What is a Spinor ?

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What is a Spinor ?
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as in and I think the that thank you well it's very pleased to be here to celebrate his young peers retirement and and the important thing when you go to a conference in honor of somebody is that he didn't appeal she should understand speculators so easy for them and I am the 1st speaker wouldn't send example at every level followed so he can follow later easily enjoy and he should if possible be able to ask a question at the end of the day and and set the tone right maybe start with the lead story my favorite story may have for Israel stories about the high school physics teacher Carolyn class in is somebody in the front row prep-school job yeah that will not pay attention so he turned to me said don't bear what is the lecturer so the boy scratches hands and over high that I forgot them so that he is about wouldn't the killed I only to let you know election was you and God and youthful and sell replace electron the tone of this election so I wanted to spend nights spent most of my life when he knows that one-for-one alone and I don't know only God knows maybe Iraq but he's no longer with us so now I have violent 1 of my favorite meditation and he also wrote beautiful language English nearly 1 accommodation he makes in his book on the radical groups we read it is about the starting off on the spin representation to the only with spinners maybe strike that level in the theory of his representation a week you could himself flourishing ruler incumbent so deftly moves in realm geometric figure in some way he geometry as we deeply connected with me this is the 2nd representation of that is to be Delsing flower market you won't just think into what he means but great value note in their classes of groups is introduction that he apologize and he's writing in language not sung by the gods and his cradle you just when you're beautiful English and so spinners there have been very mundane remind you basing our assessment of the went to read understand it you have the authority to rule listing even number of variables specials are in Group an Indian rights policies Milosevic Yankee Group has a double covering political group there was that there was little covering the group that could complicate complex structure and on to spaces and dimensional space is especially Unity group a year each season donor 1 this is simply connecting group so this voluntarily because of the
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in general become reusable break-up most Arab and Asian residue and considered to entry and bank is a space always up him complex of space is is the engine tuned to the power any break them into individual pieces as fast and as minus half the dimension you pull it back to the SUN then you find that the standardization becomes the same as a complex Teri algebra of the complex vector space and this past becomes even bothering CAR is milder on notice that the lowest price in his mind's eye reducible a couple of days and spend to end there restrictions to SUN bring covered as degrees much in the standardization body agrees as irreducible only under you using the degrees appearing now rather I was written the fact that it is has tens the spinners then what you get gimmes viewed is as the exterior out above the complex indications of will not not that not assuming underlying Center complex of the oldest forming the disappointment ,comma so the live fundamental algebraic facts about student now was founded by his model mathematics and Helen environment and provided in geometry and so geometry that I wanted to focus on and the outer does give you the framework but it's by no means explains that what the what the online that may interest in the Justice His representation of the group no I want to focus on the comparison between as good Bloomberg numbers problems numbers in know it took medications several hundred years to really feel they understood what I what I clear minus 1 was called an imaginary number and exist but by finding the useful using formulas and gradually step by step and became accepted and finally you a formal definition given the I became the square this gruesome Ireland became an accepted part of mathematics into the long long time and now I want that the spinners are analogously the square root canals cleared and geometry nothing about that the ingenuity of the fundamental elements and German are measurement links lengths areas volumes and the described mathematically by the exterior our induced by the account of the different dormitory as a fundamental tool describing together intervals so we understand very well so what is the square root the collide with his Rutherford remember that then part of themselves Is the exterior of world said the spinners items as the square
