnacle sought some parameters in all over description would going into the model if it exists and a new models stories but during not sold was because of what was originally story produces a good this year or all this reduced to the state of operational cost structures it will serve as the exponential "quotation mark structures it is bottles Jews 0 role in Iran's namely that if you're near object exists it should be in the algebraic varieties on the sale of public schools )right parenthesis and dimension as it rejects the socalled market could result report amendments schools and their potential to just to just been put in a moment but said it decided it would double its Group W should be broken up and um the sending it is as tho the object of dual excellent it's eclectic form also bid will depend 1 they are parameter ROC and no 1 can identify parameters 1 is Anuzis said at Loughborough perfume and what I can hold on to power will the rest softly intimately integrate explore natural wpm warning or something cycles and divided by integral exponent of noble of orders for the governor 0 . 1 gunman our last summer the integer chains and not recalls that so can integrate exponent of potentials the Golkar infinitive direction links from the may short "quotation mark and squared and castles it's 150 of
09:38
this RIA assists orders will be kind of transcendental coordinates some modest resources for righteousness potentials Antoine before going to different intervals when contended to structure vault Jim 0 part of invariant evidence of there but for hygienists new it's kind of extremely painful household waste fraud and hygienist "quotation mark escape until Sosebee models and not really clear to all no doubt let's consider some kind of most central cases the whole story just look on this as a gracious kind of central case and the mention of effects and seeks points freedom most Congo's emissions during the 1st shot glasses 0 then in this case ought to get essentially for Ejiofor was on the minds of costs of any degree orphanages is a result marked .period former 0 dimensional modest space and social accountability just get us
10:57
numbers and all this equation that could come multiple fields urea became completely what course in this case the whole story is divided by just the head the is all information with some serious energy mangy greeters as 0 will be functions or whereabouts expanded to some form of posters and for small dreams the Logan from corrections yeah so as you it's kind of understood for racial of structure book for hygienists there was also a model proposed but his office's confinement revolt the proposed by the strategic which worry it's called in there is Spenser series that will not discuss their Spenser series on can make it original colossal In fundamentals was holding forcible together differential radiantly algebra In degree practicing degrees 0 1 1 2 and 3 and this is 4 degrees and and although you have a differential duty plus 1 and also some positive earnings is kind of non degenerate I would apprentices because Delta will be infinite dimensional In that compatible with a prison break so NBC some causal link in the coastal scientists the occured is expensive and compatibles differential isn't going right chin functional it's somewhat estranged the island corrections and functional on the and you want to integrate theory that a government has begun this and work toward less government ,comma 1 6 I considered transcendence for online is because despairing has undergone criteria integrate exponent of transcendence functional the model regional solution would agree 0 that's organized as a serious political example for some early allterrain orders the algebra it is a fully consider the bar forms on Colombia's fault which assumes that new play potential 0 on this case known in custody by former Israeli team navigation and individuals free from the Europol Norfolk Opera fields so locally are considered as a product of functions and therefore Susie bar the dipping to concede bar and homomorphic profuse z this 0 dividend yeah wasn't as it differential is a slight problem is a painting because if you have been if you have to report follows with that performs which made the most of the 0 I form and this gives you a lot of time bundle and be belongs to use Siemens sign form that is in the area of the country multiply because in the product will be 0 Sioux Falls and then it should do some circuits ,comma fields but because it's free it should be a monk and substitute performance it said that the it's cool local it's Dubach lost the performance the doorway ,comma In sink for the world the Home Office refused to construct his home for a minimum to get before income often direction because they were close to great it's kind of India can write nice 1 of distributed it once news 1 phone call from directions so it sort you'd do essentially and integrate your place but is by forms and the parent Amy will be you to roll off the use of the military because his state's if its courses should be gobbled derivative of something no themselves slight problems among some fundamental stresses the Phoenician but you get some fields urea and is the 1st pitch cryptographic