3/4 Automorphic forms for GL(2)
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Formal Metadata
Title 
3/4 Automorphic forms for GL(2)

Title of Series  
Number of Parts 
36

Author 

License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  
Publisher 
Institut des Hautes Études Scientifiques (IHÉS)

Release Date 
2014

Language 
English

Content Metadata
Subject Area  
Abstract 
Philippe Michel  Automorphic forms for GL(2)

00:00
Addition
Theory of relativity
Product (category theory)
Forcing (mathematics)
Multiplication sign
Mathematical analysis
Algebraic structure
Set (mathematics)
Incidence algebra
Complete metric space
Sequence
Open set
Number
Sign (mathematics)
Computer animation
Lecture/Conference
Social class
Condition number
03:38
Fraction (mathematics)
Frequency
Lecture/Conference
Multiplication sign
Network topology
Consistency
Sequence
Directed graph
06:48
Group action
Building
Finitismus
Multiplication sign
Open set
Subset
Maxima and minima
Permanent
Positional notation
Manysorted logic
Lecture/Conference
Queue (abstract data type)
Integer
Area
Compact space
Standard deviation
Product (category theory)
Physical law
Neighbourhood (graph theory)
Basis (linear algebra)
Sampling (statistics)
Algebraic structure
Measurement
Network topology
Identical particles
12:10
Linear algebra
Logical constant
Polynomial
Musical ensemble
Multiplication sign
Archaeological field survey
1 (number)
Weight
Event horizon
Food energy
Open set
Number
Subset
19 (number)
Population density
Manysorted logic
Lecture/Conference
Average
Ideal (ethics)
Determinant
Descriptive statistics
Position operator
Curve fitting
Area
Compact space
Spacetime
Product (category theory)
Forcing (mathematics)
Closed set
Surface
Neighbourhood (graph theory)
Coordinate system
Set (mathematics)
Flow separation
Network topology
Module (mathematics)
Equation
Object (grammar)
Figurate number
Coefficient
Identical particles
27:17
Axiom of choice
Complex (psychology)
Finitismus
Real number
Direction (geometry)
Multiplication sign
Sheaf (mathematics)
Open set
Explosion
Maxima and minima
Mathematics
Curve fitting
Units of measurement
Condition number
Social class
Compact space
Statistical hypothesis testing
Series (mathematics)
Element (mathematics)
Neighbourhood (graph theory)
Basis (linear algebra)
Set (mathematics)
Price index
Bilinear form
Equivalence relation
Factory (trading post)
Quotient
Module (mathematics)
Game theory
Identical particles
Family
41:03
Axiom of choice
Principal ideal
Complex (psychology)
Finitismus
Musical ensemble
Presentation of a group
Decision theory
Multiplication sign
Distribution (mathematics)
Survival analysis
Student's ttest
Prime number
Grothendieck topology
Number
Subset
Prime ideal
Quadratic equation
Plane (geometry)
Thermodynamisches System
Positional notation
Lecture/Conference
Queue (abstract data type)
Integer
Absolute value
Curve fitting
Units of measurement
Social class
Condition number
Compact space
Focus (optics)
Spacetime
Chemical equation
Moment (mathematics)
Volume (thermodynamics)
Division (mathematics)
Set (mathematics)
Latent class model
Bilinear form
Equivalence relation
Vector space
Lattice (order)
Order (biology)
Quotient
Module (mathematics)
Figurate number
58:00
Spacetime
Constraint (mathematics)
State of matter
Closed set
Multiplication sign
Forcing (mathematics)
Infinity
Volume (thermodynamics)
Euler angles
Measurement
Functional (mathematics)
Explosion
Lecture/Conference
Feasibility study
Quotient
Continuous function
Right angle
Object (grammar)
Resultant
Condition number
00:02
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00:10
a 2 show the opening of the I opened up sufficiently will be motivated deserve to use of force at this so I don't know about but sold just what they want to point out is that so far from forgotten easier than some of the work with the other about then we have basically done now sits you'll sold not much a structure of the shoal NY a media 1 true discussed so the addition of structure which come to India that which eventually made it possible to do so and analysis so so I joined with this stuff now ,comma made looking just at the evidence and not later I will come back to the tools to make more precisely what I discussed at the end of last but no I just stuck with any soldiers being of advancing so this is it the following year being so it's looking at the of the week the center of the class head Of course relations fuel so it is clearly suggests that it's a set of crimes and said compilation which is internal from the incident in which corresponded to reality completion of and that's preserving the fad is following that pulled out the old places observe that compilations and so it can be returned times "quotation mark because I think that products available in cases of please and sold by the Times paper which which have a finite at the end and they are so so that this is a set of sequences also appeared equally months fault everything and that what with the quiet is that it's the belonged to this is deserving of Benedict in danger of sinking the fall on most every 2 soldiers say this is a completely and that it was too low to work to what we've been told yours but I would define this fall for the Virginia walk social condition that we add is that instead of having to adjust to bear the number also then have we had to condition that we had a sequence of mattresses and we want requesting that almost all of the isn't
03:38
