1/4 Spectral Geometric Unification

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1/4 Spectral Geometric Unification
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Chamseddine, Ali
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Institut des Hautes Études Scientifiques (IHÉS)
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A brief introduction to noncommutative geometry with emphasis on the essential tools used in physics.
Geometry Axiom of choice Group action State of matter Multiplication sign Sheaf (mathematics) Complete metric space Rule of inference Theory Spektrum <Mathematik> Goodness of fit Energy level Fiber (mathematics) Area Spacetime Forcing (mathematics) Closed set Algebraic structure String theory Set (mathematics) Bilinear form Connected space Field extension Vektorraumbündel Computer animation Order (biology) Quantum Gravitation Fiber bundle Local ring Fundamental theorem of algebra Spacetime
Principal ideal Quark Complex (psychology) Group action Greatest element State of matter Multiplication sign Sheaf (mathematics) Group theory Insertion loss Mereology Weight Food energy Explosion Group representation Mechanism design Roundness (object) Area Product (category theory) Spacetime Process (computing) Infinity String theory Prediction Connected space Flow separation Graph coloring Symmetry (physics) Order (biology) Cycle (graph theory) Four-dimensional space Spacetime Geometry Point (geometry) Presentation of a group Tournament (medieval) Rule of inference Event horizon Spektrum <Mathematik> Theory Number Power (physics) Morphismus Population density Lecture/Conference Natural number Well-formed formula Term (mathematics) Operator (mathematics) Energy level Associative property Addition Series (mathematics) Statistical hypothesis testing Diffeomorphism Forcing (mathematics) Physical law Expression Projective plane Independence (probability theory) Axiom Approximation Estimator Commutator Physicist Universe (mathematics) Gravitation Game theory Family Spectrum (functional analysis) Gradient descent
Geometry Computer programming Musical ensemble Group action Existence Observational study Direction (geometry) Sheaf (mathematics) 1 (number) Food energy Open set Prime ideal Frequency Conjugacy class Operator (mathematics) Square number Absolute value Units of measurement Condition number Area Theory of relativity Spacetime Element (mathematics) Moment (mathematics) Physicalism Algebraic structure Price index Measurement Sphere Local Group Connected space Category of being Field extension Spring (hydrology) Commutator Hausdorff dimension Physicist Right angle Object (grammar) Table (information)
Group action Product (category theory) Spacetime Theory of relativity Transformation (genetics) Element (mathematics) Algebraic structure Oscillation Group representation Spring (hydrology) Computer animation Root Lecture/Conference Operator (mathematics) Right angle Lie group Game theory
Prime ideal Product (category theory) Logic
Geometry Transformation (genetics) Thermal fluctuations Sheaf (mathematics) Mereology Distance Event horizon Theory Grothendieck topology Frequency Mathematics Operator (mathematics) Square number Curve fitting Social class Area Spacetime Minkowski space Physicalism Line (geometry) Bilinear form Functional (mathematics) Measurement Automorphism Approximation Connected space Category of being Computer animation Quantum mechanics Right angle Spectrum (functional analysis)
Group action Musical ensemble Building State of matter Multiplication sign Decision theory Sheaf (mathematics) Water vapor Parameter (computer programming) Mereology Food energy Group representation Mathematics Mechanism design Positional notation Analogy Position operator Spacetime Product (category theory) Theory of relativity Block (periodic table) Moment (mathematics) Basis (linear algebra) Physicalism String theory Bilinear form Connected space Category of being Projektiver Raum Arithmetic mean Symmetry (physics) Hausdorff dimension Normal (geometry) Right angle Four-dimensional space Figurate number Geometry Point (geometry) Computer programming Similarity (geometry) Event horizon Number Frequency Lecture/Conference Operator (mathematics) Subtraction Condition number Addition Series (mathematics) Focus (optics) Numerical digit Forcing (mathematics) Physical law Projective plane Independence (probability theory) Mathematical model Quadratic form Local Group Supersymmetry Field extension Spring (hydrology) Doubling the cube Thermal radiation Universe (mathematics) Gravitation Table (information) Catastrophism Spectrum (functional analysis)
Complex (psychology) Group action Building State of matter INTEGRAL Orientation (vector space) Multiplication sign Sheaf (mathematics) Mereology Conjugacy class Matrix (mathematics) Forest Rhombus Area Spacetime Physicalism Connected space Category of being Proof theory Hausdorff dimension Order (biology) Fundamental theorem of algebra Metre Point (geometry) Momentum Presentation of a group Parity (mathematics) Letterpress printing Number Frequency Lecture/Conference Operator (mathematics) Theorem Initial value problem Condition number Statistical hypothesis testing Scaling (geometry) Chemical equation Projective plane Algebraic structure Set (mathematics) Line (geometry) Limit (category theory) Local Group Subgroup Commutator Physicist Universe (mathematics) Game theory Film editing Family Local ring Spectrum (functional analysis)
Group action Finitismus Momentum Presentation of a group Variety (linguistics) Multiplication sign 1 (number) Sheaf (mathematics) Distance Event horizon Number Sign (mathematics) Lecture/Conference Amenable group Condition number Social class First-order logic Physicalism Mathematical model Price index Local Group Connected space Proof theory Computer animation Symmetry (physics) Angle Hausdorff dimension Physicist Family
before the end of the world and I don't know I and if a In the war what do you do you the choice I was trying so the topic of when lectures devices geometric unification my message will be for the summer so so by genetic unification and that I would be using locomotive geometry as my but achieves the things can have to start with essentially for the 1st and who are familiar with German duty it's known that the genitive D is the example of the Jamaican unification dramatic at the anywhere that gravity is described through the geometry in other words there is not known madam was does the space helped to clarify that you know the capitalists would would dictate the motion all articles and things like that so I would be seeking anyway In genetic setting the new file fundamental interactions and that quest for unification really started a long time ago and did not Indian southern with Einstein but in his work with the collusion where he tried To me the quality too little forces the good kind of electromagnetism and cavity within its area which is juridical which is 5 the mission of the area 1 of them my mission is also to be smaller and was compared to find out about it then .period actually that that that electromagnetism that star in In order 5 dementia CAD had a lot to the electromagnetism but this is different what we had hoped would get the Falklands doesn't have the correct that exception