On the geometry of the adele class space of Q
Formal Metadata
Title 
On the geometry of the adele class space of Q

Title of Series  
Part Number 
27

Number of Parts 
28

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 

Release Date 
2015

Language 
English

Content Metadata
Subject Area  
Abstract 
Abstract: The talk will develop several geometric aspects of the adele class space of Q, this is inclusive of the scaling site, as semiringed topos in characteristic one, and the description of a geometry over the absolute point.

00:00
Group action
Greatest element
Scaling (geometry)
Multiplication sign
Correspondence (mathematics)
1 (number)
Insertion loss
Angle
Solid geometry
Mereology
Food energy
Manysorted logic
Positional notation
Topostheorie
Flag
Körper <Algebra>
Extension (kinesiology)
Descriptive statistics
Social class
Physical system
Compact space
Process (computing)
Point (geometry)
Maxima and minima
Connected space
Category of being
Funktor
Order (biology)
Phase transition
Right angle
Bounded variation
Spacetime
Point (geometry)
Geometry
Slide rule
Functional (mathematics)
Observational study
Characteristic polynomial
Maxima and minima
Similarity (geometry)
Mathematical analysis
Event horizon
Wave packet
Frequency
Centralizer and normalizer
Natural number
Integer
Analytic continuation
Absolute value
Set theory
Newton's law of universal gravitation
Time zone
Algebraic structure
Grand Unified Theory
Line (geometry)
Computer animation
Network topology
Set theory
Bijection
Object (grammar)
Marginal distribution
Spectrum (functional analysis)
Maß <Mathematik>
10:14
Group action
Presentation of a group
Building
Frobenius method
State of matter
Multiplication sign
Sheaf (mathematics)
Mereology
Total S.A.
Manysorted logic
Topostheorie
Oval
Körper <Algebra>
Algebra
Descriptive statistics
Social class
Area
Beta function
Process (computing)
Point (geometry)
Infinity
Maxima and minima
Price index
Permutation
Connected space
Category of being
Arithmetic mean
Curvature
Oval
Order (biology)
Theorem
Resultant
Directed graph
Spacetime
Point (geometry)
Geometry
Slide rule
Divisor
Maxima and minima
Event horizon
Element (mathematics)
Product (business)
Prime ideal
Morphismus
Frequency
Term (mathematics)
Wellformed formula
Natural number
Ring (mathematics)
Energy level
Modulform
Spontaneous symmetry breaking
Set theory
Mathematical optimization
Condition number
Addition
Scaling (geometry)
Sine
Physical law
Model theory
Algebraic structure
Basis <Mathematik>
Grand Unified Theory
Incidence algebra
Line (geometry)
Statute
Subgroup
Numerical analysis
Computer animation
Quotient
Set theory
Collision
Object (grammar)
Maß <Mathematik>
22:37
Group action
State of matter
Equaliser (mathematics)
Multiplication sign
Range (statistics)
Sheaf (mathematics)
1 (number)
Insertion loss
Mereology
Food energy
Fraction (mathematics)
Sign (mathematics)
Manysorted logic
Different (Kate Ryan album)
Topostheorie
Square number
Körper <Algebra>
Descriptive statistics
Social class
Chisquared distribution
Area
Decision tree learning
Point (geometry)
Infinity
Maxima and minima
Complete metric space
Category of being
Arithmetic mean
Isomorphieklasse
Order (biology)
Theorem
Relation <Mathematik>
Bounded variation
Spacetime
Geometry
Point (geometry)
Classical physics
Finitismus
Link (knot theory)
Divisor
Connectivity (graph theory)
Characteristic polynomial
Maxima and minima
Similarity (geometry)
Infinity
Event horizon
Element (mathematics)
Power (physics)
Product (business)
Morphismus
Frequency
Term (mathematics)
GaloisFeld
Operator (mathematics)
Ring (mathematics)
Modulform
Integer
Associative property
Condition number
Multiplication
Sine
Physical law
Mathematical analysis
Algebraic structure
Basis <Mathematik>
Incidence algebra
Group action
Subgroup
Numerical analysis
Field extension
Loop (music)
Computer animation
Sheaf (mathematics)
Quotient
Universe (mathematics)
Set theory
Bijection
Object (grammar)
Ranking
Family
Maß <Mathematik>
Extension (kinesiology)
37:31
Point (geometry)
Group action
Scaling (geometry)
Correspondence (mathematics)
Covering space
1 (number)
Mereology
Grothendieck topology
Sign (mathematics)
Meeting/Interview
Topostheorie
Modulform
Descriptive statistics
Hydraulic jump
Position operator
Social class
Noise (electronics)
Process (computing)
Nuclear space
Point (geometry)
Content (media)