principles of if you're 1 stop the coca late exponent of chose Sam's actions it forces them to divided by age bar and the intake the expansion is should get aged 4 the government Jim I'm still stands strategies the unfortunate business and think it's a very illdefined as a means of this room all refinement in intervals that got them but also there's really no way to regret Canonica relies asserts is in excess of extremely but shape yeah so but it gives some idea of what a home only accretion the was gone only equation it's been very close relative to what must seem Catherine explained just before essentially it says that I didn't have to explain what is called ,comma integration his that that you get something infinite dimensional space and get some the decomposition told Russians of space and functions of rotten submanifolds as hasn't tried took contests led residents of meaningful to get direct renovated presentation and the scope of the nominee questioned means that if you kind of change parameters he assumes vector stays as saying so that's morals of famous secretions which he explained yeah so now what we want to skate agrees that in sense in it's so insulated regularized this baby Suri antics and in kind of an appalled by that this is jaded seats each conference in conference subjected to the green sectors series can crumble under so the those of project which was started more than 10 years ago and 1 of the richest have not yet ruled incomplete his satisfactorily shape which is a fulllength solo carbon called as this 1 a role generous some older break data there is so hope for simply as altering until there's full Inc until they find a collection of complex numbers which can be sold here is a critical so on W in this example exclude guide principled this potential should be 0 from just 1 number 0 than for each number you get some algebraic gadgets which is called its most compact infinity it this colonial structure and so the category C I in this example of respondent show
20:13
isn't I actually like to explain it's a critical minutes of W or it is the same as I did all operator of quantum product by church and glass yes some can't make the comparison that 1 in In the model and so good anything to get a good there is a category will it'll be but what untreated defined for K category for manifold consist luggage manifold the blood of refills will some kind of the upstart obstruction to exist ordering the category and 1 consumed by the but a addicted to provide Wissam Eid invented gets subsequent to select and not 1 for crack at about several for caricaturist Crispin regulators and fears of the 6 school to getting much looked decision fact that at the end of now so that some of the regarded most competent 2 categories but whatever it is it's 1 concede some fundamental issues super Reppas space functions some generators it was a bunch of times also often does on a train from a bunch of Kansas City's ISO question but the model dish a fine at infinite number of parameters so did thinks it's kind of algebra is well over a number of branches so in principle 1 should have gain some kind of mathematical problem for programs repeat effectively resist that stuff like in public's completely different coconuts is a global structure it's also 1 conform Is this way Calabria structure is and the falling gadget for each category like in a sort of something called negative sector ,comma soldier the emphasis is actually more all I using honorable which in this subject is available not weightlifter you know it's it's gone from from commuted from German trenches Kwan operator and some yet and a whole think it's the system you rock from this model section of free will find a trunk yesterday kept a bundle and this is Gaudio structure is a section of line bundle this the violations 0 and derivatives should be invertible element in the most of the sense the census Maxim explained some inevitability property that will be colonial structure and can make but but existing the categories colonial structure gives not much it cheated located reduces functor from Woods Hole college at all the a horticultural affectionately called 0 borrower ends meps store up for each category at the site fiber still full knowledge of what the space of but his bar is all bark and his arrow over that minute Eric music it's stable costs stunt and direction teach .period not as this is pure love game and culture roughly constructed very and gold saying feeding it to various 6 times the councils and the psychic Denzel suport roommate forms environs is according to Rubin graphs and it be "quotation mark chains simmering graphs so that's basically it's a spirit of reconstruction behind the plant abroad this whole singles at those this peerage reconstruction Lumpkin this specified for for quakehit you really identify was growing freedom environs all specified as in complex manifold insecticides 2nd of regularization exists that the Spencer Stuart castles as a problems the arrow and bar In front of fraud the ball from to replaced engine fed by Amgen bomb over need you may additional chairs this is appalling but now I just want to say that the vector bundle this let connections on and miserable