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4/4 Growth in groups and applications

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finally which has finally turned around so last time I was close to the end of the proof of the main results to source was saying he was proving that any state TV said Tuesday it petered out it generates and as as it's not as large as encircled by someone in the middle of this let generators he said the group for simplicity we assume the taste some university degrees and it contains all the results of its elements under the conditions the entity and so the conclusion is that high not bounded number of steps I was very all of them quality in the Member States right away really for this but it's nothing grows by about a number of steps it's just something bigger and indeed the ghost I'm in shock 1 constraints and most of the state ministries contends that simply and these from inside was impact from places like they kill probably intended to implement a approved the marginally weaker version which is more than solution for all practical if you want strengthening consideration leaving at any rate we were in the middle of the troll for others close to the end of the proves what Class 11 months decades we left for today was the most important 1 but it's when you have some people and some some non periods in the statistical induction so I went directly to the people so it's called the these going from a to the effect a man the year of Kerry .period point seemed so which marked its given by while it takes a committee is to be decided the excitement so it's all the people at its conductivity in this map East India Co all right so the induction case is what happens when you have the taste some appearance In the time he noted induction in northern India hideously generates it is a game that the case there's going to be stopped as some activity in the or rather some monkey voting see as something such that exercise and not the favorites but 8 sides of beef of Indian you however stated that the solemnity and if Holbrooke you have a generating the world some of the ruling to have some element of this steadily staking out of this said by the action of development of very well so all of his size that appear as we saw last time this implies that there are some of Bostonians would refer investment that there are many elements also strongly backed the ex-Soviet Union humorous and therefore I very well but detained us in the same time CSI secure so this means that excising objective so as you felt you have that you conceded so intervals and what you mean it's they X gets X 5 years accepted so on right so it's going to be injective all on the elements of the tolerance when you have a hearing you had when you have the Toros a excited he explained here intersection we think a few referred so the it's going to be injected so it's he missed soon to be at least once for the daily for some exciting the for years comes from the moment here I'm at the 2nd sentence 4 the host of disintegrated consider because these is of course at the lakeside base going to be so . gets an arm a what were the recovered yet so all of these all of this market is going to be contained in today the Holland's corporate tried Jr all the way to fight I didn't mean to say Excuse me so so excited be this so this is thinking this way touted condition the and the chorus ceased at last most of the time said because of the elements this is interesting intersections and so we can see from this perspective and they gave us chests what it doesn't matter Keywest for seemed so this was a clearance straight kind on sold we haven't they do the 7th piece the size of the aid to the forest teeming sold over the weekend so we have solved we have confirmation that assumption the was the new unlike so much listened to on the the same ideas that they have presented vis-a-vis there are contemporary provision which meant they could prove that he's a streamlined that he's also generalize more recently tool on crops and so media supplies and give you will agree grossing is amending its and so no fussy said last time around this is sticking points still there in the days dependence and then that therefore results of the site but that shouldn't be there and the consequences of those problems are tied up with the fact that useful limited bombs foreign-owned forcing difficult stand there until rather recently but now they are so we have some potent so
let me devote the rest of today's talked to all of this appropriately plainly not so that this has been proven 0 4 times they denounce the professed become shorter I cannot yet give you our full proof 1 hour 50 minutes forcing but they will try to give you 7 of the as of the press she was reading the 2nd half of basics and difficult exercise for the audience all right so what was the previous unknown so soon and assistance probably is Citigroup was sent from the elements of of of imitations of so what does not so for the semen or even Wisconsin friends have the are there also you however that for any 18 that generates the the 1st was published Monday May 18 so it was known that the diameter of the group responded by well recently eaters controlled all of the candidates so this is of course very very far from being but powerful so what we showed was not a paraffin which was something close to that was called the requested permanent loans so for these things and more we can also