Propositional formula
Infinity
Lattice (order)
Affine space
Open set
Numerical analysis
Hand fan
Category of being
Arithmetic mean
Network topology
Bijection
Musical ensemble
Object (grammar)
Extension (kinesiology)
41:38
Point (geometry)
Polygon
Functional (mathematics)
Observational study
Transformation (genetics)
Scaling (geometry)
Correspondence (mathematics)
Modulform
Sheaf (mathematics)
Maxima and minima
Similarity (geometry)
Cartesian coordinate system
Affine space
Product (business)
Morphismus
Different (Kate Ryan album)
Topostheorie
Operator (mathematics)
Ring (mathematics)
Convex set
Extension (kinesiology)
Descriptive statistics
Block (periodic table)
Gender
Point (geometry)
Polygon
Maxima and minima
Statute
Element (mathematics)
Numerical analysis
Subgroup
Category of being
Arithmetic mean
Isomorphieklasse
Computer animation
Ring (mathematics)
Factory (trading post)
Different (Kate Ryan album)
Theorem
Set theory
Bijection
Ranking
Resultant
Extension (kinesiology)
45:40
Point (geometry)
Functional (mathematics)
Group action
Equaliser (mathematics)
Sheaf (mathematics)
Maxima and minima
Continuous function
Affine space
Product (business)
Frequency
Order (biology)
Term (mathematics)
Finite set
Ring (mathematics)
Extension (kinesiology)
Set theory
Point (geometry)
Propositional formula
Algebraic structure
Connected space
Loop (music)
Computer animation
Theorem
Set theory
Ranking
Directed graph
48:00
Point (geometry)
Injektivität
Dependent and independent variables
Multiplication sign
Point (geometry)
Algebraic structure
Maxima and minima
Grothendieck topology
Affine space
Order (biology)
Length of stay
Computer animation
Topostheorie
Ring (mathematics)
Theorem
Set theory
Right angle
Cycle (graph theory)
Ranking
Identical particles
Arithmetic progression
Set theory
49:46
Point (geometry)
Complex (psychology)
Functional (mathematics)
Group action
State of matter
Sheaf (mathematics)
Analogy
Student's ttest
Mereology
Continuous function
Grothendieck topology
Affine space
Orbit
Fraction (mathematics)
Frequency
Manysorted logic
Natural number
Different (Kate Ryan album)
Topostheorie
Analogy
Körper <Algebra>
Gamma function
Extension (kinesiology)
Social class
Area
Standard deviation
Process (computing)
Prisoner's dilemma
Point (geometry)
Thermal expansion
Line (geometry)
Group action
Statute
Subgroup
Orbit
Category of being
Hausdorff space
Computer animation
Natural number
Charge carrier
Mathematical singularity
Theorem
Set theory
Bijection
Spacetime
Extension (kinesiology)
55:25
Ocean current
Group action
Correspondence (mathematics)
Sheaf (mathematics)
1 (number)
Similarity (geometry)
Divisor (algebraic geometry)
Infinity
Orbit
Affine space
Morphismus
Order (biology)
Natural number
Different (Kate Ryan album)
Analogy
Quotient
Modulform
Lie group
Convex function
Model theory
Curve
Propositional formula
Algebraic structure
Subgroup
Numerical analysis
Elliptic curve
Radical (chemistry)
Arithmetic mean
Computer animation
Sheaf (mathematics)
Order (biology)
Quotient
Theorem
Summierbarkeit
Cycle (graph theory)
Fiber bundle
Resultant
Spacetime
58:58
Morphismus
Jacobi method
Computer animation
Sheaf (mathematics)
Theorem
Division (mathematics)
Maxima and minima
Divisor (algebraic geometry)
59:56
Computer animation
Vector space
Different (Kate Ryan album)
Wellformed formula
Multiplication sign
Theorem
Limit (category theory)
Marginal distribution
Dimensional analysis
Spacetime
1:01:14
Geometry
Point (geometry)
Greatest element
Group action
Existence
Divisor
Multiplication sign
Correspondence (mathematics)
Characteristic polynomial
Sheaf (mathematics)
1 (number)
Rule of inference
Product (business)
Expected value
Frequency
Goodness of fit
Strategy game
Meeting/Interview
Modulform
Gamma function
Extension (kinesiology)
Absolute value
Physical system
Social class
Condition number
Area
Uniqueness quantification
Forcing (mathematics)
Closed set
Projective plane
Moment (mathematics)
Content (media)
Morley's categoricity theorem
Algebraic structure
Thermal expansion
Line (geometry)
Variable (mathematics)
Numerical analysis
Connected space
Category of being
Algebra
Order (biology)
Universe (mathematics)
Thermal conductivity
Local ring
00:02
around what time and would would win would think
00:16