singularity which category and the chances of falling in consider the direct some of th and of the skaters CIA multiplied by kind of onedimensional bundle this connection Richard in way exponent of WIG weighted by you so consider that connection costs and when emission obstacles solutions exponent attended some you get from bundle this foot connection 2nd with a poll on a formal disks and sink it's formal neighborhood it in future 0 all connection of the falling that is who beat duty you kind of people bundled and connection is consist of Dubai by 2 mattresses the agency was changing political liberalization according to the report noted basically collagen on Sunday editions in earlier this year CI lf category I have no doubt says that they desired .period summed it up formal guy and now you just room want to make some additional summation together just 2 mattresses Amy houses will begin finding many parameters sculptor good and if you don't use a new extend engine for good different places and in different ways but is is different users are related by this given that group that just solo was very nice and yeah so some kind of kind of account of this story by given cost lot that but he did it somehow here also communicate with him a lot and this is also kind of final problem we cannot really made to the was it calls formula it and as it is there is it's completely your tickets that is the spirit of the natural question home goal from beginning was based the sterilization should do some Boulboul promoters dungeon bark and eventually construct but some felt complex the boat which was publicly at the engine block therefore there will be wandering in Google at interval fundamental tasks like have G and the promise of this complex is of infinite its infinite dimensional so caught up a contingent but infant dimensional and I don't know any more Nice representative of fundamental plus will be represented on both formal and American consists of it's that fees that's the problem was solved the Altus that I eventually got so it's really kind of some of stupid stumbling block about and that's why it's not really yet kind of formal official kind of picture was the story now just so that's that's that was a peach about where are in calls to profit invariant no I want to say a few words about under the following permission was also saw some important think those weapons proposal by it's the Byronic of well know the company it's slightly different linear algebra so instead of a hearing cases In few Delaware and all this data he
29:30
has a vector space which also infant algebra and dimensional vector space and a lot of elements and symmetric Boris oversight click falls of my prospects city sank some idiot doesn't in there such things city saying some the Indian market immigration now and then gives the glasses and soldiers of energy and got lots of Brigham and Prime is if it's it's it's indicates a contraction of the engine block and many have it on stable Booker forget components which are free conditions have marked .period ignores them the local structure on Saturday as it's said to us is the space which is hope Puritan mediation my performance is a function of which conjecture some intermediate space and the glasses set him up on bar it's it's it's it's not terribly perfect story Wanchope relate to removes brand and it's looking called this parameters are related to the spur interest is not to me look at the economic status of the and all the rest of the Donald only maybe we get call because it's it's a limits and all also talk a good game but Susanville Brazil satisfies the systematic sits there is problem not free the hockey possible applause and brand analysis and pretty interesting story about the Bolton militants open pool during and lets me I'll concentrate on the case of the levee Elsie faults they also said that this kind of case which is completely ,comma perpendicular opposes it seems simple case which makes expensive as the freedom of future debt blame functions and no recreational boaters can consider hard before because I want to say that the Reagan cholera from all the speeches focal ideals he folds no 1 can win this gage changes alone can make it's pretty explicit and dramatic situation you forget why Colombia's twofold and you have a choice of wooden element and so far right it would choose 1 amendment and falsehood used as substrates this was the nonsensical doublespaced Innovia for what you did you complementary spacing Elliott and which is helping Peach Street when the Dow complementary pool don't support filtration poetry's Europe less each 1 rejected a truce called for extreme this was filtration then the forget such things zone the whole story all this the changes to Soviet allegedly made and then a good number of G plane end it is stored and as this number of city wishing for repeat any button but you could what would be considered as a genes of functions so some old break Florida the so is disease it's kind of algebraic functions on the model is based all of this and why and warning and that this algebra clarity and to discuss with you really can vote rate parameters for categories regulations and from the police twice Samir Aboul tool I
33:59