might make the sources added .period eating dig government so a and B F of the views are phone users so and the so what about India the insects can we find to book so and that we have on suffered so we had accused which which Wednesday into the screening of a dead simply issue date of Western millenium and then you send it to the constant plans and because of that year was a finite the denominator off almost every time it's you will be a bad eating together so
04:34
we have a sunbathing and beef up we have discussed would still be on which is the same social agenda and I'm evening and so constant and in all cases and also so we have so we it we can also see if we want to be inside so ugly that the is of others insides of the that inside the editable this by sending you a sequence speak to the sequence of each species at barely pine and then we budget hole consistency in the concept means is the OK we may also amend the so far we made it 1 2 Longmeadow soldiers dead so cute it's so we can hide the deputies to be somebody being of cutely into the air air which is weather dedicating mentor and you send it to the sequence With that it's Bucheimer people is the whole declining business today and at work so you'll yield OK so this thing is so when of on future that visiting uh so it's appalled octuplets socalled has that pulled the tougher of topology televisions in use at even the topology
06:50
Delphiits and the than we meet created and sold operate 1 may want to deliver to the use of English so it topology which is someone delayed dead 2 was the Jews to apologies its effect
07:04
on them and the you can that so it's not a good idea to deliver these things just the socalled because he would not have many good public that instead of 1 but certainly it is and they don't Fallujah the topology and a dangerous side will be finds it encouraging that the new findings open set off better basis of open sets after the of the phone so so an open sets off on a basis so you you take independent of the shape out of although all of the above only dead we've only she will be useful plants and what we ask is that only get clearly is a is being fall on most of the time so I manual lets users the topology is the building of standards it's it's both open and closed subset of stupidity so it's a it's a vendor but no permanent compact subset of of Cuba and so this and and likewise you give to them as of July finite that there's uses the same as a stimulus to collegiate and it makes us a F close the additive Sobel both air and the church UPU become close also to the inside of the reserve full of single for this look at so that fewer showings that 1 can say now that we have these stupid so when we have used a sampling of a which is just a Ford product of came and then this you when you I think didn't apology to reach full called elective and you just obtains a chicken of topology because of the effect of higher up compact and so this is no person complex so 12 of the past and that and it is maximum infant into maximum and madam and Juni wonderful neck solely to maximize opened compact something of a and there may be some things which it can be In this to India this is just now we want to see next year and it's maybe it just will be more concrete about these basis so that of the neighborhood of the conductor of the identity of the man from the additive Gold recalled structure also of the opening of a S from his May measures OK and in fact complement compact it is given by your allocated sort of enduser notation so that the application of and collected it's just this product and youthful and at an integer 2 when all that it can only taken things and the law and all enemies DVD burners of the smaller funds motor fuel your neighborhood so values of his which are being popped onto the floor area is that's so if we look back at you so I know it is open to you that's a queue of embedded into what there is is that it is
12:12
a discreet symbol and the soldiers and 1 of his own music so if you Is this could so if you invest sector virtual so he my young bidding event that and mentioned here so if you intersected Kewell with so the spokesman said so what have you looking at you after looting get a hostile manner number which at should fault which appeared editing danger at every time which means that the question number which is a ably whether the teenager is an integer and and then is danger has has to be between minus 1 1 of the yield on the average also its use as always isolated in by this neighborhood so when you get so discreet and was so it is discreet but it's not to small neighborhood less and because so it's sort of figure so if you look at the squash under so what you there indicates that to this question is allmale not to end module is so you can see it needs exercise so that it carried out a season began finite but the season compact but so and because we think is Compaq it means that Emmitt cure is a social compact also 1 on geographic I just thought of income if you look at the unveiling of of cheers into the air from then you can show that this is true on this way is dense and the other day governs this a consequence from the Chinese mainland children and others say a description of the of of this business of open open sets of neighborhoods of of OK this will so depending on whether view of the evidence including the wellknown were often not including Zen you see that she was there the front of the Soviets after some of the big cheeks and no idea what they want to