root not everyone form of argument agree but some of them all so the very deep notion and think it's already a these long-lived took understands good manners 1 that assembles bidders are and they've only been around for about 100 years so there's still a very early days of the Cold 15th century into the mathematics and so I don't know the answer to my question and not by the long period said maybe drachmas knows what he's up there with God so that we're left on our own and if you have a complex manifold Matelda studies complex then as well known to the world Hodges on the differential forms on an iPhone 3 broken up into the formal type B Q repeated roars there isn't too low the involves mixture of the 2 product the park so you have a complex tragedies he has Beirut the square this complex human C When you complex geometry you found growth is evident ,comma extracted given was there but it exists without the need of complex structure so what is this spinner within a complex structure that you make and complex numbers because of important only a fallible important geometry and there was no was on the Duke and do what they the said is fundamentally development formalized by uninvited self and so the important thing is in there Commons numbers is the analysis however the scourge was 1 is convincing window of the complex numbers the other record of real numbers it's only to keep going higher higher up just 2 the to but the leading the bottom up ,comma numbers is their role in analysis congress analysis could you see a role that has a very so unexpected bonus the people outside the EU's eyes formerly used to thinking only in terms of solving pollen and immigration but then mn and analysts coaching others indispensable tool so that's where the part of complex analysis assimilated they would be part of that is not liable for more properties of representation theory out of but in a geometric mean it's question is what is that you and your job I identify like Jean-Pierre with analysis of you just John Junker spaces you you have to use analysis division equations so let it stand analysis has to be found a substitute for complex analysis says the 1st stage going from cohesion is idea of the square root of Yemen well this course sold Vermont did you mean by this there introduced the lack operator inciting the way function of the electron and I'll come back to the drawing to imagination in doing that but basically it's a Lorentz invariant vessel operator and a bit fundamental role among the 6 and the nite equation is the equation down and so that this is the lack now the 1st step is to learn going for physics mathematics is the Reds Michigan State of the minus 1 and in the remaining Doherty also cited possible so the very different categories half my body grazes defamatory equations but in fact instead of going from physics mathematics to tracing the greatest matching my mind was already made them whole pointed regulations and developing his theory of harmonic forms was Max will great actually equations on the question of later mechanism and Hoggard took equations them In order to many dormitory and developed the harmonic forms which as you know has the fundamental In the developed among geometry was not ready damage in particular to similarly but officials here privacy as other vendors student that about 50 and interesting enough that and my supervisor was Hodge and his colleague in next office would direct they were the same department for 32 years and listen to each other number of mathematics yet because that was the very body and and said if if the as the transition from Maxwell equations to do harmonic informal biology with great found implications Johnson for the banquet and corresponding mathematics will not made by Hoddle act and that to people like me and sing and a reactive 102 spoke the direct I would've and no matter whether Korea so we had a grateful somehow that advises don't talk too much to be done now so the the the the likely Union reminded of and it works fast-paced think of space beginning this summer visits and you could look at the equation for harmonics that just like your grandfather wanted form they are the solutions equations Jack I tried to fight was 0 when equally well you can think of is solution signaled equation the Star TV fight with 0 Susan on combined mangled are the same the leader are marksman play a fundamental role In geometry and the reason is hardly beautiful 0 this is the harmonic forms the dimensions of space is independent of method you choose the very magic there no drops in the in the 2 0 eigenvalues others operator which generally respect the opt for the hunch operator there are no jobs and the harmonics forms always have the same dimension and give you the making of a topological so the question was Is there something similar to far more experienced 1st question was asked the answer is no he started then had to dimension to it is really that this is a complex topic analyze everything in the complex drugs and you find the stay-at-home wife that depend on the magic but the dimensions lies abounded range between 0 the gene so that's worry some information you years ago about the ability of the dimensions see where things changed that my decision was that the student he also I suggested to him in a meeting to work out what they the harmonics Venezuela emergency services good examples of 30 example of sphere is not site before Magic any candidate in the 1st place harmonics winners for the Magic's what he found was that this dimension on Monday an identity Missouri case it can go on and on increasing their exposure formal as it is values the magic you bigger bigger dimensional space so looks like no particular role expenses they don't give you any information of a topological kind like how my forms so as to be disappointed that's the conclusion you get from such a preliminary investigation but you the more carefully you find the topological significance so the 1st result and this result was that what I did was secure and motivated by the look on his before I put his book ?question mark not because the ?question mark bodywork could remedy that dates back to