mean digs then allwhite depends on 1 parameter warning depends on 1 parameter and leverage space before they're suspicious vessels the parameter To get 5 dimensional algebraic varieties the and the Evgenia Lipton the causes and Evgenevich you can see in actual new generosity is is obtained by restriction for some transcendental submanifolds here In but it would be so this is adulterated dependence Jose there consider serious coming from the genetic functions those people animals and fell 5 serious and young company rejected and to the Office of the US but up to now and below also correctly uncle collated maybe 1st 50 but as spring animals but because of the technology is still not available so he was some kind of Bondra data but to philosopher alleges that not sufficient to get some freedom their golf tournament Commission does the determined to 6 completely out so so it's 32 it's authorities unswayed exist but in practical terms it's not hit here where is this is the only condition is that he is the owner of this it's only to finish here the area essentially they yeah Costello has some paper when he never definition of duties all going to constructing the coastal fields to review the Tolia so here but it's very hard to extract and not in a number of sorts and now it's about cooperating locals gulf between grants suppose Michael obvious you felt so it's simplistic manifold contains threedimensional Lagrangian some infiltration and fretted about the essence of the fury of 1st supposed that the sphere allusions city can might emissions in London only those under 1 can try to college in the fall and guys 1 can consider can't make a genetic Series MGH all number of GH it's the somewhat agrees to 2 . degrees and
36:25
here get a number of ghosts full June's G In the page calls and wondering 1 of the most was his threedimensional sphere that has his speaking could not to relieve illdefined problems in the area which agenda was getting wonder a modest spaces real but then was all suggestion by the vetoing the Quilliam the cultural as a room 1 considers gaffes and also draws the sensor clique roughly gradient lines on an on underlying sphere connecting points yesterday just that little bit of allure of speaking constantly consider maybe the German surfaces which consists of several components and to own and radio it's a bit long stores in Britain planned connecting Point and 1 struggled to an analysis of 3 and then the whole guy have no wonder if so it's a really well defined numbers fall ,comma logical spheres now so that it hasn't been a part of it to certificate variable the 2 to raise the ball age that man what is this new wearable and then there was a picture refuses off or on a full transition if you get this year in the inlet in Sicklerville twofold Zeneca construct a new family at familiar the program until the responsible for this age all the simplistic manifolds limited following you consider neighborhood policy neighborhood looks like it could dungeon bundled with few and and uh this into it can also be adding to 5 is of complex exploded this city could this complex Boddicker can
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degenerate To get going to singleA the complex for item such as a contract 3 2 .period but done but now we can have a small small synagogue joined but they bear make kind of blocked but only gets going small block you will instead 1 instead of if you are this it's the whole ball pupils uncle Westerners across if you want but you just construct 1 soon receive about sending it divulged could use the new contract and form at a store In what to get you get puddles double loop space of tridimensional commanding officer 1 he also replaced Himachal sphere by twodimensional sphere and an hour in the synthetic manifold has extra pummeled plus holds most this year and there was an incident has more parameters this eclectic mindful that can change very simplistic structured and paramedics went to sink as a claim is that it slows claim is at Gloucester rolled region environs for can exist maybe until the for still the global open calls for general projects and this is initials here and in moral it's kind of clear because it considers this outcome are there is an officer's procedure get a calf and we have to some caucus off city wanted it doesn't occur yes so before kickoff presidential searches Lefteris innocently resembled the officers the decision to get a calf and importance of 61 where as the salmon can this several as serious and weird this World Bank unemployment some more parameters and get to it this pinnacle parameters that now I want to say that what is good font and the model indicated language model Bloomberg but a new model it's that section opposite station supposedly color fault and it contains what's called the brightest light while the traditional garb but which is rational covers all bundled all minor sample 1 said typical Russian commercial businessman summons was issued as skipper they can contract as a result of that 1 parameter family of new defaults of would do and coats of paint you construct but they go to point and and then try to small summit of sorts exactly this procedure but insensible opposite Racal me and I