you have to all the organizer for the right here to get that off its sad he's find comfort in central OK so this is that the title of the explaining that I joined branches in collaboration with Alan Cohen so I was saying midst stalker is in collaboration with and here is a schematic overview of what I'm going to sustain the stock that civil let's say that our latest amendment of the year study of underclass space of Q has brought us to the dead minor correspondence between AIG regimented spaces which describes these cautioned that and the the event last basing original and that US space in which we Connecticut definition actually for zones which have to do with them in connection with the feeling that the description of England's at the function the property of the demands at a function we take cautioned that of generic class base of killing by the maximum compact some of the event last but so that is the double cautioned that is going to be there putting variation With the energy regiment they can have the distinction of being fact that and the 1st thing and regimented description that we use payment last year its symptoms of what we call an enigmatic side and so enigmatic .period say it got it topples all of them the and and and it is when it provides the 1st that and the collection of following the continuity of points of the inside it provided us the 1st firstly who went and with this squad with no visible pollution more recently and we extend this gallons of the 1st and not in topless actually Irene populists I would explain later what they mean by that is the 1st thing I would like to sign .period listening to the recently extended their buying by many for extension of scallops from the needs the same as the previous Parker is the city's spaces that the Juliana as mentioned in the 1st day so the is the smallest say my field of candidates that 1 is the set that you so before the old 1 and it's the same I feel that end is the smallest ones and so if we extend this calendar from this in my field to and Maxine for that and we obtain a new version of the admit excite this flag has will say later it's like there In parallel with what happened to all the indictment occurred over a finite fear the when you expand this calendar impossible not to break margin of 15 so this process as a 2nd description of Of these dramatic spaces which and then at this point of this getting citing factoring onetoone correspondence with his double motion and all these this through sides this conducting excites added the final over it's similar stature of characteristic 1 so when they say characteristic 119 I'd important that same my fields and soul stature for which X blast accident 1 X and and in order to up the spectrum of the indigenous win the final in 1 phase mothball point at which marks a primer in spends eh for the before being used the army to fulfill being its action in the final over points of the sides actually on these onwards we obtain very recently in the Montauk so then I'm going need so slides will disappear the mainstream that would be left the on the last day on the list laughter and has gained so that there you can along the way you can follow locked and the values that I hope you can follow the lines that say I will describe and the lead the issue at some point was that the indigenous there is no connection how straightforward a direct connection between the integer and is as moral very small said my field of characteristic 1000 important stature so in order to and unified these constructions and we had to think of a categorical approach which is to rule it out of the the Dili of Naumann said standing by the caller to the definition of the CIA spectrum even as easy as possible approaches by AT and gamma sets so In this way but we obtained at the Waltham Indian villages and they become SIG but once 1 that uses a fully fatal form fond of which embeds involved the z and being and instance of geometry to the construction of a F 1 as in the the they all become as a sole asset it's on the bottom of its characteristic phrases in characteristic zeal he attacked speak 1 year as is characteristic freed it's very basic care yet that fundamental structure which has already been and develop their in engaged the painful that might be putting to break apology but there and here we use the most that easiest spectacle description of the speed CIA spectrum so in order to do so we and we have been moreover although