hiring anywhere that I was wrong because not all forces would normally find actually we know more or less the full set of forces subtly swearing in better shape to define In order to to achieve the goal OK so the main and that was lost when he attempts all recent attempts for unification and the to you know visible 1 is assisting the area where the funeral I did didn't Is that you know you were replaced there .period structure of space-time with no strings and there so and in that case of course you don't think of it and also drew with unification but that's not the same spirit in was 3 based on all summer the rules of dormitory and actions and things like that the so what is it them you know essentially among the problem would like to to attempt to do show there's also quantum gravity so they say often demand that usually file fundamental interactions of course I really mean that electromagnetic for but the week the strong force under the the 1st City Of course the general structure of unification is known on the idea for the area and show this section impressed but when would be the 1 would to do German degree of course is the based on them send the geometry which is that you know was told that the bundles of fibers so 1 can do that look up today is not the complete Jewett unification and the suspect but punk and you give it dramatic closing of what's in it we can write everything and and this state and this language of vector bundles and connections and that this and well this section in the 1st section Seattle well understood because that is what really can develop form of local people of the area and the called off its theory that realizable seizes me that unique pretend region and that is you know it way behaved I was I want the reality of course is that the quantum level this is our Boston nothing of the little is known but as a classic AT the NEW very well-established at work extremely well and so that they shouldn't have to unify the 2nd 1 say within 1 framework in natural the simply comes up
In year when you when they say this is the 4th now course you I sales forces now of course the Shelley that that the name of course it is to explain but spectrum so somebody going Chile and that the particle spectrum that we know our course that we have the families but watch in the US and also want an addition we have excuse and exceed the feed responsible given all the formulas on the border with the so of course actually is in this aspect fiction even there is no or because heritage that the bungled appears simply that simply Boblett of skaters Angel published no these forces there for example of the Saudi described in the group theory terms of rules and former petitioners effect connection the you costs due to persistent which 14 for this this no 1 has when I Shakespeare the party spectrum because of course after the family is the question of Washington be able to say much city we know that it's wouldn't tool but we don't know why the city in the world while you have blocked and that because you know the way these particles have set the representations which we will derive annually why did the 2nd loss presentation I would be able to see at present everything was developed historically body all have a part of the particle when it was discovered it was placed in a set the multiplex endless financially at the picture took shape I think by 19 74 75 you know the picture was more or less complete except of course the book was not discovered until much later but people are convinced that the picture the the the the from his wife and that should be there again she have to explain all of the informed simply I sit down it looks like you know there is no reason that looks OK but there is no genetic that the weight why why things are the way they are OK and it's the best perception of wireless sensors that to show you that we are almost uniquely to predict actually but the forces With the gravity and the presentation that they are not exactly of this fall I will not be able to predict the scene we have still no way of knowing or finding out why that only the families in nature and we don't know and not only that we don't know what I think nobody knows for some time in a long string theory fault that we have an explanation and explanation was always you know and that's also the lab space is as some topological number however actually it was always in all the 3 came out as the number of families and 20 families and if you know the the game as something like competent 1 modernized .period 28 equal to see total it was lovely the association like Gates will offer you know families and anti-family will be supermassive under city before the lightest 1 would and say in Nigeria's in reality nobody except that this is an explanation so there's a cure for the problems that many problems or not be able to solve dictionary may unwilling to would be able to answer why they exceed will be the because of this question wiser Dublin but why do we have what would you have let those you know and all that charge representation will come out as I go so this sexually the long when he's the outlook so you so I would I would say it's out and analysts said that I would I would say something about that should have been out there is there the next year much of which was made the next year and that's 1 of the actions that we haven't yet connection the connection is the union is connection is lenient we get that if the connection is looking at that level the prediction that it's not that should all of this would fit but to have also bubble this would be the lawyer energy the presentation of the I have the area which is really the party was to coalesce grosses you to ride the growth estimate for adding the theory of course the let the little the quarks on the unified and the laptop really comes at the 4th color because there you know walks of the colors of India to or whatever so the leftist folders for but of course if you this is the at much higher energy and then it's broken and then you know you want to get more and things like that so this is dealt that his picture and this unique was the only on the side of the sort OK but there's so it's 1 of the axiom that for a long time he know we question whether 1 should take action would not and now we know of course is the way I see that there is this is a very good approximation probably this it would be the way to you I think it's unlikely that a law that things would be discovered sold all around there are you know you wonder what he but of course you cannot part because this possibility and that is very nice possibility this pedestal I'm unification the revised and that it enabled people to board whale this is that the round setting there now occured suffered by the junta physicist and you you know you'd like to unify all these forces and you say I'm unwilling to look for did you geometric way of doing this initiative so you try actually affordable tiny circular Tennessee mechanism of all of these forces that are you talked about we know actually that journalism it is really based on the few offices everything we do which of course is linked to the economy as principal and then 1 way to achieve it of course is that you make everything and applauded invariant invented on the board and purposefulness cleverly action that you write must have descended OK which is pretty strong but they know actually the city away guarantees that the dramatic all space-time would have this universal interaction because you know about the method you won't be able to write any invariant expression usually accept apology the politically correct but the bottom for editors and that actions the Matic is everywhere and in a way that would as a consequence of that you see that the gratitude and that with everybody because there is no way out when right to avoiding all the density that could start by electing energy to get these galaxies everywhere so that's universal willing to look at the universality of the that action that action we really can apply to except by using them looking and then and 3 assembly line of products with what is the matter at and as you see across the street would cost 1 this is electromagnetism and the weak and the color so this is the symmetry that we have and
