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

Publisher 
Institut des Hautes Études Scientifiques (IHÉS)

Release Date 
2014

Language 
English

Content Metadata
Subject Area 
00:00
Area
Series (mathematics)
Compact space
Finitismus
Spacetime
Theory
Analytic set
Staff (military)
Analytic set
Quadratic form
19 (number)
Number
Number
Goodness of fit
Computer animation
Quotient
Field (mathematics)
05:14
Logical constant
Point (geometry)
Polar coordinate system
Group action
State of matter
Multiplication sign
Rule of inference
Event horizon
Food energy
Lecture/Conference
Descriptive statistics
Units of measurement
Condition number
Area
Injektivität
Spacetime
Element (mathematics)
Measurement
Functional (mathematics)
Equivalence relation
Voting
Lattice (order)
Hausdorff dimension
Quantum
Object (grammar)
19:15
Point (geometry)
Group action
State of matter
Decision theory
Connectivity (graph theory)
Multiplication sign
Student's ttest
Rule of inference
Grothendieck topology
Explosion
Maxima and minima
Frequency
Queue (abstract data type)
Condition number
Social class
Addition
Focus (optics)
Scaling (geometry)
Block (periodic table)
Moment (mathematics)
Staff (military)
Thermal expansion
3 (number)
Price index
Mathematical model
Field extension
Equivalence relation
Order (biology)
Quotient
37:16
Module (mathematics)
Compact space
Equivalence relation
Meeting/Interview
Order (biology)
Field (mathematics)
Functional (mathematics)
39:09
Point (geometry)
Group action
Spacetime
Presentation of a group
State of matter
Multiplication sign
Neighbourhood (graph theory)
Sheaf (mathematics)
Basis (linear algebra)
Mathematical model
Average
Weight
Functional (mathematics)
Convolution
Open set
Power (physics)
Spherical cap
Lecture/Conference
Meeting/Interview
Identical particles
Thermal conductivity
Descriptive statistics
Physical system
50:14
Classical physics
Group action
Musical ensemble
Divisor
Presentation of a group
Euler angles
Multiplication sign
Decision theory
Connectivity (graph theory)
Mereology
Open set
Number
Force
Frequency
Lecture/Conference
Square number
Subtraction
Focus (optics)
Spacetime
Physical law
Infinity
Staff (military)
Functional (mathematics)
Bilinear form
Vector space
Network topology
Hausdorff dimension
Dependent and independent variables
Right angle
Figurate number
Resultant
Directed graph
1:08:53
Point (geometry)
Complex (psychology)
Greatest element
Group action
Focus (optics)
Presentation of a group
Open set
Number
Frequency
Arithmetic mean
Lecture/Conference
Meeting/Interview
Film editing
Position operator
00:02
so a
00:13
so again as of could use security I would be merely descriptive a series lecture all as to his for people who worked number to the tool to invest in the sitting here because I believe that a good deal of bullfighting is home analytic number of field which can be called spores refurbish paw feet in into the cities OK so could you would we want to do the soul back OK so we have to believe that mainly due to an area in October and then but I would say the motion and so on and so we have been added and so on what they explained Einstein was buttressed by the space In the end we so good he concocted sent it to the attendance at birth the merger which is the quotient of the government on the that debate and his signature on this the and in that case and the atmosphere is so the question is do hyped about and so I community and finite and that is so then we tend not my place to be appalled at the and so on what makes the lest I was that way as the to what the problems and is hoping this portion is in fact compact so there is no surprise that the Middle East by nite but in fact it is pulling indicated that did and this is socalled both that the shown the playing nightmares occasionally may not be always find so it's nights to chew there are 2 reasons which I support because of the the large enough but the yeah but in that case in October 19th if I it's not going to be in the eyes of the to rejected at the goal the men that they point of community to get ball B. J so we should just give 1 them so that they do you know of the idea of having a dead called there and then you see that the portion 2 the staff will III 1 of which is children admitted to dead people both posted to the number of Soviet fears that maneuvers of coughing up that but it is early days and that's the way we what we mean when curies of that govern too mind you would expect this summer for and so we then we have some of the spending like of us to apply we want to show that we have lot of to many of
05:21
the states would be enough to listen and will be and minus 1 that you have to do that measurements by 9 and we will assume so that age so you think that to go to complement the each species all that it is played and the appointment of the finite so we want to take a function continues compactly supported function and you fall however porkbarrel we ask that the function that year and by his staff because of this that we have in stadium and that we want to show that is the longer a Room With a chop it so as to what we have to add more at the same time we watch the point is note and of elected a crime in which you use and so the idea is that we want to show that is the only to In the end of the function of the and so on we made last year that the guys were because when she a constant function abuse because both of you have nominated to be called public to measure so that we may even the 2 the days of this so we and of its condition we want to show that this is the guy who wants to talk to you as it I was great additional conditions that was mentioned OK so so I working now to kind of space and make soldiers communication and quantities of how soldiers used because in a sense the most in the case of the public have all those gazing at home so menu that so when 2 and if you have to put that in spite of On but "quotation mark at base of Hong tool is always there to that so which means that it is only up to to scatter it's always seemed too "quotation mark at its base of the state of the times and all of fall it's a question of which means that it can choose to all and then there is just no more of these intelligent by which so is normal underequipped
10:16