do is to cost would go a a bit more complicated objects and I want to go to G11 of and to go on to therefore offers you will both look enough overnight hope so OK so so if you have any than you can constitute therefore the poll ducked and added public to pollute and that's OK so this is a topology and you can't pull a lot of people over but the product is fewer beds and their savings Maryland pulled so battered to death sold through and to pay and the is displayed because just because of the Paul contrition and so on and and want to play with this and so OK so what now what they concede that easily is so I can see that we not find so that not find that he did I find that it did so here this is the end I mentioned that I find space of a few would come and the soul our soul 9 jolted it's there is defined by Europe 1904 polynomial and it is a set of an such that we just can't said that by bias by boards of bullying and which contains some of the idea the findings of a heating but In an ideal of putting on your own and so what you you may
17:19
want to consider his interview of the saying that weather that this thing which is the acuity of on the new ideas that you so you may want to find video and to date is the set of now they end such that 2 of its inquiries also hold peace in 1988 cancel she this is and this putting on the island which coefficient Safin Q so they African but it could happen in SOU knew it's in the it's legitimate to 2 computer Bowdoinham and polynomial functions after continues on on the of advanced because of use to political opinion so this which is a subset of aid to the end user is I'm going to close subset and so Van this evacuating them as approve subset of their hand it this is the at the topology so and that you may have a concrete this screenshot of forces that may be but Novell's unless you can to desert as a set of industry we speed speed in the competing and speed in the yield EPA fall almost daily tainted so it may well be the case that the citizens in the middle of a less under the new may look at a video of fuel and because of the fitness the of Cuellar will be differently than the sold could be emptied the of Q will be displayed as 1 would be so as most important example for all of us will be the case where he is position Italian ankle so I remind you that adding and Lopez and I find that so it's a you it's so close the Serbs refugees of the pulled out of and entertainers and make the city's diner there are fine lined and the deserters who I defending the idea of and that is the ideal generated by supporting a determinants of idea the times the minus 1 so too is the coordinator of wine and the G idea of the government of the method City Mont OK so if you want but if you take a matrix and and you take it to and that U.S. that that this may create spanking minus 1 equals the always means that that the teacher times of announced a wall busier warned in fact said that the team will be in the interests of the data and so on and then sold the the land that get in that way which you see a gain as cruel as the subset of Of these although it's which a item offered to HUD and square this 1 as a quiet out there and deservedly took pollution and is a locally compact yet they didn't see it compact to pollution OK so yes Fernando stages so when you equate July this week that the topology the guy future of what you get is that you ought to put television that is locally compact and surpass so that good sold locally compact said that I may be OK it's been said that I didn't think that teaching tool topology to hoax and so you can do now is the same with a any idea bytes of so linear algebra walk because you may see musical by the as cruel the severity of these I find that unity and you did refer to the constant energy of air the killing area which is Klausner sold locally compact and just by yeah OK so just an exam by the end of the 1st GP services based on October 9 Walter itself idea and so the survey so sold the idea of using against the prime ,comma equations sold calls for all of the time you then you the question and the determinant of he is 1 so he added a truism is that matrix of of the quality problems and to reduce as the candidate at the season and then you add this equation which is a set of of polynomial equations of coordinator Virginia and this is doing the bullying of my earlier question so you have something which is look any questions so far up the body welcome accused 2 these OK so everybody be yes look at a guy attendance at Macy's suffered plate compactor neighborhood of the identities because so you get your view it it contains many small and compact so it's the sort of thing mentioned that you want if you want to do is unable to put apologize for Soto apologetic and understand this OK and so then you whether the on Beijing's so socially of fuel and beds into the air and into the streets and the other hand the Europe density of Q on May the intrusion of the Air France pilots and that so it's not necessarily dance it could be quite big but not maybe not dance so what started in delisting object that you might want to see so people so you have been so often it's said he of the efforts the surface that but for the time so I just think it once again into this definition finally adding idea gold yet you hold this sometimes so he of the clean so we just met creates we've coordinating GP and maybe a mock enemy dead weight to widen his year of the Pig is like it as G of QP has a standard legs of the of the square lectures at the University of Cuba please so you and this and that when you ever inside the the issue of the Journal of the which is just called Art of unity of zinc lead which is you is an open compact some hope not necessarily Maxine and what they told you can find it if you are