know that I'm really brought are you can have the point to get to sing the contractors Wilson so cold from single right to this contradiction character this absolute parameter for defamation now that so that the story and and also in it in categories the souls nice maybe consider category cricketers issue somewhat and the right necessitated which could before credited with and the staff see or see it is that its object photos escaped to grant its currency and it's a spherical object said means it EDS group from this object to himself alcohol Mitchell's here isn't this contracting to correct 2 .period mixing variety perfect princesses directed caution category Watson not to Pawtucket research it's inevitable that complement to all objects he said that from the names of the spherical object is your own interests it's perfect complexes this category it's it's kind .period dangerous it's considered the origin and you can get a new form of music this is a category prominent statement and a good sniff and it does this thing said to not really we get done there so 1 can win the it's whole behaved were necessary at Amsterdam's Columbia spherical object and that you want friend and now and also the 6 should be kind of as at areas open gloss in various schools and overgenerous sure should find some kind of formulation waters open broke open global numerous improved 2 different frame ghosts confer in be orderly more secreted work on more so but the thing is meaningful Open calls open closed the new model is
46:02
a fulllength they model is a Holy interval of exponent of transcendence declined to adopt off or what always fully algebra if you will be nuzzling wrote known to give new life forms truism is Minnesota where that general and get to know me that's open calls at the door and resolutely 24 the moral and trust in you with the workers use work within inches along with a bundle which is spherical object could be a major in the rigid home often bundle there are still considered bar forms of there is lesson and the morphism sources and Mandel and this as a Scottish that'll be another there should remove controversial suitor who call Norfolk transcendence that was essentially a much better situation here disqualification Sammons you also get environment diagrams so expansion and the whole thing is divergent as fall over and as necessary but canonical organization of all there have been final there's still the call sinkers mill In can improve could articles thickets and think it's sobering systematic central it's 6 and categorical in your injuries the new much acceptable the fruit with question and here is a really interesting point here the whole thing it exists thus also kind of this additional chairs make area is gauging the speeches and should end of offenders metrics interval as well because that's how we define what a stable course and so the again Gingrich is not Kitri really done so can make a guess and if I'm John Salmons finished over all the race situation break from both of which will be 1 needs manager on on space of objects to the degree only bundles and any day way mission and that's not clear told because the colonial structure gives our in what's called she wouldn't mind shifted wetlands from shifted selected structure on 1 this what does it mean as it is considered the formation of any of the roughly considered before before missioncritical often bundle conform detailed was getting rid of the tunnel space will be eligible books reviewed by 1 and get me this ability of bearing gives you sympathetic structural degree minus 1 on the Super space and as on Monday in this situation on guitar all such essential function will be some function calls the commentators itself and the 0 but for this Watson collective structures a small canonical volume element and not unlike even at this additional data so we can and we care for our kind of classical questions it stinks commuters assembled but there is a small world Norway to record a slot last sentence of this year or next no thank his awkward amendment before amendment to censor cannot called for free and fair I think it's really come from this the additional to realization of negative sector ,comma it should be a form of the disease has not yet "quotation mark identification negative sector culture should be cautioned Susan you finish materializes Len bothering a bundle now that the actually break who got to destroy tapes and Baldwin's and we can see that civic just infinite dimensional intervals financings to some games dancer In Hessel said the use of force who wake on and that in fact if you have the erected Seifert's if you recall bottle gets kind of them and fulfilled series but if it's coherent chief supported both Senegal it looks very twodimensional serious this because Goff could become trapped appointed in 0 dimensions to usage should be reduced to match its intervals on the walls stuff in fact that this is the home of John Salmons you depend upon and mention of a support of where she will be controversial servicing different dimensions 0 call 6 just this quarter transcendence kind of quantum field theory in dimensions to talk for 6 I actually received its 3rd who will just 146 there the in this open