that 1 would let them that she too 2 find enjoyment CD based on the severity of what actually the problem that doesn't exist In principle the 1 can show that duty cannot do it this way you cannot simply find higher symmetry well without of course having extra molds for example alone can lose a client is a way of doing it but the price you pay In that you are really going because what happened in there in higher-dimensional series of quality in all 5 disappointed by the have before by mentioned in this case you did you find that everything 5 emotional and in this case you have ceased yeah that's the future of the sex of the fetus if you'd like to think of it from the four-dimensional point of view and then you you say OK what do I do with them With dependence on the 5th sold you know the independence of squatters who stuck expand and yes to the 5th Court is like a cycle and then he all 40 waltz and they have an infinite power of states so what people do that from paper would drop out of the state and you know you get you only so all the candles more local climate is staying CDU keep cutie next states and society is same as but you know they can enjoy a material which includes only so now my the assumption is that while he was not permitted geometry as myself the setting for unification the the 1st question that we ask is that you know why should 1 goal of committed why should we will welcome it so support actually analyzed by Qantas and which the diffeomorphisms calls G and that Be My symmetry With morphism summoned girl and what would like actually entered the Profumo affair enrolled this MySpace and it would be this would include looking at include but he said would be dead there is is looking did look at 10 In other words if you know like actually space stuff that the you heard of the space would be what we know and you know what it was through through the magic of people proving that unique ability except by by going we welcome its process in which you really involved maybe this is the same then in which involve well and there OK so I knew it let me know where to start without discussing local management fell into that made many ways of further trying to lay the groundwork that OK we have to take commuters but in reality there all are would be only suggestive and then the question that if I take a look at those actually this a appointed so what do we do however look at the request of the scholarship let's take a curious the data that defines In the committee screen and this data political and this way could suspect under section of the core issues shall discuss them know that none of geometry went in there and of course 1 may ask the question would you be able to recover what we novels Opel would you be able to recover money manager material and there's the report suggests that already includes Romania dramatically so it's not that you don't you get completely off and you have no way to ODU communicate with what you already know so this is really wood is a big test virtually and there's of the construction of the amendment which show that you can obtain actually on what we know all or most of what we know about because the project is complete most of what we know about the only major material from the formulation of locomotive to so that actually defined it as legend the gunman outside defined each in a minute or so however I would be the alley what rejection for visitors that there be a charge conjugation Obama's Kiraly to him over the offices this that knowledge when is but there is an engineer patent Watson it also measurable With Yates 1 and evaluation h complex Hilbert space carrying a faithful representation the presentation of all of that In 6 of started here here during the descent that John says enjoyed 38 1 h where there is all events people understand invest remember what tournament for India's Compaq is the is forfeited to really the appetite generalizing cooperated another lesser Chile for people who are familiar with the operators you know that all guests spaces you know for reform with petitioners and in order that the Yaseen getting this isn't there so the gap will pay that Kadyrov but before the formation of all the quality of the space In other words you know with the DAP operate it's
equal wouldn't to know knowing connected you know what happens is that in the construction that operate at you all the status quo diplomatic with the FIA and attentive so there and in the spring connection there the John met the specter of over that operator actually did really has cat inside the walls of the genetic information about this and have a lot In the light that the animosities the all the Gulf from took off from the program for I see license of exactly OK still learn missionaries of study the 2nd version of Okinawa villagers Eleven Denio greater 2 Place units it said today that it has divorce Congress with relations across on each this city's unaware very energy over there lower 3 takes us from public enjoyment regional the the the all of the GAO take us through mutual interests sold for physicists charge contribution well if they needed to freedom age had understood the guy talking no properties I have finds things for Celestin all how these objects stopped each of which you know you the former it was example of the use of English the proposals there will be released know that there exist as there is I think the animal to you need the I find useful if you applied by some of the dead and several injured look at that what is the hope Roberts 1st gift this optional where absence at the front of prime removes 1 or plus 1 for example the consumer 0 story 1 this 0 elimination and minus 1 and she scored on this 1 then we define so that ABN element of the were and B the then we define global statement being jail restarted June and this is called opposite Benjamin this case received the opposite the amendment of Balkans the is defined in Minsk no I saw the enactment of the Andromeda led the space you can think of to spin you then you know you can act on environmental November space like this you get that from the left action From the left then a opposite would act from Goma so this case we write like what you know this is OK if you have some with the coolest action from the pockets of of something being