27:17
fit to changes coordinates you make you mad just as square pledges to work 12 maximum complex of but anyway so just at least what you can say is that the using the visit maximum open compact for Arnold widening the condition of the reiterated its overweight and because of the unique pollutants from the if anything better OK so and a gain of so what is interesting is that In The Hills fake therefrom admits the basis of neighbor who Of the identity the solving of open compact SUV along so that's very usually 2 of the many many smaller open subsets whichever find Brooks and we checked nor the compact is after princibaru once and all and which are so it's equally capable of handling of an item and 1 careful and easily pulled out of the case people and wish to appeal and is the set of GTE in it said if you have the Soviet economy faces with GDP on 1 cruiser identity of mud and all that so if anything that's about as a condition his voice so it would be the year of the game but if that is very good at it but so it stays that is a at any clue as to the identity element and so when the becomes more on what is it that you get a sector shrinking the set of of of open compact socalled look at him and then you you can just concentrate in this neighborhood and translated into English .period so clever nice neighborhood OK so now I would Sovietera merely look at information so no I want to come into some important the finite nests seal them so due to Wilhelm and what we make certain Linkovich acquitted itself fall of carefully into you look the end and both complex sold man will consider quotient GF Ferre divided by G of and develop invite care and so this apportionment is finite and the it's a step so and the real fight H. G. healthcare effort from the class members for this open complexity so I thought we couldn't do to what we have done enough to just a small the Nafta if you want to hold such a statement that it is sufficient to pore over the statement for any open complex of hope so so you the known for a while and news always for because uh if you ever sold tulip and compact simple Gareth anticrime conference so the sanction it would be an open goal back said and because it is open and compact so it's contains the tombs of intersection and of finite index was involved in both of you in a bit of the big sold all
32:38
units and to pull the CEO and you you you know you have a choice of development compact so it's just thought manner OK so long of course you will have a nice day what they did something they had stayed out the so if he is pieces of medal and a and K F is the safety a at soldiers pulled out of the February the deserves closer in the fall .period electricity so this in that case the fact that these "quotation mark Ashanti's finite and its overseas this is a family name because he still has Hawaii and because you whether she sold in Virginia's identical use agendas of the letters spell out soul this is the obvious stuff and under this section and so it's natural identified with the quotient by users tabulates from the coach Entergy of advises that the legs of Of those directives which is a G of the Act and and if you someone push the Soviets have few other gymnasts she had a set of genius pessimism and and you know that is find the children of HBO and it's a wide digitalization of of the to assume but OK we will I will give a report of the Sule Hamma now it is in no special cases so calls if a so far she Jesus has so few and so I'm as the fuel is fewer than appropriate so meanings that few of its is not desirable for all of its in Cuba and my will fill the quadratic from ever on and none the general has you know that and so far it's just a year and we just don't know the code something so used them so we so the fact that it's directly linked with the notion of factories so I will jolt constantly statement into some concrete statement about lectures thought which we the win pull the COM and even something stronger so that me use a love for half halfanhour hour to business sector lectures season being that he sees In an not necessarily Bastianelli and Huston and the use of the and that is so this images generated by European business affairs and and OK so let me take so OK a so as I said to pull Silverman the justification to do it for open compensable so it will take an apartment complex of Popovich shape so I take as a hostile melodies and questioned in use OK and at a constant as a photo we mapped so from the and thence into the reality season OK which lets say I never banned in New Delhi Lamont GAF times he an aide mapping tools 4 win so I think G F L so then may get a hostile melodies and now I act by mind in really meant of it said by minus 1 something like this OK and what's the doorway gets in and of these maps so yeah so this month OK so what do we get so there is a major this is the the union of of reality series which shaft In this the GAF albeit a fault of the natural election also begin on act on lettuces sold in Virginia form in which it considers years of the new Out of some letters in a minute Virginia and then and so sole mandate so that it could lead to you Web identified or so you with this man and this map of course it's not injected because you can see that there you can see by the the support of Bastianelli many months if you define might but where is the of GQ acts of soul not so does not do anything so what means it is dismantled gives you it's an identification between them the portion to Fiji a module too module the use of a pact and gets identified will be set facilities and that bind this single OK of you could do it directly also beat it will be identified with the dissident union well the key test module game not hiding look at it with the let's