show at 4 in the 1st fabric of cities then essentially tied for non transducer this 1 for it's not linked to cementing its 2 I don't have the power of prophesy and even hundreds of something that on the sofa in a transitive so let me explain to the stress of sexually tight for the summer months discover because if you have at the cycle as the cycle of white of Phase I call joint then you have something of huge named as psychic probe of Houston so it is a fantastic several conducted using from this result but using come yet using classification when you consider that more and more a moralist choice that I have to tell you while results for the latest challenge linked to this week so too the designations here made away also the 1 that tells us that basically the 2 cases by the matrix wrote the range of strokes on his head as soon and as can be seen as too much else to do all right so far the audience humans they said the recession and things that ending but he didn't think he proved that the fees for most of the so what events he knows there's a difference there and it is this kind of conduct it's good that is called "quotation mark recording now the again and have to 1 then yes the process used at 1 step classification not just to obtain this coronary but the proof itself I don't like that if are a nice to have a without specification and gives fees I didn't know I did say I don't to get something in the sense that there is most of the problems that use it but there is 1 step that use it and if I knew how to that statement of the situation would the group has reported conceded that while I suppose from them it the idea might in that I haven't tried and I knew do depressing anything because everything will work out it's afraid of facing its it's the mightiest of place of states works well with others cage because it's reiterated its overweight to handle a special things so some of the guests and not just confuse people and the bumptious others the nomenclature Prof fractions you see friends for some of the groups of people right next to the instead the GX products to the a breaks the agencies for the orbit he also writes a it's considered the stabilizer of Anderson the 1st such more intuitive replacement always like to blame the on for the other conventions now of the source reported that of stabilizes and deciduous 797 so that when you start realizing his error said this the decree itself but only the meeting tournaments the point was that person so in the case of both the just system to reports said there around indicate the action of on a visit to Estonia as there is normalized .period realizes that the so that evident from the worlds the show exactly what they sound like new wall this year and the decision the but the 1st following me tell you what kind of crafts and working with in most parts is this which is what mean what many people prefer to call them on the drafting of repeated allowed the he said the draft screams further you have the descent of rights this is just our acceptance of the failed due to its eggs Excuse extended so actually graph the suspicion which his cease-fire graph for the action of American itself said it possesses several of the most properties over the seats they will connect as if actually eastern cities isometric leave it's usually a case in the names of unusual convention many if you think this is a complete search for work to be into the old 1 and we don't really know what health warning symbol believe it's 2 classics and new antidepressants for limits to this conviction however the international then was a very nice which was beaten at Logan Square yes C will be nice to them so nice to and so on
dilemma so what do we know about random walls well priority we know almost nothing almost already just because their Orefice connected it was therefore any connector regular grafted and it's a very very very very weak expansion tape resolve In the sense that you would know that landed there that land 1 there's been valued at Eastern region that is not the 1 that responsible functions is a bit bigger than Zeno and were already at an even lower bound nominal constant or abound for number-one itself and that there had to be useful says his focus on that tangy got lead still another abound on the turned regular army everywhere Texas agreed the connectors Connecticut had improperly said we send then what can I such that there and what precisely case said Anthony acts with probability that if you'd almost and many of the respondents foster the Spanish Steps this problem what our somewhere in Paris to know nothing about anything said working very randomly and often enough time you will be in every anywhere in Paris was improbability without knowing anything about the map of even in the city of giving them so there's anything that defend largely fund was horrible right but this is very useful when it's not lot all right so it is 80 of for the both I certainly tell you very quickly how do you prove that marries the year nuns Zito that got you can actually go insists that the constant so small ball for the work here were presented the country's the system fixed which is from the same his operation threatened so In all instance constant and the between them and me means a equal to the set of the inferences for which the body of foreign spirit and the spirit I given that the sun off any of our necessary smaller clearly told smaller that this I was just plain old ever feel this is very easy to prove is that the writers set of privilege .period skirts slightly contaminated by the of this 1 guy from the outset but because the graphis connected efficiently and then the only thing we have to do is talk like this the constant you might say wagons countries might be complex ideas of course but because this summer to grab aircraft the idea of making values was will be real value and Yank vectors McGuigan vectors can be taken to be re-evaluated since can take combinations of Fagan victims in value so you worked on the list re-evaluating so you apply these and you have that candidates separator