main entry is discovered early on that the environmental dimension for K a French has all these various called upon the item numbers it is a matter of all satisfy the conditions for United 1st compact edition 2nd the witty costs is 0 then particular combination of . numbers called 80 roof this is called a roofer could really find something without a roof which wasn't there but this is where the better ones and conjecture this should be an integer knowing he proved for indirectly that he wasn't but the exploration why was it was really the start of my investigators feared that conclusion was that using ideas and act that our cooperated you take the Dirac operator acting it into Cheney's role of customers of the minor spinners isn't it to cooperate and 1 to the other day I don't go backwards so it is operating index for you the dimension Of the harmonics players plus minus the major nominees winners in mind this number the index different too on my face is stable and the perturbation election with the individual dimensions and keep going up and up the odd equally on both sides of the difference remains cost now is familiar with the .period characteristics which ended quick stability where individual Molly may change but I can't think much more robust and in the case of his military morass 0 India complex manifold and dignity the case was the 1st Gaza 0 civil Calabi-Yau manifolds then the modem of observing or the Kansas City Chiefs of homosexuals is a topological invariants that I think he has and that is included that agreed exactly in the middle rock operator in a special case the Nasdaq operator the formula we generalize is the it's will rock formula the tawdriness essentially become the same as a routine as having recently introduced Is there a while pub isn't this the index owner-operator the difference of 2 dimensions this is a very satisfactory on formation of a sum of cereal and acquires hypothesis for the sake of the way because his that we use where they spent his because of the political 0 is the condition of the manifold structure to spin therefore the drag corporate can be find globally In general the demand of operation and the redefined locally and then shortly after we um thus having the wrong here there was images some 40 other article the same year it was observed by the marriage was different drummers embarrassed who was closest to her that if they need known about the Iraq operated relativity theory he knew that you could define code background and that is well good position make application the ceremony because it is that if you are manifold now all Riemannian combined manifold oriented endemic to go 0 it used to amend manifold has a magical positive scalar curvature yesterday we condition only scalar curvature of the then this number a roof is 0 topological Kansas for example of the month was four-dimensional this is the 1st book Johnny crosses 0 ahead of all strong surprising 0 and approved as one-liners you know the geometry you can can compare the Jack operator a joint we would you will come in the for by the joint the involves much more the water in his address covering most part of them and the difference between the 2 In general the sum would be completed expressions anemic amateur involved only multiple of scalar coach the instantaneously since the current level of talent I don't always non-negative he had opposed quantity that stick people the operator has no solutions conclusion the next recommends no solution that apostle mind he makes his said a very beautiful simple crimes this by the way is have his idea they buy the boxer who played his individual forms easier these assessments but if you have a major threats and I discovered my brother give it to out which was again money W 2 0 the manager spin I assume that a nontrivial circle action some Compaq group susceptible enough acts not Montevideo unifil on means of 0 . 6 the conclusion is a roof is that is used as a model the index Obrador but what we call a covariant Kleenex including the images of was you when you have meant to convey another circle would assume it's very circle by averaging Bentley biden species of the prospered as the spinners would decompose further according to the representation of the so-called a of survey's 40 component Yoni next so much more refined and the conclusion of the theory is that he is a is called major 0 Phelps direct and particularly confident of his era now this is a strong result and interestingly enough late in the week hypotheses using exact relevant during my closet Nigel's which have synergy for example the company which is faced with natural in very measured but you still have this has made me re-examine why fit conflict Iraq earlier this year the 1st Gentiles is impossible on if ,comma status these dimensions and another 1 of the generator this if commenters you don't want to the same condition W 2 equals 0 it's easy this happened only if it all made all the dimension of colleges Motherwell 4 so to really a Europe went into my voice also so you know you can't have 1 without the stage of the European very nice fear his shop now the 3rd .period next to a deep result about the spinners is no different although they leaders others Ibadan which now I has summarized here but this holiday period work of time and also my student the very same as soon as a graduate student he discovered the remarkable things about 2 minutes before a fantastic news stories of about 40 methodology is suddenly became much richer at uniquely the dimension for and if you're later as I was with them have different approach to the same in various models on which was more physically motivated at of have physical connections provided little more physical and it involved local solution the migration but the same dimensions fall you grind down at Exeter the 1918 is 1 of gravest because you could envision the feels he there while we mathematical climb the collection visible call electromagnetic field the 5th visit to couple the value equation to electromagnetic field and it's follows us on the outside but you can get is capping emissions for you mean squares still with the religion