the same as the old boss no action from the right music over collection although postage area all right direction now this is a first-section but direction the directions on the left action it is very good for the last 2 yes these are the properties of the fuel engine Galileo talk about victories so I'd stop and actually this is you know it think of it this way if you want to dawdle charge should property charged with judicial apparatus the proper those 500 additional pray that really in UK industry the panel dimension and their properties the square is 1 of not 1 and you know you can take the action that you for that and you discover a achieved that they satisfy all of property and this actually the usual method by which however these operators would work on something called the cable dimension which is that apology over for Williams a local will and there they have at the same property so usually we defined the dimension is not the dramatic sense but the substructure at least dimensions upon actually was the properties of the charter colleges you go conditional beta off-spinners although some the groups in this In the corresponding by mission that exactly simple the northern section is the proper visible produced 1 and the last thing the Clinton you could also say the election was less than the right action group the 2nd is actually a difficult to 1 property to that DJ all in all it is J. up to assign this with me music dignitaries yesware's Buser minus 1 Digital Media Center commuter JDA Alzheimer's .period from plus 1 then then and then said the garment origin to commit the D but Jay Garner this and the rooms no not secure that now
I've interviewed 3 science and depending on the findings it means you can classify depending on the size of the World the crime from other crime you can classify them on in the table but there and for real issue can you know enabled give Nova election the abundance of chocolate and 3 people fight revolt because of press freedom .period annual anything like its stake in Tupelo side without classification all of what called my your on advice spin there is my own advice spinners In when you are talking about it opted for the algebras charge conjugation this exactly Simkins kitchen so that when I say by mentioned doesn't method by mission it means dimension that for usually liable to get because it's you know you have to science it means yet only a possibility right because a small data minus it's too few traveled to get a possibilities depending on the size of absolute maps Prime from accuses Uganda of and then you start taking table and know against the ones 1 1 2 . 0 then you have 1 1 minus 1 this acute undefined except for easier spaces for in all 1 plus 1 -minus 1 and so they can make a table and that is that got killed in Newark and so on the New World way the former swimmers and on more work "quotation mark this skipped the new 1 and so this section called this killed and the way it is chosen as Italian features the with with the existence of what we call you my arrival advice for example people the compliance usually the dimension actually then lectured them by Matias and you have to look at 8 which uses you choose when in a wide because there is the best beside by those by mentioned the ability to get miners lost last nite .period riots and the 2 would certainly doesn't the 3 of talk about dates and if you make the classification discovered at everything repeats itself will date that's the reason that you or I might run a vise president of the Istanbul dimension than OK and the teleological the plus-minus Cassidy saw the Israeli government In all 0 is equivalent to tools and you know more than the Exxon will become combined and I want to go he adds the to gum of clarity yen for further measures will double 5 afforded them by mentioned by the existence of the so-called government revenue that cases of television at the end of 2 the U.S. Open here OK so what was not alone should keep you here said there are no more no action to which option the last victim want throw to see what happens if I don't you the DAB all portraits 0 what must meet actually were shot that is not the case here that this book is about the media to show that if you don't assume this then the connection not the union would have to on aquatic pipe which is another cinnamon here because we don't know that in any other fees the "quotation mark would maybe element of but fastened condition however then on employment and geometries colleges but is not to actually and this year .period of sphere then actually gonna supporters 1 without commutes with elements of the algebra for all day the moment of the day and therefore gunmen the pilot which implies that space would fit into its pluses and each 1 which would have actually no indications for physics because it allows that you are able to get left-handed split-level pretended my now we do assume that gage is endowed with :colon a viable deal structure such that extended it's he a deal the sector doesn't exactly where to put Lopez document when transported did they pose a the following you a group you enactment of and you start and you could mislead you no finally coming to to an end to this definition because would finish sometime the Netzarim a joint action also fuel when age this so will you the opposite not secular
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more that and that is very important because if you don't believe that make the visit for thinks you know I did not preclude lies at the root of Mutharika wisest thing if they had big implications on the structure of the representations of particle physics is not obvious but this will become a come and this today you'll Jr you start so you due but just CSI :colon remember your positive is that exist so you story the UK's I start so it takes this form because remember this comes as you thought when it comes here it comes as the star opposite rights which means that it is you start scholar just thought this guy can we had minus while Kanojia minus 1 is adjacent to reduce in the game yeah is 1 which we musicians just is actually back here this you can go to jail versus the yen good disclosed that phenomena also yeah because you can do what you taken them although excluded it'll that relations not next now way you find general almost all of you know that you define in the spring of product that is product in the space that the G axle the CSI naturally nobody wouldn't that give the operator would act on an element of that but spaces then you can begin product of former Scanlon and the fixes for you know what 1 would like of course to that there being upon them doubles transformation the oscillation above the transformation which is hereby this would be very under