makes any known constant items conference face the said but warned that there this summer residence that means that the eigenvalues must be the smaller ones such as that Sosa small known constantly mucositis non-constant primarily about 90 seats because we know the fastest said the C-suite but fortunately or what you have forcing the symmetric group is that even tho its representations have no station dramatic structure they do have a very interested in the year to have representations an especially in sense In their presentations sits there much much smaller than the group known the numerous indications the lady solidify the sort of thing to accomplish it's useful and when any would be scarce member firms effects it's much smaller than Jean Philippe the example of the interface just the thing do the 1 of 2 and all are
all capable CityCenter Missouri and so and reconstructing I did not the they sang example of how to use the new system opposition to Republican fetish they said the Sitiveni touch-sensitive history to post sales the walls of this sentiments undertaken he indicated that he was appointed neither international skiers know this will be the cooperation will be interesting to on monitoring so there was this will tell you given something interesting when it's a proponent of East not on offer an intimate knowledge that most analysts think the the of itself and then and we will also as influence then there isn't the primary need to be where students to large sentenced 7 Logan excellent such that the support of the where is the support of cheap have explained it says a set of filaments small baby some of the things that most people in this the 1st of the 1 percent said he but no it is the plants here is scary but I wanted to be there it's useful and fact I was skeptical briefly I will just give the details of how to get about thank you this approach but something here 1st the EC 1 force or the use of these 1 6 the tells you that the new areas of the Prime will be 1 said it consists of a sketch of proof while there is it is so exceeded you have coalesced some of the the simplicity sold forces system in which the age to be what happens when you can't even keep pace human support of sage and going to be just as displays statements that signal I don't support the simple exercise of the age will be a subset of this intersection this signal as efficiency monthly strategy and there's been this section of the law and human beings they sold to support decisive support of the age is going to be a ministry time the intersection of pheasants and know what CDs if you pick significantly exceed my just completely random then the intersection of fares and the signal was will another issue become I ask where I'm old thinking so on much of harassing Miranda How large decisive phase intersection a signal the the other right furious I now take a random permutations Sigma the mayor and the police as signal what is said was your half of the Rome What is the size of intersection a segment like Italy was the existence to personal question while half of the room-size associated interventionist signals should be a sizable Tenerife or right but it was sold for similar truly random the uniformly him and we will have that size affairs and 2nd signal he and can sold your size is half too because you have of the world not can we see that there was no proof of that statement in detail yes and they would have to do to you in detail in the few lines because we don't actually housing memorandums that will actually have to do to show unity at the argument is sees it is recent history soft property of Sigma that gets stimulated very well by a random walk because of the all we need is at sea ,comma takes any elements to and the other 1 was currently has about the same for the so we'll have these but because its kind a substitute that is actually quite good because he is expected value is the son of a relates primary next off the probability take it from so what ability 1st signal announced ,comma from the wall not of Land's Infinity because operational alliance and began and the will both be reasonable the so for the outcome of a random walk with this is probably while ladies authorities about 1 over the 1 the that's that's almost cost this year this cancerous this