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say that so let me say like set of focus on patches of Virginia's classes OK it it's Whitaker said the focus on petty but these in season and uh it at even I don't even know that users of the services of decision is a genius classes is finite just the set focus on patriotism and the sole what idea so you I don't want to make a mistake so it's the fuel intersected with the best idea for care for the if I 9 1 year and weather G F I need is such that it sends an airline according to the latest step back so OK and so you can check your offer up it's a set pursuant to construct that he knew of this identification and misidentification it's and allmale Of all this this and this is a discrete survival Prodigy are so need a sizable Perugia and you take diligent union insiders sold was beaten side to this of for lettuces so and on and and you get this so OK so now I'm going so this is a completely Jin added that no and going to use my put his soul we I have to you we may assume that a queue of airline gelatinous Minnesota weathered the phone used in the guise of balance and so knowledge so far of any hits the nail on Monday of what this implies that you are a few weeks in absolute value is greater than 1 because it's Nunzio integer but then is look and see that In useful but is told that between 9 school for any of the so it implies that is called so Q of Ed kind is hinting Island all boarded a prime incision use of airline because if you want to check that something is being taken union demanded to checked its fault they believe you're the editor a bid to in Edmont and so there is still felt following a plea for a new prime numbers and then the utility said climb Yukon that listing which is much from to spend because they offer because it is a these days to different from each other over the environment by you enough to limit confirmation so you bespoke rafting and sold phony in skin and climate and that is UHaul whoever that few of its users the demand 1 and but then that if you just you apply you know Joe Belfiore October another confirmation of that for all the skin of a kind climb in In the both and where it is yeah health and just as it's not that they have beaten there you have it it's not so you have that you have the it's because the government because orders that is after all a diesel to each other OK and and this is a very good because what it's saying is this goes through so it's a quadratic from this implies that fall it's a dinner a Pine crime Division from the old Oakley speaks in this is bigger than circling the enormous expense to be a bit by some Konstantin which but which they buy onions alleges that and not an native entirely so this announcing that you shouldn't always that you may look at the volume and so that the kids get volume of this election is a crime so which is which is that Geneva Kovio Youngs so the volume of air would you know it kind kind and what you can call of checked is that these volume is in fact equal to the volume of village elected so the volume feet so I know what you have is that you have a set of letters using all of the same volume which have no other smaller vector so now you have Manitoba compactness creatively implies it so you have to show that the city clauses that American backers contend implies that that this which is a stronger after deserting the legitimacy of number of implies that June the pair of misconduct so not only it shows that this cautioned his compact but also by the student union is finite so you get both 1 and some questions so this is a very basic there is the simplest case of cough of bullets your it's and you are going to want was to Seoul any any support Beagle to do exactly the same thing so that solar so you get the fight of the testimony of a number of years no 1 should not but the OK I don't know what it calls football players so you can if you want to wear those Liverpool football and fit finite still and suffice to waistcoat because its provision that Agius so hope the attention it to do so you can leave and I believe that we few In the plane I don't remember volume but beyond that it's own promises so when you see that so at least you see that if that if at the user through unmusical it is at the core soldiers and module
49:32