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that front line and it's known that you really have to put things in science right plight and if you let this be a function of X discovered that there's nothing reinvent anymore and the solution of that is very simple what you do that you introduce a connection To make this thing in violence and then you said you knew was going to do new Class or price is the usually is of course most France the other 1 and so what happened and that this is the pastor replaced with DEA which involve fluctuations well it is defined to be a wonderful summation for possible our solidarity with the theory it really is a connection on this ultimate space once we define our property space would include all engage connections as well as excuse so they fit in that case you would be another I want all the explanation 1 of their engagement 1 thing that you have not including the 2 robberies including which takes so the section .period in their own this type of transformation here the CSI goes this was 2 now that other thing which and of mothers out of office which essentially Hassan do with the fact that deep enough and that there is no way I would like our own part of the leaders that this way even if I start from Achilles heel slack-jawed material I'll be able to this all the mood among German geometry from fluctuating around the again this is not staying because after all you know therefore people are aware the body of physics below all of life to obtain genetic diversity I was taking a flat space and then introducing some somatic fluctuating around and of course you would be able to cover all of that all the camps space the and things like that by doing this this fluctuating so I actually is not notified that the area dictionary hostile fluctuated deed without automorphisms to generate to generate actually the care the began there metric out even of flat so in other words actually impressive even for knows very little known also some flat space you'll be able to generate the mall give space In the locomotive context OK so what do I this essentially no claimed that even with this to the mathematics that introduced by somehow I have enough information To start and at end the physics probe How should I do now for in layer that they're thinking about betting that look 1 instead of fueling you know Maddox starting with the and equally chairman you knew would be extremely would extremely we are really embracing this with some but fairly sold only in place you know things with them at the make and how to measure distances by saying Look I'm not able to study that'll double to study that I define my space through someday back and then I look at the spectrum of the Dapple beneath the spectrum of the DAP operator in principle has all the genetic information that buying In other stocks abstract but would show that it is indeed the case so that this this way it all of all course I can define distances in the spaces and things like that but it said the new elaborate because you don't do it that way everything is done by making a couple of on their own by give value so everything is done through idea values over the depth of the deal the additional quoted that goes directly you immediately think that it is simply for missiles that's you be here it is the fear that it it can has the television site in quantum mechanics and operator that can have on the quality of get both said even before where some cannibal OK then and you know that when the alcohol our diversity and to make an assumption :colon assumption alone to make and this is the lacks from Iowa knowledge in way because if I really know some long ,comma displays in which I can give you the date of the brands like predetermined thing out of it and I should be able to drive the physics but I don't know the space along what space should I take which is to an uncommitted we make an approach which 1 of the separate and anyway is approximation 1 expects to hold October extremists Walters was not brought a measure that this space that we live in 4th witness a space-time then the fundamental problems faced welcome dramatic space it is given by a a community Jay Garment assumption that is you pose the problem of 1 Pontius which is mission we know a lot of disputes which we have to find out OK so in this case I can see a Europe-wide anyone in area the tool and a friend of each 1 per cent in each tool is due on tools the government of all government do however the is not the view it is you on gross 1 sleepless Gumbel 5 fitness Sumio called the 5 it has been suggested that Gross G 2 0 and wetted down the 5 with you wanted to come now it's structured this looks like a TV products face however not media anytime and that well known to the government that all the physics and is indicated by the spectrum of the square that the squad the dramatic events of you compute quite yet mixing In all 4 described this case reviewers but because what nonetheless you know that squad knows about both sky this is then look at what anyone that we say OK said hello I won't be very conservative and I'm able to big to be they usually want to convert to any minute they bear with costs mostly made in many forms was the day that was momentary memory of a valuable and that brought functions and you professional functions scary and it is the best place of squatting documents spinach and then d amateur mildew wants to unload
ball bomber Mueller the new Oklahoma did you know of course that you really stop objected then we'll call you know that you are really going to be that as I said even if I don't know I only know that I have that space that I have gone mom you would you OK I would be able to generate this story how the genetic disorder while you know you apply gentle 1st of water in the nominee alone of course is not invented the general which you have to make it invariant and then like this here and then of course that you when you act on the spur of the fine because the spinners you know what they have they they would then they would be transformed on there and that was another group you discover then you are really going to work to make it that you have to put connection which is the spring connection upon this spring connection and then he can I do the compensation if you're interested in which I assure you that conditions on the Mall June and indeed that the chemical stock which is really a consistent with With the property over the head with the city of greeted the then I can assure you that you can allow spaces with special portion which would correspond then all of 1 of the beef in string theory this is consistent you can go and completed further but look anyway that sensible additional but cautioned that can duel so let this get breaking can be number broaden and think that yeah this is in principle is part of the Panamanian geometry for the continuous aspect of this new permitted priests some well but now where he faced with this question I said that this space a product off you know .period genius behind the screen for the state to wait what I'm going to go know they find my page .period might due for moment ,comma some finite space there is a need In his speech a one-sided and I said through USA and Togo only about you know 1 tool in sky now the question that we don't have to ask is What is this thing might be for a long time the getting knows so this work have started to do that and you know and the longer boldly to 7 and for a long time therefore stake in adopting the space was simply taking into being Dubai to make decisions and 1 by 1 the diseases and things like that and then and then we the ,comma corresponding to the Illinois somehow was constructed technologically looking at and and see what would fit dramatically so there it said the spike you know