assuming wanted security on redundancy plans here no we're not going to the tricky because so I guess I can tell you what an immediate corollary of this series which was very useful result in less around before and on which we do use to treat efficiently no matter what you should really take away from this season against the respondent felt coronary area but alleviating that some probabilistic proves that mimicked very well so because you really want a random stigma now we just wanted to show that there exists a signal for which it stroke now the probabilistic methods ever since television company considers saying well known to prove that the same opportunities I would pick a random Sigma and show that it's going to it's positive probability so the city sisters plastic our version of the broadest admits that you are not allowed to take a random stigma assuming the element of the municipal property fixing was the ultimate outcome of around the wall on the immunity in some circumstances it is just as good this of so coronary conclusions published with the study that is found in the law where clown but I was with upset when they pointed out that he has put spending if patrons from inmates it's it's the same thing tho applied for the 2 of be you by the hand and G PG prime years spread that await us every time gets smaller bites actually much more than it was in fact because 3 the crisis monarchs you all right so this is useful insults the example of the public statements yeah and 1 this week all right he has to go out and release something it has been indicted on the eve of the many costing me hope that results when it 1st several known for so I'd be invited over sets numerous efforts this sometimes the Woodland Estates agrees 828 and sometimes a trade to the case for some months political deception large forbids consolidated the medicine that is really said speaking unless I want us to this amendment at approved I was this them in both hits all the new variant that they will get you use deodorant and I will actually give them translation of the prestigious next which were not following of this model is on the wall swivelled to score published the guess like classic think this is a roundabout way in fact he was working in the NBA teams back when it wasn't clear even whether the people who were the intensification believed that justification was that so few assigned to with successive year arm of much shorter prose achievement the process of some consequences of specifications and the process is for the following so it's hard to several of the men meaning assembled attacks sensitively on theirs and so you have subset of singlet under assumed that ignited displayed some of the 1st what they mean by splitting fares so assumes that there are these about abortion growth prepares for which in effect various existing elements such that Sigma service over a possible question of bears Sigma seperate sides and b what they mean by separated the eats known the 7 nicer features Specter Siegmund deployed with 7 since these comforting to interview these was called so you must have rights and so this is entered through a definitive statement contains an but it can also Ravinder Singh was separated for the moment with happened to disseminate the stadium which face the favourite's everything but you could do it those egregious something well what is it it was good about conclusions and that it seeks to seek Lange assuming age with this stuff too large to fulfill arrangement signed the point is subsidized with the same with the SEC East theory of the case the union of purchasing went to the protein all right so how prove to say if you displayed of abortion of all couples the independence for the enhanced version of yourself splits so I you point out says that he faces continued the gage if the prime takes for conveyed to them then HQ primed making various takes "quotation mark fingers abatement thinking volume on the political flat out and that's what do we do now so 1 here taking
random things use of her age and thinking random and uniformity each face of the plane and the problem was wines containing personal calls itself certain of several Paris since which but you could also say that this system year so appropriately the king debate to "quotation mark forbade her from complying with the crimes such a stigma separators if a crime and by the time the Comanche so we know that stigma separated Lisa proportion parents so Prodi the stated that Beijing suffer Baker to some of the primate of entities separated if that this summer no the self but at the same time if this happens if each university because of be that's prime to the I mean In the same way treachery seperate something they have wide simply because what and if all right and so no this is just a lot of random elements independent but settle far from the moment some idea of the probability that the Beijing this there will be some elements in the major start on the prime if it is so the radio for every aging now as seen with age would not seperate telephone while the 4 given element of Texas Instruments said it 1 minute from the revered this never happens is 1 minister told the but these would hold this looks like a very strong conditions for no 1 deliberately small but this is what even where some Jean said age stabilizer segment to the years because that he would be good for underfunded purposes there were deeper into the way of the prime so the Napoli the death this happens we have shown the small inadvertently couples for some terrorists he said most Square most in square in small but this was not the but if these things were about finding work for them what would you call that entwined so what if they don't be so if you rob separates everything within Europe stressed this was associated with so all you have to abilities that are large enough that society apparently what is this constant and floated so in that case With positive quality age signal