the line bundle to it and this is a quadratic equation the monitor Graham the question is can you solve the greatest simultaneous equations the directly equation blasts this additional Molina constraints and this is I would be grateful if Paraguay and they invited wouldn't showed babies were about that and he wants to monitor solutions for this equation for a geometric then that puts a constraint on the possible churned blouses alignment the Nightline model must take a chair because only our finance possibility and those possibilities other variants of the life of a different sort of Londonderry these are Unitarians or manifold Delaware which which divided would agree that solutions the meeting deeply into the Dirac equation With his extra conditions and metaphor you get some event fantastic new results these new invariant 3 Riyadh translation involves looking other language at a particular time it was shown by with the wrong that if you have a complex manifold Kilimanjaro then was the Stars essentially reduced ,comma ,comma costs and made that's not generalize the notion of Chronicle clause of complex manifold the real nice for the go without assumption of complex manifold get them analogous to the Monday this about using that is indeed the way this is a very very deep results and that inventors gets most use out of that equation no a few minutes and lasted until the time they were very tight here
and I think we took 5 minutes beginning so that I wrote a paper in the back with material when you admire you don't ties right of your paper leave at the answers you write like died like crazy people which might be so that crazy idea was this we wanted to introduce into physics but the emotions of modest different operators usual but his Tottenham advanced differs from its wanted depend on Boston's retarded and then on future lost and that if you have 1 variable is tried out for example that you consider different operator you move considering that value and is delivered and the new readily relations but advanced equation you you take the derivative at different .period he drives they buy from Mt now that you attributed to a write-down advance a target equations like that operated but you know that you would observe that the translation it is as invisible generator review differentiation so translation conformal Britain accentuating so too will the trial they might have you exponentially a diamond UNIX elementary just formal be translation of the nation but this is how do you find a reduced to the invariant retarded operator when there is no proof that time direction 0 .period birds of his hearing aid under which which way when it's time so now that is a co-author you what you need is to use a vessel operator because that's what you need to expand sheet which is politically very well fortunately interacts how about forests rack operator was precisely amended by direct foreign affairs although residents of invariant operator and therefore you that the define advanced retirement creation for every year that this the paper we found by some element accounting Phoenix but that the the possible variables you use the integration the 2 very reliable mouth be 2 constants that and "quotation mark say immigration officer to become a from a rebound by which mother by the way the X is related the physical comedy called the common the wavelength of the particles so ,comma calculation is involved in deciding on the degree retardation so you don't have instinct link potentially I'm only here is making migration when the Rockies reduce operator his reasoning was that he wanted to write down that and the sharing equated will not that you would find a relatively invariant that 41 the the 1st great and he founded nearly died was successful but the loss smart-alecs leader on the of let see that was clever enough he could exactly could you can do it with a single robbery you don't need to have those that was a mistake he found this week but he was taken in a good combative without that the spot antics wrong here I'm using for this purpose you have to have a you can't explain she's single Rob was a result of this by different so here for us to use the right equation has even by that women
are more industry To say what about Einstein equations gerontology can you a clear atop those sums broader write-down retarded I'm cycling and we had some success but only partial and a stable which we had we know what you're going use he then not operator actions John as a on formal which is what you need to get to generate the reason you you take operator in on differential forms we deported that dealt little but he never he has operated with 1 reason being the 1 that agree that all 4 fights but now would use credit the spread eagle veered others that he was here you get up Hunter because IRS forms and that's what's Hodge jaded view emphasizing operate further or remote fundamental and many that have you have to have the view that is sensible to consider in use for them that already radical is the 1st step to spend and if you do that right down cook corresponding story for which we did before forces because then you find the scalar coverage this time is replaced by the you know the market and this leaves intervals when it enters into the ice and a great this give you a bit of a clue as to how the eyes and might be retarded and the final hour constant In the prosodic raise to govern 1 of the degree of the shift we of common wavelength .period was the the size of the correction but ordination parameter Jacoby at nite and media interviews psychological the same ideas which he declined mechanics means the erection of college but this is very incomplete paper 388 5 you've got no we're talking about them