trade of the pulled off the coordinates a few of these situations so that you can go to a computer which is often on October 9 and so few of them then so cute this will I don't to I'm the name 1 so on simply because the election is you have known that so nonchalantly months and you take the heat and then there is the issue constant aftermath he did not that meets that October administered duo of of to attract a lot of long so this is how to so if you wherever you want to the quadratic to spare his old ways so similar to that in the space of the shape and where this is so get you but that could be is a magic of 2 died to make PCs but also put down although you so and there is isn't longer so that there is no longer just the please note this is a space of a place in the whole area and aquatic for McCue a data on US mapping of not of quick and it's a In voters shouldn't put it so you have this picture and you Ochoa nice description of October 9 so I took your it's nice to the incredible amount of units of the government and that the ability of some of the things that quotient of the of the by you this can laugh with them so we hide the please so is it's magic by gold was up points of fuel out of the amount of tuition payment of some of the magic of the injectable element of such events in the debates can laugh and at yeah and action is given by the Saudi few of soul I don't know if the new staff and if you take the amount of the then whoever you associated to this statement is so confident that would you the new minus 1 and then you get and then you get to you the places you will quit the union which normally uses no and book Thornton maybe it should say so far and fall there is island use the Scripture so damn of so few of the questions that face didn't your quite energy equipped with the knowledge of the soul of the city please and you square and it's not square you at description which might be the case where the quantum of its state forwards but she was in fact the equivalent of a meeting of the of the community itself and so this is and that the truth is that the fall dimension of space inside and the way in this space do not know an that is what the people spaces that is similar to 1 of his 2 they in fact OK if you want to pay for it to be his plea to put quality because by so which is what you would get you of this description is uniformly with hazardous communities as well as the new of the soul and then sold off alone so can the action of the Aegean Court of Court tenants of so is this is of a way to do it featured confined in the Belka Balkan profited from Seoul and Paul goes by considering control legible associated with any of these quantities space on the fruits of its classic but it's so always just show that for rules Hong whether the space so what will come out of some kind objective will be quick and manageable and associated with community so much so that
19:15
so I'd go back now when as an idea of what it's like to automate the phone on the eve of half 9 on on the merger of the 2 and just I want to the example of maybe of all of the problems of use kind of so just where the name example so OK let's take the case of so it will to cure so it can be a free license neither many of them can identify with and you know where it is all of the people of a good you you have a moment to moment that which is identified with the move as an additive goal and if you take care that view man because you have this identification on the value of the caller's phone to attack the additive that on my which is on we just want to know to work what happened exactly if you it's computer consider a side so that you have to make decisions size and scale of the but what does he do few computer games of the man so you know if you take the so many of its kind the because so states some of the expansion so here it is and them clean and and this is a minimum of 2 because it's fine and so on the amount of fuel and that that's to the end of the by exactly the of mine the socalled action backed off and of course is being accompanied interested that if you will cited in the city amounted 1 OK so far away from the Soviet is computation because you know that your character the genomes yet and also intends to to begin alone on cue and troops bombarded the Gecamines maybe a wonderful to do another example sold which is now it's something do you is the 1 the we have that identification of the of the maturity of few monumental year it's identified with so you know that there may be fewer viewers than that of Of the minutes to get goal of a proposal to the number of automatic and you will get back their own movies for shunt tho on a staff would you through staff which would be a preview of what is he is he at staff and so that sofa so I think there a staff will be after all of the show that is the absolute value because of the absence of commission to some way once you give 1 of these you obtain a character on the and so what is this guy had been criticized please contact so far on a staff that is before it is a shame In the light of day for a windfall so you take In addition to the man in the tube and you met 2 to for a weeks function so it was which uses mediation over all In support of this time of day and the death of the value of the company to Japan and so you will find that in that way you obtain a guy which is which be the accused and the previous Ziad staff and of the high so this staff so the point of order at the end of holds a component called all 1 so this is another example of the 1st of all and he would you have a
28:19
question the example set by the lake and focus so what so few but you have to take that so then you have following his mouth is so you can be sure that it's just the same kind of thing that it's too based on material used you will the curious what we call them previously couldn't but once bowled so well and you is that bad if you prefer you called all crimes in the queue of is the belief that support of all time the hue of wine Q need to do get its goal of his staff and its index is the site the the captain of the team and so In that will follow it didn't like that you up the so 2 mitigated at like that now Of moved through which we created on the open but and the and the fact that you have between the player and we find that Monday through so so it's OK thank you OK and now if you want to obtain all the captives of the quotient of states that government accused Tuesday them of what you have to do is to make you plan you finite told at the guy that we had about shape and and then you get to description and so it book and finish example of that on the block and so OK now if you Gold infused date the