an assistant the but he said if something had happened this busted probability happens again the significant so there exists and there is a police force size ,comma of course it was someone 3rd seed approved the violent are of these of the a prolific India and all of your exercise is just too at this late date so as to leave this but this insult for 6 million would tell you briefly how this result gets used in the overstocking of the people at the end of was the work of a place in the it was the 1 here but seized many hairs such worked with the sample ballots of the aides say to the the 1 where the 1 is named in 6 on separation they then they face and answer they will where was the sense that they point to point lies on time on basis of realized just is there more very well all right so hard to use its them within the approved off growth of the small diameter instrument but as you see there are actually the result of Taipei speedily to the ones that don't have the stuff actually tossed Minnesota so be it .period part appear the concept of stabilizing chain of women's relays the chains concessions from Lithuania father isn't always committed this expression comes from sources from seems in fact before so on rights so what can you do views from a conclusion that that 1 the danger is that the point having licensing entities what does you have to deal with the top by implied that least locally known as so the assumptions and can happen only once he lazily fairly large went before so the only way that Sigma Woods played with the spitting image telling you then the thing principles of abortion foe focusing pretty hours seoul when lease knowledge yet the nonchalantly was smaller than the own his 26 lot a lot lot than squared and there are no less the proportion of crops and France Scotland it's 1 soul willing to use that leader going to use that crossing mother tongue not very large have not separating the 2 and 4 In particular you have a large for because if you don't have large for its if every if every orbit it's size most of our told them that this cover from Paris to so what do we do
so 1st of all there is entitled has no but even the point 707 that because this 1 polling is going to have some 11 lawmakers from the University at the point was very nice of 501 infidel scene of sites which facilities and so on and so on "quotation mark of the stock which called so I mean using pseudonym under fell them we say freight you have any really any state aid in recent times and decent tiny you're going to be able to find a point with large for it and then you in there .period assassination of document defines mud mud which went into the 2nd 1 survived Harvard Business and Indians and .period tabulation of the school year also willing to find some sort of forward to this on and that's extremely useful let me tell you something that you can do that we have been doing that but it quickly and so on India's that and exercise that then this implies that the 8th time bill interest rates a lot of excessive and reflects the very interstate the police morale prime claims calls the point where satellites are contained in the cities I just chose to be so when 22 % within the scores that's what about the costs of the Savoy terrorizing point have nice look like when the the Juventus restrict them to 2nd all the content the unions for them to Sigmund the acting and they're giving you this many different elements of same so you you end up having in this way if you want you can identify these sentiments to 1 tool up 12 and would you have in you have built the prefix so you have that aren't among the elements that 6 1 of 2 said you have almost all permutations of 1 of the certainly the beginning of the lights in growth the knowledge you have decent place prefixed with you than with it Siemens signal from some particularly said on Monday .period ways have realized by conservation SOS signal here is the 1st guests was 1 to say of course that to be facing a tricky and going to opt out of Ireland went to work 12 firemen is 1 arms on right so offensive on the liquidation but we that at that point we civilized Hassanal more wine because it was the trigger that could lawmakers mainly due to of fail on what we can assume the so solid that like C'mon alternative much less than that so with warning system that uses the configuration what we need is not ready for the free to act on semen on than make that we need to us that we need to be would assume that it has taken to address the subject under aura some meet stronger and immediate we not all views we can find an answer control
of close in size Council at the the setting on the sorbet and new attacks on dissidents to tentatively on and your door almost entirely on if you find a way to to show and it's entirely possible that that that it could be done without education excellent emissions it's so these are the only people who want to diversify its who you know like tactics seem but symbols of the orbit of and the the same moral did very well and on the right the standard you have something so you yes baby recovery defined a set of generators for the incident to trespassing and so you have on the 1 hand I get something in the plane was and I said that have it's a couple of that generates from orbit In that address given that on the other hand you have these long prefix acting on that recommendation so what the that surprise your cerium comes to the rescue I'm going to have this tension between so what it's going to be our options so