calls sinks and have a half hour blue injustice Dusan hold and here I get from people possible parameters circuit age block but also consider and corporate support my where to bundle the assertion that should be apparent speed bar and an ingenious age I think it's contribution local branches cancer so some kind of club last when here In recent years the means threedimensional images nonelectrical quantities not followup multiple topological you could not songs supersymmetry shows reservist postapocalyptic hopefully stuff but it's not political yeah at in principle of did some special cases 1 can write sinks it all in a model has also on the room .period here essentially got all the sole my story I have to say up to now the screen only 8 example conduct colonial civil through their noses number yes it's all because the whole success not to put down as a Britain's decision that sits there and it is not in In sense effective sure numbers physicist that's a those room and I almost lost all things which physicists explicitly it's some kind of limit case the you consider complicated plastic manifolds the sole consider noncompetition hectic manifold which in this instance the folic expects me it's citizens summed the public synthetic manifold there even if have a device that we should be seen ample that means that intersection is any Godfrey Bloom negative the of a surge the synthetic Metals again from each whole story look are usually
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releases complement to devise a hasn't considered Julian Lennon's would mark plumbing and passed at some the kind 1 of its sometimes a class of Dubai's at infinity it should be positive no major costs which makes sense and when Epstein was 2 0 in the other you can go to the limit and only wife Kearsarge intercepted was so incensed the open what manifolds that kind of limits of calls guys from reaches resist a good picture unfortunate alone would also break translational does not comport mindful the asserts sinks which is still missing but here's the plaintive call commissioners have done very redundant empowered to grant and applies to the case and X is a good start and 1 local some threedimensional many Street just on the situation and and then this open role for and weapons in the story it means that you could call it channel semis urea a real chance and Johnson serious but for you again bundles and boasting the to spent and can be weathered beige box surgical parameters and the Joie and in particular this creature to think that vote of what it is to be some kind of reneging keystroke is of threedimensional sphere messages exposure from calls I I think that's someone 1 can get also threedimensional series in it's 1 of the and injured navigate finally you will see what is the role of firm the political repercussions from this perspective the and to political pressure on animate generating serious you could still be seen as an infantryman it and principles of .period was also looking registration could grow additional descends would hold on the dramatic meaning it seriously infantrymen whereabouts In variables that you wanted to know if you want to be infant to many rebels in Colorado Yukon practices is variables is beach isn't like rotten mindful too should consider not least not connected but has fills ,comma Leja supposedly plant production manifold across article so some kind of think like this and then if you get now you got into your old manifolds this boundary the each bonded couples who erupt some number of times and 1 can see its number of times will be it's and of course we institutions could be going always positive so this number of Pennsylvania items problems associated with HP items thinks necessary copper introducing Finchem maneuverable so and and what does it mean to sink into many variables so so another way to arrange a wholesale single storm however In Semitic functions in you can't have functions something strategic them off and and wearables wage and semantic educators rebels and then expand you get some until proficiency should be arriving not think and the so submitted to following assistant variables 1 the and In this sort aspire amateurs 4 objects and for greater degree because vendors have this as 1 grows up to 110 . 0 on this disillusionment but also can we fight run 1 local system which depends on whom all or 1 parameter and I my guess is as good as its functions which appeared in the functions of many many variables which appear in this the IRA answer some algebraic varieties of some uncontrolled recovers but this all direct costs from a crisis objects in the video for cricket agree enters its again should be kind of translated to some room to breathe it is a game but in principle considerable pool more examples from the Balkans consider thinks it will store generators of Hamilton and of Moon said of course to get surfaces and as the emperor course in real life In principle can get leverage mindful arbiter Runkle H 1 and so the computer criminals object categories and my guess it's it's a game chances all in circuits involved the Pentagon CIA and my guess it's so what quality here to Colquitt Jensen was export of interval and sends near so if you