your argument to solve the problem in regular someday than by to and you find some as and last fall and then actually valuable last fall for example to being for a nite was found to be like the last age left and feel C and this was done after Nelson trial-and-error and that the longest we will actually be put so much the same problems so that it can fly bites out of the analogy after many attempts then we decided to make this the ship Of all possible finite speed In what other possibilities to get a good dancer calls a slightly it should not be given you that we take this because it works that's not and this was 1 of the criticisms Julia program say OK you know there are certified to sit dancer as so what we tried to do is that we classify all on finite spaces which are consistent with that it than before OK now want to show you that you know almost uniquely because you know Barbara mathematics there is always some little cases which come out ahead would be difficult to exclude but for you know what practical step his the license gives us you know almost unique yeah but we don't we look at it and then you know we don't have exceptions will an exception the problem that they accepted than other interesting but the problem how to rule of law holds the promise of a higher principle is very difficult to know because you always sure you that some pungent don't some symmetry to the temple was then unable to get some lung says but the question is that of course is not convincing that he faces the I the are something look at how you know before before moving on I was born to 2 things that we are considering festival since you are using spectral appropriate Monday before us to take you can do it now they show how to bowl the Minkowski on another withheld must find a marriage is the question and is the very similar to this is exactly the same to the other question facing people who do battle in the egos and called them gravity because they're worried about the forced take a million Canadian species of wild things don't make sense the question about the ball back and what's become interior for a new show ads in all it's a start but what he use in here and you have on but if you are concerned about having a useful it is the use of the word is unloaded it's not involved in the south of the country contends looking emboldened this is the problem because what plus-minus signatures you can go the negative and would like things as you see with is exactly the patenting in for gravity or even a four-game series know you like things to be positive and this you can only achieve indicated that he will not yet the the is not the problem and it'll probably the disk which is usually both guarded the specter of the duties to disquiet in the deciding spectrum and then things will become unbounded if you take negative yeah so the action lower-valued union the the of musical the state it was called to deal with Miyuki did not say the university I think given European looking similar centers in office think there's enough the focus of this section is 1 of the problems but the problem we face is that OK with the inadequacy of was on that of course then the question of unions which were able to get it would become problematic because known should that especially Sperber faced the letters gage status In the event immediately get protocol doubling funds the reason the following in wake the support that you know you have a client page the configured side
and then the province's digits size and independence but there are not know if you have no relation then it is not too late to CSI and then it would be a new spin that and then you only physics was about to find it every particle as America and this of course is unacceptable it was essentially we really have to acquire that we have to solve the thermal bubbling problem so the 7 problem it would mean the following that this project space that I talked about less time must have something like 0 why because then underlining I can imports for example both but that Kiraly condition and the Marianna conditions indicating if you don't know that they are able to double firm years which is a catastrophe physics now we knew legitimately the four-dimensional part before four-dimensional part already mentioned you know and I think custody for employment in the former National Park is the equivalent 2 as we know no whites too because the plus-minus of the signature a member of a told you that if you have seen the serves the blast on minus 1 plus 1 plus 2 minuses my thoughts such as slavery because each other and then neural tube about the victims and there so obviously if you only takes place by by itself unique and never put both countries to recognize the Yemeni forces to 10 senators on space would've killed mention should be fixed because local 6 is a ate this will do this year will be a right so this really forces so to start production solos Vermont problem will finally forced but they can finite space to be the case was killed when In other words achieved the top and space should really have permission templates exposed None of this should not come as any surprise for for people who are familiar with supersymmetry local supersymmetry you know up further the further major American employed Wallace conditions simultaneously too and this is where you have the strong year signal modeling until dimensions and then Exxon instead and that's what that other thing would exist so this is the norm for a long time and is is it cooks the front of the sea In mathematics is exactly the same in the wording is the sort of like a it's only you want you exactly it for formerly known locally in the form of what I did but I want the product to be dead and the project to be 0 before approaching this year of a product position this Europeans of the exact of the free space because then I get bottom for this condition of course and I the Boston bottle model all of that makes us after both on the foot if I want a bottle of 1st place them I know the they can mission of the free they should be recalled that in this case and according to my table the lineup no 1 1 1 of these emissions 0 for 8 with OK now we know that dimension for now of course argued that we are cheating because you think your talking about 2 key jails of the new jumped on Murkowski it looks different action UK again and I will talk about it later happens and that's what I believe there's a view that the way it solves itself in the UK signature is different than the way it solves assessed pneumococcus exist then actually determines long it better to get the coffee innocent and the asserts that it's serve as different as the different mechanism was say to solve the problem Our come to the for the consumer yeah outfall falls for authority the yesterday on you and Year's lose the you need to know the exact exactly so I'm not now action yet and the way it's says the 4 as I said you know because the way it solves itself In that you take actually a 6 and this has fallen because we know that we know when we continue analytically this would be the answer now how those it solve that several talk about that later that uh when you do a patent here as you don't really get them of deep you got to get that far thinner the the and the popular of the means