let's say after all areas of the law and when entire with that cemented by communications they orbit 7 license the ACC amendment of the this that community we estimates but differed from its facility and Defense Committee sodium of the group generated by but the group generated may surprise you and if you commute which 2 tries as there some cities to transitive on set you must be what that this is the man if you community which at the time in the Stavropol without the analyst oppose what was to be so if you have enough elements that you know you will always find 1 that takes you to then asked if your commutes with that element of the new undertaking distinction between those 2 if you commit tweezers enlisted happens from Paris must Bisbee date entity so the fixes every X you know what going it but the number of skulls admitted he has small supported India's everything they totally about public him so advantages of course either this happens or what happens or renewal going to have a no more bids so let's face it and set in particular because you're not going to faces going to be some element of facilities to the sum paid to oppose what they say that's centuries to have some instruments yes they've pigeonholed the 1 with the largest of its and to have some such that the storage of size of police said that 1 of its spherical bullets taken to different capable and you know there's going to be some that he told the group that promotes around but whether the sorbet leaving that is containing being made To the world authorities and all Logan sterilizing signal so this is contained in the point with several rises so you have constructed a lot and a lot of elements because signature size health authority of these being moved to the entrance of the area you have constructed a lot of enemies in the .period wasted life and no 1 was able produce music and conclude right away that you have problems with you because you might maybe you already have a lot of them as the plane was misdemeanors but now Louisiana State Police have nice and warm moreover you have long lobbied for things do generate makes mineral 10 if retired and now work on that but was revised and there you will find long prefix and that you will continue working toward if it's major medical basically so that's the overall really working my induction resuscitated grows you call you work with those having
a searching for them so then you have no for 1 tried but failed Friday as long and it is said to have to repeat the steps locked times every time said this is a bit shorter and shorter but it does work so this was a very brief sketch of the main argument that they were the only 1 device to take home with you is the destruction of the for that with light from the point is that these are the moments strong yes there you are building up a lot of things in the winter that's what makes it so I think it's safe to say and they think if already stated that the main problems so this stole repeat 1 of them that was already mentioned people actually believe that the diameter should begin in the polynomial and might even be entered the post-Sept on some people believe that when you pick a random pair of generators of cement or 10 and in fact that
should that should give your might even expand the RAF was probably too rigid for which there was a so the cost of funding the reckoning will use would give states of realism masses indirectly there is that they provide obviated by Bob finished this shows you that the amateur all 4 groups of this retains the generators is basically delay the ambit of the loudest significant alternating factor so that's the way in which please NOTE it has been years you're working with this is the kind of I'm losing my face if somebody trying they're coming and that they might be but he said were in the audience who would say this is not a mathematical question but he recorded the head of work on the problem it's very interesting thank you thank you lose
Gewichtete Summe
Gesetz <Physik>
Gerichteter Graph
Gebundener Zustand
Gruppe <Mathematik>
Translation <Mathematik>
Vervollständigung <Mathematik>
Kategorie <Mathematik>
Flüssiger Zustand
Rechter Winkel
Sortierte Logik
Explosion <Stochastik>
Stabilitätstheorie <Logik>
Logischer Schluss
Klasse <Mathematik>
Abgeschlossene Menge
Auflösung <Mathematik>
Überlagerung <Mathematik>
Spannweite <Stochastik>
Algebraische Struktur
Reelle Zahl
Endogene Variable
Inhalt <Mathematik>
Spezifisches Volumen
Stochastische Abhängigkeit
Symmetrische Gruppe
Turnier <Mathematik>
Abstimmung <Frequenz>
Prozess <Physik>
Statistische Schlussweise
Element <Mathematik>
Komplex <Algebra>
Arithmetischer Ausdruck
Uniforme Struktur
Nichtlinearer Operator
Klassische Physik
Endlich erzeugte Gruppe
Kommutator <Quantentheorie>
Strategisches Spiel
Kombinatorische Gruppentheorie
Physikalische Theorie
Inverser Limes
Leistung <Physik>
Wald <Graphentheorie>
Orbit <Mathematik>
Zenonische Paradoxien
Physikalisches System
Kette <Mathematik>
Quadratischer Raum
Dreiecksfreier Graph
Numerisches Modell


Formale Metadaten

Titel 4/4 Growth in groups and applications
Serientitel Summer school Analytic Number Theory
Anzahl der Teile 36
Autor Helfgott, Harald
Lizenz CC-Namensnennung 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/16444
Herausgeber Institut des Hautes Études Scientifiques (IHÉS)
Erscheinungsjahr 2014
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik

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