want less expensive and sets this is a quantum theory of the I think it would the local currency used in the office of the president of for the year because of the volatile situation in the both of them Robert Holmes but nobody but here there's something singular because calls between if you have objects Dominican parameter sitcoms really jump from the identity of morphism disappears this concern between different objects "quotation mark itself I'm not about to consider the incident and under martial law was vague on this mission ,comma Walter Johnson .period stop to consider notice that's it the the provisions the this is a new and you have to the government and the decision is I don't know not to make a general collectors to falter and to have considered general Roger manifold city Kinkel of fulltext 6 there isn't so the chance and so because can work .period stuff the southern many fulfill conditions infringing mania Mitchell the boundaries of homomorphic disks or maybe collection .period abundance of course will be isolated blinked over it boasts and you can modify Chancellor section by Hiddink considered connection flood but have some defect to the assets which a complicated story yesterday and scan visitors can focal functional it's it's it's has some information coming from amendment for 1 rights section this In a few young
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Building
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09:33
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10:56
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Direction (geometry)
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Sheaf (mathematics)
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Fundamental theorem of algebra
Linear algebra
Color confinement
Computer programming
Presentation of a group
Link (knot theory)
Theory
Wave packet
Thermodynamisches System
Lecture/Conference
Natural number
Wellformed formula
Operator (mathematics)
Green's function
Field (mathematics)
Subtraction
Multiplication
Twin prime
Projective plane
Element (mathematics)
Dependent and independent variables
Fiber bundle
Local ring
29:30
Axiom of choice
Perfect group
Connectivity (graph theory)
Kontraktion <Mathematik>
Parameter (computer programming)
Food energy
Open set
Number
Prime ideal
Goodness of fit
Mathematics
Plane (geometry)
Lecture/Conference
Ideal (ethics)
Symmetric matrix
Condition number
Stability theory
Time zone
Spacetime
Regulator gene
Concentric
Element (mathematics)
Mathematical analysis
Algebraic structure
Mortality rate
Mathematical model
Limit (category theory)
Functional (mathematics)
Category of being
Voting
Vector space
Game theory
Local ring
Algebraic function
33:54
Point (geometry)
Computer programming
Group action
Symplectic manifold
Tournament (medieval)
Real number
Connectivity (graph theory)
Manifold
Parameter (computer programming)
Mereology
Number
Causality
Manysorted logic
Lecture/Conference
Term (mathematics)
Field (mathematics)
Algebraic variety
Condition number
Area
Series (mathematics)
Spacetime
Surface
Neighbourhood (graph theory)
Mathematical analysis
Line (geometry)
Sphere
Functional (mathematics)
Spring (hydrology)
Clique problem
Untermannigfaltigkeit
Local ring
38:50
Complex (psychology)
Musical ensemble
Group action
Decision theory
Modal logic
Sheaf (mathematics)
Kontraktion <Mathematik>
Water vapor
Parameter (computer programming)
Manysorted logic
Quantum field theory
Negative number
Diagram
Covering space
Area
Spacetime
Block (periodic table)
Sampling (statistics)
Infinity
Staff (military)
Thermal expansion
3 (number)
Bilinear form
Functional (mathematics)
Metric tensor
Category of being
Arithmetic mean
Hausdorff dimension
Right angle
Thermal conductivity
Resultant
Directed graph
Point (geometry)
Classical physics
Threedimensional space
Perfect group
Variety (linguistics)
Civil engineering
Manifold
Canonical ensemble
Open set
Number
Frequency
Morphismus
Centralizer and normalizer
Thermodynamisches System
Lecture/Conference
Absolute value
Subtraction
Series (mathematics)
Forcing (mathematics)
Projective plane
Element (mathematics)
Exponentiation
Algebraic structure
Volume (thermodynamics)
Incidence algebra
Mathematical model
Limit (category theory)
Sphere
Local Group
Supersymmetry
Field extension
Loop (music)
Equivalence relation
Doubling the cube
Commutator
Physicist
Object (grammar)
Fiber bundle
Game theory
Family
Local ring
55:01
Decision theory
Multiplication sign
Sheaf (mathematics)
Parameter (computer programming)
Perspective (visual)
Manysorted logic
Cuboid
Physical system
Social class
Product (category theory)
Generating set of a group
Infinity
Variable (mathematics)
Functional (mathematics)
Connected space
Category of being
Arithmetic mean
Mathematical singularity
Quantum
Right angle
Identical particles
Directed graph
Threedimensional space
Real number
Manifold
Surgery
Theory
Open set
Number
Frequency
Morphismus
Finite element method
Lecture/Conference
Boundary value problem
Subtraction
Condition number
Algebraic variety
Series (mathematics)
Physical law
Incidence algebra
Limit (category theory)
Sphere
Field extension
Voting
Homomorphismus
Object (grammar)
Game theory
Fiber bundle
Pressure
1:04:02
Computer animation