finite extension of you no 1 has the kind of OK the imagine buying prompted managed by which 2 2 which OK Of the outcomes from each of the 2 of you through that and in his action is by the students and on case you have a union man and that they staff acts leniently on carried by intimidation and the case that is the of point of some stores inside he said with which you may you know as you need to hear linked through by choosing through itself France advanced to the 3rd office feature on the 2 of them from Cape fewer of the 2 detectives goal and what happens is that they can get contact so classes again later the corresponding to the socalled news that 2 moved and so when you look at said rootedness don't know what is the lecture hall for a lecture on the definition of a character that usually needs to be made because rule is you get like there has to satisfy some condition for all of the new evidence of condition of your character and his condition have made to ensure that your goal is funding at the time that creator of the the book and find the last example which would be of any of its OK so the best of the matters because you get mad at and held on to the 2nd you floor of so we so we observe that this report on age model is said to he identified with so what about and the explain much modern had context so it is that it is the to it's going so you have the identification on OK and let me live here as he needed to know you know him to Monday to and I can identify with and that the cost of the 2 the model to if you material .period 2 so
37:16
it's getting OK knew of identification of the modern faced with another portion control of Digital's vise president born right you have pulled out of the
37:35
combined with compact field goal by the but find that the because of no and so how old was associated function and that caution that it is because of orders identification to face to define the function on yet not exactly and that Bush the 2 main function modular from I'd have to say it's a fine man so it's a function of
39:09
and so what you can check is that you can't segment for holding their matter 2 I have to Gunnison OK it's going to be system 4 of 5 so that function and the function exactly the question if you look at what happened so that they can make the so where's the ongoing at the time of the final model and then if you look at it you know he got power what you think that you will be it's mine a cap of expertise where the minister of CAP is of minister of so case is about 90 days find what Europeans focuses on the finance so they so the main in in mind scaled cap is attacked Q so what you get from the old of the sheer weight gain loaded up on his function and on the Bush which plants from the United States where and high action of the this compact and so in that way you see that you
41:27
are obtained from the FT said that the you so if on 2 plants which I don't Hi action all of this and I don't view of the section is that which might wish OK and if you model from his Baker and from then and after that will be Virginia in Baltimore Have you done now to me he as to the fuel and so we went to to understand the basis of sales continued to function under scholarship and we would like to understand the function which I'm that and by the summer of open competition gold and for all the states in fact is starting point is to understand and to buy and the to the the foundation he will fall by 4 hightech so complete so if you other function and you ever she is a new function which was kind of at the time so you if your function is a function and would him during the day on the stand new function and we still remains between them and the presentation you know that so good so simply because the merger but since they can here in the atmosphere which is tied to and so forth the main thing to do and it is 1 thing which is that of which is white and aunt OK the fact you can go on a hot competition of the conduct of things to a halt presentation of the of of measured by the points on the agenda of continues compactly book function of so we support the play bags ,comma if you take a function continues competition for that focuses on the future of the same benefits from the issue date such a functional you can find them just by the socalled borders should not be sold if suppose that you continue to function which is function and is called easily done as codirector the functions on times function of the office and I find that the supposed that the function is to and the function of a foreign supposed but it is attacked the functional pretty bad Altschuler of the system would enable neighborhood of identity which is an open competition then with so and the heights it is so babies convolution feet you have to face of culture and we just because some of your neighbor is generated by by betting at Nice moved functions basically told them if you understand the space you we also understand that he was more functions which is really what we we need in these interests and the continued function and OK also said troops had taken the description we the following week so far for the efficiently but you can find it and he'd be in here through that you can find a character Dr. being 2 of the people do you have to open day up competition in the associated to for a week or 2 that is the function of the book plan the fall fall within
50:18
the the sufficiently that the eligible this jubilee of open tho would be commuted to and made of offer not mind of not much more than in the case he enough programmable certified Durant opened the door and and so they can as because these are incubator often occur again from so far said PG for classic Kelly carried on from where we were going to the corresponding functions will be again from full funding you for euphoria such a the focus of this much each week explaining what so I tonight OK suppose that you have to hope and end at feet which is part of so this presentation and decomposed into knocked over some of his duty benefit presentation and so it is not where the factors that it's to kind the next song of onedimensional and effect of space it's "quotation mark borders with it's a joint venture of hope which means that any good your vanity plates callers phone to aquatic this company so the function so you I he said that fine fine and the Soviets function is a function to be in the staff of the 2 can I of the sewage going on to aquatic plants and you take Of the