GQ module is the bad actors it's a very nice space because it's complex compact space here and can although this portion because then figure will be compact because you cautioned by the compact and that this Saturday as a very concrete to incompetition needs of finite union of quotient of the by the by these feats of and the I remind you this is basically a bank we wanted to study the offer we found when we were looking for the discrimination Pope of tearful presentation of an integer value menu quadratic farmer so I remind you that the whole Wingo so we can and it but absent from the book not exactly but that so what did we at the UN on what side if we think less Jenny we had the is according China so we have made some minor gymnastics and what we have reached its according to China of her age it's notes of bits so can I wonder what is OK we have is obvious and it was a year it's the so far off some of the competition is units despite is of the unmet creates here defined by the I this note acquires its valuable square foot of perfectly so I want problem about a quick distributing the Jihad presentation was about looking at a set of agents knocked off meetings to this union and enjoy the site we had to look the sold this Fink was essentially so it's not exactly pool because maybe it's OK bodies map and not exactly an identification so it's not an inclusion and if you on that side you ever if you take it then going to be a complaint he became the head of the crime and that we have this and what of his years and years time OK so he have his easily eliminate creates defined years of its note question excuse me all the rest but the twotoone and if you time and it was a finite too but at the beginning Monday at finite that there is such that kind F of X Equus and time OK and you know and that is so it's not always the case that this socalled shunt which which you send which report jacked into this question correspond to doing this but it's a subset of these questions in junior high land and therefore Folsom condition it can even be in the form of a set of 4 presentation that you want to work so and that just like my music notation and so you have the A12 SO then you had called you wish I would just serve as the principal of a presentation of debate you In some latitude and climate and the owner of this and that we have this summer blockbuster PGE which was established as a whole the Tsuen intuition and so you can do exactly what do we do this year we we we have this quotient and we look at these uh and albeit into these growth this summer walk into his big question OK and they're so what do we want to do it OK thanks notes In the very beginning that we add to this the Arab solidarity in the manual we have air the of Microsoft minus 1 of their friends so it was you need to hear it all you need to go below it and this is the end if you beach but it's not into his Beverly the ban you get an identification so this is no merger news space under G F so you you may identified weaves with age takes note we so based takes note of which is talk the award where excellent so OK it's not whether these maybe should .period external as to become so maybe a sweetened its invitation from produced OK so you you make a choice just to identify this is gambling that we phenomenology news show "quotation mark with questions that the just have shows and until dash answer .period incident at bottom so and wet what we're going to Holdings the and so to pull the acreage distribution statements statement OK so the and the a Each day after looking compact 2 pollution can watch so adamant it said left investments Avenue so it continued yesterday and because of the fear is that is a GQ is a creates a bowl then you obtain a by taking the portion weeds accounting manager of when you get remove you which I would call it again and said and we've got a new issues between on on that portion and in fact in a data and so and and then you have a new page on this is a moment teach him at age 2 OK so that's assumed that jurors and the public so we uh is
58:02
so what I would say is basically told but it becomes a bit simpler and that so you wear these 2 and so that is OK because it is based subcompact this measure are so UGT and the new page are finite again because you have a finite and that in fact major museums there however also heightened that jumped from genocide feasible it's not pull phylogeny added Najib by go lifting the hint of majorleague social hiding the him but in that case of will suffer it's for so after after the sole rights to the huge investments and the assignment get and so you can normalize the to be of Volume 1 and so we normalized 2 2 Mass 1 and soldiers the merger of the 2 dead space is 1 which is always pursued and so what do we want to know what we went to pull that following she which is continuous under said here Monday Europe and what do we do we want we want this continuity function in fact to be a continuous function and the quotient by this so we would ask you to be here and act in that good because this is a combined all of this is that the of space is a the closeness of space of the constraints of the Hong Ok justice almost too just like there's a statement by 1 2
1:00:19
other so I did this and what I want to reporters that I consider the intake in Ireland she'll stage the new of states and so what need to pull idea and is that this and think about going there 2 is danger so the goes to infinity and I you cast some additional pushing the additional conditions "quotation mark and so what happens is that its forces but she had to take of a wealth of functions so she 2 million of space and shape so it is with so this function here that the young considering so you you can see disaster continues function and the union of of quotient so all of be the result of this victory None exotic objects saying would and this after autumn demotic farms and so what they will explain all of this kind of makes next time he is a Sudanese assess the bag ,comma the tool the London and use that few the incident few