you don't indicate over the farmers and that conjugate your new then you can only be grateful firm music so you you cut you cut that the degrees by half and the solves the problem in this very and what they think of it that should be just that this way that we really need that kill dimensions 6 for the final dimensions show this is acknowledges the problem is how to but was the 1st thing about this fall the this is what we call the figures on the topic the fact is that only people city and the year and the you can hear the music of all year and it was in the water this was not the solution to the problem you know something on the to take they experience as your basis that's what I'm objecting that they would spend half as Europe as a whole lot of please don't the way Casey a question that is I know exactly what you what you that but that the question how to formulate jaw mentally and those of other particles would become more and more complicated notation 1 that is being asked is the building block 1 key this is this you can't think of it as as a a question you know if you can't read a book you always thought that that spend half the building block gay and indeed action for example almost Spain African spin 0 and 1 sprinter will be committed to the local phone some Prisma you can think of this that and the building block but of course you know you may I wouldn't why should I take this as a basis of German is the 1 taken but I think if you take the other point it becomes too complicated I would say this become so complicated the life of me that we are proposing that the I had to move you have an acute problem that OK that the the the proper will only give them actually then you have actually to consider enlarging Europe dramatic space to call to the operator that pact on the Ohio higher representation the and then of course that it becomes more much more complicated but of course of buzzards would ultimately come save complications is not allowed that that's not the case "quotation mark energy without at this juncture at this juncture we have to know say what other spaces that would for all of action so what do we do no put the classification all
the finite no local faces you there while actually in L. King Khaled in the Appalachia part part of the classification would now without this dimensions 6 but the balance 6 immune mutual cut with local cut things out the not before 2nd out there that he only 2 investing in to do set told people but of species that you can regardless of the 6 OK you have fluently pursuant to the end of the Edgerock maintenance is are they kept Orioles already 1 of the art of the bond yields see this is a question the wishes and Europe revived his us make set of meters they had OK Phoenix lies ahead summit of the Group a New York you can get at the question of what the set of all possibilities and discovered you this week there should be nothing but the Yukawa coupling of what was conducted at you have to a do what we can for them yeah that is the OK with them not to be but before I had a long relationship yes but do you know this dance of all also people should year yes but that of course in this case of course that we will exaggerate the scale of death and it again that that is that they could go on millions of people will be extinct and these are optimistic and that an only hope of the people of the area but this is not allowed actually is not allowed on the possibility of breast went down after being and offseason when on this case questioning all or a woman in what I should say the complexity financial the complex of 5 major bro I can only be just off the only bookcase so in this case the center of the giraffe it and what is that OK that and what sexually I always use on His painful back no-load of the government of the I hear them it look up and down then only as a order the came William Q was the 1st of the condition on this that nothing but commute this action and action commute is or what you need to show up but these are the only 2 possibilities and possible as breath of you he said that he would use the the of the Jews used our looked up but this a that's our property that was half our properties which funeral but busily you that Ecuador's you'll learn about but Nov what if you make them maybe everything is a mature religious choral work and it is much too but at least OK knowledge thing which is not used in the end to this condition the DAB applauded it is not fought this classification the play connection and want to use it to cut down until then to that answer which I told you about that comes in and the military has physical implications all the neutrino mass which of course is in a mess impetus for 6 now Howard that proved on another proof is really involved in what took all the expertise of alleged to improving the theorems into a tool corrected down because there and was really very surprising that you you've got a problem with a lot of good have obtained millions of possibilities and there however it will you the approved it is based on the following I cannot because that would take or simply to do with approved by the media were due to expire in which I I would I give the steps of the proven that would give you know some this orientation for everything I said today items of meters is still to become more don't laugh because up to now London musically using its abstracting the only thing actually which is used to and that they exist perform I don't put in Panama and squad equal to the he would do so you assume that the sentiment this a projection operator does exist and that once you do that then you can show that you can have at most I know only 1 only Paula 81 92 such that you know so in this case 182 would be easier to deal exclusively with the squad and would fly on it means that 1 can show that need you can call on the way it's done that you assume you have many and than using all the properties of the jail and how you got all the protection because of the Act on each other how they they would that they would talk to the jail and you discover that you know what this is all you'll probably not that complicated actually part of part of the disease really difficult but part of it which the spot that you can have only 1 and too it is them is not difficult to you be external go through it and and but at least let me hear from this case actually In this case the jury would grant from banks like explore 1 involuntary games geophysics why would we want because leisure Barroso the so it actually that takes competent conjugation ammunition could you didn't know yeah and therefore physicists said no know what we do after then essentially here but here actually here the 1st place is inconsistent With gala and is now you all this is inconsistent with the Golden that you can think it'd would give you and all your firm use of things like that so this is the from out and you're left with this guy no but this point at this point so executive