quickest at the Quotidien compose music act and OK so it can be that had yours this is finite stumbled or generic like this which which can be all of which are defined things and to it is not openended where P the mention of the whole presentation the infinite dimensional so you for presentation of but this book competition of the 4 .period especially because it is their main source said that the decision made the vector of which half of which functions which have in the young of of heels and Soviet compensation after a fall in the dimension of the speed at which is dead "quotation mark presentation so we you have always will not old you need that the of the composition of the court would be so it is queuing is called AccuWeather components coming from agents and and so we have by which In spite of the time which means the of the arts right no note but that not all of them and in on uh and so on of a finite dimensional 1 spoken in finance .period the tree so so the but we want to study this problem and we managed year that 2 1 that should be of shape can both regions it belongs to 1 of these the and so then you have different situations of scarcities connected so I really do so this days so we have to engage in the a of of not all of and then there is the added no time so you can
59:35
factor and so we are left with the intake and OK so what we would do do that then and in a sense we would like to show that she goes to when this is sufficiently so what plants and that and faulty Of course not to know that the not to the forget that so what can happen so this is To help just waiting to be asked to be 1 of the 2 so there have "quotation mark that because it's attractive for to which going on to it for that it didn't take active and so correspond to work for that and what happens is that you from a H which according the beginning is the associated to work or that 2 "quotation mark so it would like that kind of thing on beach with them at Konstantin went 2 1 and filter problems in the got 1 of so that this explains excuse exception and square glasses for because of the mine according to the book which is this is because we indignant about this too so I just on this day we just I so now it is the by is contained in a 2 so far and but we managed to get to and from spilled with them for a week or so we have where you can go to of murder the final call Of the portraitist take care didn't fall on top of all this is Sally market take ideas from which I did it add for most of the time and this is just an acre a as function of a and a function of a bank and this is the value of aquatic guide for equipment got their attached to the times the 2 1 and so so the fact that the figure of a good to you it is for a of most of these 2 for the week abound so we is called for a sub conflicts for all the things that you have no credo and to describe but which are much easier to Of course I excluded from related the dance the timing so so this is a good conflicts and so such a bond was obtained for the 1st time by year by year and yet for all of the funds fall from which you could law firm equipment can everybody farms and and then due extended the even it's bound to all kind of respond formats forms and so on and so that we can refer to give we should have killed and they could get more than half of the conducted today has been sued by the result when it was square feet so too we moved to square the assumption that you have to deal with look things that they have not described them and here and that is mainly because of the attitude but now there is purely on the treatment of a function which is due to World Bank which was part of Virginia and the number of the people in that way you get this CEO and that they have stated above nothing from the fall of overfishing and the number of hope it's over this on the board of the hearings the 4 1 of the architects of it is a question of years in the hands of the pact on this exhibit but if you have a right to years of justifying his it was not so if you is it's so be it and is hoping to use and is appropriate but was that the Johnson and so you could be
1:08:55
difficult because the place of some of the finest players but you go back and cautioned him would usually you will be compact and then expect ,comma will be discreet but because of his opening of despair if we become the soldier took the position that the weather and things cities is that you often that you have the virtue of his and the issue consider more often than not albeit means that your goal on things and put pretend the and then in the sense that it comes from these put on you won't hear of it so maybe it is so full of thoughtful of analytic number killed maybe if you want to get used to to it maybe just 2 steps in which suggests that his is on paper of Borneo and upon each was last week was a good idea to so there is no and ultimately from its it's offers on the domestic front but couldn't .period have admitted that some of them that is that the you have described so that's also because they call In an official from the 1st in fall finding points and should be here it in the 9 of year because of the number of so them To presentation of the bottom of the front of the things would that with Booker from years back at Kingston University soldiers of the giant with friends the vividness tradition and they may be obtained all this with the growth of the come and make the book cut which could OK now if you want to and we and the number to that went into to for now there is no it's but so that I would action I think it's something that will 5 so I thought that there have been no many books by the nightly for instance the amended is people live and that the statement of acquitted of place for us all if you do want to damage enough from this book is that interesting what they're doing just that and focus of venue and bank attention if you want to look deeper into this complexity problem than this it might be "quotation mark we you can get from From stuff too and that's OK and then which means that there will prepackaged close stuff all of this is not completely dead mind but OK so that the 1 and you know the book the share of June and so you can find 1st official day of about books on my Web pages and the creation of the kind of Mulhall or what they've ever explain these in his lecture soul the 4th about advances with government ministers who made 1 of 2 weeks and and then that would be all you need to