but today's society it's a crazy idea that was not insane and well and another in other societies invented a very thin line my father the local Knight of the mind and that he has references that you want to follow it up I give them better by paid with his response to spinner the index Monday was saying Exira and with more of this shift in they believe that each on home they bewitched the cheery develop sided with the theory and I should include you never got left out his diseases with which he calculates the harmonics crimson dimensions she stared my quick summary of what has been positively to not know I have but we learned that has hasn't deep he magical significance but quite why has seen what it means we're going to go we don't really know it has some with Miquela deeper study of the link between and dimension for particularly between spinners and geometry added another approach Biegelsen and for treasure mentioned we hear other Penrose stressed that is the way we Dugan the rate for dementia damaging such across the mouth of the dimensional complex analysis to be beautiful scenery which links reside in many ways and another way of trying to understand spinners intelligently incumbent John G. 4 ,comma geology of dimension expect when the different in anyway I think the end of my career I like to use a policy for the next generation so let me know when you know what has been reasonably listening a lot thank you few this information from ,comma from that of the common particularly in view of the mentioned like this work on the about the same as much of the interest .period units for which he was the mother of all you can have all the regulations would cost the city following is the introduction of the the by the Treaty fibers you on the you will usually uniformity thanks to the fibers structural think it is this that's exactly what we wanted to use the computer and the launch of my question is you this has been reluctant to do concentrate your pension only you have to say but the so strong that the election year
would you like USA I'm also uses 3 of the I know what is that we looked into it needed before I come back your 1st point I should say that this work which he wishes there are particular values with dimensions if bigger bigger bigger than this I have a topological signature lies and you don't get direct awarded information out of the space is harmonic spinners but if you look at how you how the matching various has been mentioned varies with the match you find particular some space is match expect people metrics where dimensions jumped this year the the topology it has a job in fact when you know the topology you could think but that's a jump had to be there the character of London Fashion when carry is double-edged the not about the money but by the group of 2 from office and of the rudest mobilize is study said his study vibrations or on that acceptable answer and knowing when the the reason jump this give you a topological homology commodity classes In the classified space movement a few of the latest of Roger information very inexact is things and I decided it is not quite what you expect it's different because are jobs the damn to examples of specific the variance in the general theory why the Germans were overdone mean and calculating the commodity of time so that it the spinners have stopped wanted accountability in unexpected places the time you were removed 1 of the hour investment is taking the mickey in at that no I knew I'd like to put his and as others good a job at a series of it focuses attention on the the depth of the problem and you think about this group miners 1 in here lies at the takes a long time to understanding something is really difficult notion but uh the notice of horses of difficult question yet to pursue the geology has also the Ways and then along the CDU you'd be adequate I should say that the current miners 1 got the ultimate justification Wisconsin mechanics call the mechanics at United ,comma exam was born with avenues used and so you could say that the DataQuick which came for that matter that were serious but Spinella deemed too physical means physics and geometry are my view that is said to very considerably he said AEA we we knew you don't answer questions like that but eventually after losses struggles and many centuries of work body a city emergency I now we be understands that the time is done I hear the orders meaning they contribute and albeit sees the next a directed by 1 or 2 of the will of the obvious Jerry lecture where the answers given chairman and founder of German yes but also because she has been announced the decision some of his decision that the significance of this is only the views of of people who listen the fury of the community environments so I would like to know whether you think they're on the right track of this direction to go along with the really the view of this society ,comma as again difficult and I myself have never been very enamored of supersymmetric in geometry and his supersymmetry is an added gradation and you just plug in the geometry .period formerly that is doing very successfully and have good physical education and people still looking forward to this image in the real world and our said experiments and all that myself I have added as scientist distasteful but that could be pressed but you will have happened otherwise the copy could use had been used against 2 symmetry but I recognize that I love my good friends using the system it is very probable technique so I think the question is still open and my view is that the disease well supersymmetry is instantly exterior out of work I think I think I III Busboom Altadena Christensen a century in but the on the and all the and