complex fired and roads 15 OK so anyway in this case the community abroad is the same as the complex from the debris of the question What do we do in this case and then and here we were forced to make an assumption that 1 of the algebras 1 of the gibberish on on 1 on 1 of the jurors that exists lies all to ask what is minus-1 and the tax the first one and limits on aspects 1 actually no it's on like Jones think of it like all support that tax and operator on I actually Silverman's you like this it recorded the some Paulie writing good you see them it like and photographed with something like that the freedom .period for barbecue the exact condition budgetary limits this summer and see for become ,comma overreach question where and he's doing this case and age in this principle to on an otherwise actually it clearly illustrates the fall of and by and made this is to be formed on the Qatar News becomes a tactic in way don't think now of course that you this is why we do we have to follow this condition without the knowledge of university building but this condition UDF after this case is 1 of the cases really could not rely OK but if we think get good or something physically connected to and you know it's ominous and things like the drug users there an operator attacks on diamonds Avenger brought in this case you know maybe I am following here I think I have 5 probably maybe I I would've almost complete integration of this question is when it's 1 of b you know must think of it that you have a matrix like you know sick of it that having matrix was 0 1 minus 1 cereals and then each matrix like according paid he did not and you want to interview the work that initial conditions on this but but I think there must be some complex conjugation and this and this 1 OK so this it acts with the complex would you give in in this case the that's what should exactly action but something like that and that limits searching the and history rumbles like to conferences even it limits the structure that it is a sub subgroup is sent off you know for example that instead of S 240 media test she took courses at that but in this case exceed becomes in space of of Katonah so this actually is something that I end in a lawyer Chino now the spacey becomes pleasurably comes amid overreach and the North Sea what entities but we have to remember that would have a Kiraly to operate down where Anderson and this to me exactly yes analysts so this is what the agency into it now we have also they exist Of the Kiraly to operate from Goma and it has lacked all may have here what we have here no usually we bake it blocked on the and if attacks on the forest this may overreach Split In due to OCC anyway not only the 1st possible optimists say even that OK let's Bob Michaels the easiest possible What's the easiest possibilities and that's happened is 1 now you the small but here of course actually here I cannot operate with dynamic because if I put clarity of after put it here than it really is in all our because this section just like a for for you ,comma packed with current with Jeff Dr. lose God is that all those guys that it's fantasy into Suplicy and it means in all your yard Parker spectrum anyways is too little and that correspond to that you know originally to that you want to YouTube all involved line but what if you do physics of this the old 1 but get more multiple plots to step courses and a list of everything but this is the easiest but of course knew about because you cannot impose honored the parity doesn't work look I thought then simplest case when can impose import currently conditions industry they wanted the war to the space isn't to French once and for all OK much attention will make its way after losing all we have to put in memory of this a is gone soaring time she told me coming in ,comma breathable discrediting around the parity and then if you employers cannot until this this place is to H left most of the time In the the 1st know you know now without doing any any and everything as it should be no ID can barely you my family comedy friends I have in my speech people the number of fermions this year by mention of them in bed spaces in this case is that he has planted in the 3 2 1 squad but was cut by carnality you have to squad the squad when this fall it's 6 so 1st of all began a printing pictures number of fundamental concern is that the space which of venomous of space 16 if I stick to finally punished they are they follow presentation as follows recorded a blocked it all OK this is 1 2 3 4 and this is 1 tool which was like the slow right-handed and this is left-handed hitter so the that almost that actually as far as a part of the spectrum "quotation mark because then you have to know this actually is new arrived last year I actually usually of course states of Boblett so the new rightly I knew enough I hope you don't the denial of
bridal variety of everything because this is 1 class ,comma sorry I'm going to get some new arrive here I knew that you have Top bride riots and event actually mothers with which some of the kids you have already predicted that earnings are going to get 16 firms and your and this is like the 1st possibility no other possibilities we can we can go on but then they believe recovery they give you something extremely complicated you know talk about extra 6 Stewart gage groups and will they don't quite so what the claim of the following if you classified and breasts finite dimensions down 1st monk immediate possibility obtained that'll what what what would turn out to be a sign that momentum and actuality appalled that 1st on the condition because when they bought the first-order conditions it would be really give me that this this would follow in his this comes with yes this is no irony toward you or I or anyone who arrival beginning that we have no explanation for the number of families that a distance from the local alone and accused the number the S in the work that has been a able To give diving about why this number 3 the multimedia the you yeah no 1 in this section informants picture amenable walk because of this you already there before the 4 the laptop looks like a 4th European it's misleading fathers ,comma you and if you really would insist on the symmetry then you can have it all this year when this has on the weekend that revitalize mobile but we had no education defended the of the physics of presents gays this is the model to formalize and that you know that many many more indications that will come along the way but I think this is the fact that out of a simple classification and Michael Fortier the fear appointed or I can go through with it and that the it's a amid that some funding the Abitibi angle and then locked in the attic universes before give this vital by this amateur is called the by the 7 unification and it was not always the same time as Georgia you know Georgian 1974 she said almost side with this problem really bothered to choose between this and supersymmetric the Mitchell supra effective but the but the sellout but an Indian physicist so next week I will let you know maybe I will further proof and then know not this I'm going to the way my plan is as follows I planned to do with this connection is that bad data indicated I would be able to derive the food connection also the model and dead how big she comes out naturally former as a specific thing is you sitcoms unity there is not and then what to do with that after you obtain the connection how tools pretty the bottom south of the world so soon please them


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