after amending z the into the capital Riverside about we retain what could be a possible definition of absolute .period of absent so this this spectrum and so then I started to develop the definitionally called the formation of the enigmatic side that and so this is adopting a topless 1 start the wind actually is a very easy example you could carrying apparently carrying part information in the province as someone stacked with window and the natural number on and 0 I had the indentation it will come up later and and and notably by and costs a set of positive integers sewing classes is what happened .period With a single object that will take minute and not the end of the year in the in the indemand of not days and cost so we analogy is apt this Capital where there what has been called the 1st mandate and that training Capitalia topology and this year for school the Caltech topology so then that together with the least Tania cat and apology we have had a pretty Schaefer of firm Of the only on its side and costs Jr and I got an exciting factor in because of the use of the conflict topology anyplace she fears Schaefer so here with 2 the Phoenician not coincide coincided because of the apologies and in I that so at the end of Indian any object here in the Schieffelin over and losses is in fact a and I'm not being mapped it is said that which is the images idea this not that of the unique and unique object in that category endowed with an action of and costs so that the description of the sheets review system as simple as possible as a sector blossomed actions of Intel's and then I go and then quickly to the the definition of points in the garden apology was sort of the 1st day in the talks and the Phoenicians engendered by appointing spectacle and top posts it's a Mafia softball .period from Saxon cited the notation it's a single out of sight denoted by Schieffelin a single on focusing not among the captain sets to and that the losses so which means nothing the data which we had when we and provided to a joint font of the upper stand people will start get style that has been here it is right and showing the Soviets left exact and solids left joined the Swiss Knight exact and we it I would say that the other style should be should be only to me only that bad exact but in fact should be also left soapy that is exactly as a form of and these following his from uniquely determined by Lion photo after using the unity that contravariant about implementing often costs in another costs so then you composers and the condom valiant unit and meddling with that Gold the audience appeal process that and you get the call was informed before and lost 2 cents and the main
10:16
factor is that spontaneity is what has been called the incident stocks flat on the field during which is in agreement that the flat this means that the capital in this catalyst in with Byzantine means that the you I had given it said that which is the image of the the point that of the law .period that this act is not empty on this said that there is a natural event and the Mosul the capital at that time of winning here is the capital made was objects ideologies of any of the eggs and Morpheus mean the category Adam for example and that so I by element in and which connects 2 points in nexus of 4 since in this case that this is a morphism which connects the 2 so too did it its fractal featuring collide in front of it's the same as associated with it in this case and spectacle on top of things that is the same as associating a nonentity said and the action of an kind costs of which is the amount by which some property being being featuring soil the 2nd step in the term that describes the meaning of field going so far as to objects indexes there exist at the end of June the nexus for any future condition and so that the air and sea is marked as to exon experiment to move the action of 20 minutes and costs of these are elements of its fancy indication but in fact means simply that there are 2 elements in and also 1 which maps of the twoway exit in the 2nd which amounts to the 2 experiments of political points there is a point of all the and the map systematically is mapped to X 1st and going said we don't condition from being featuring says that the flanks next summer in this sector indicating 1989 the costs so that the excellent is and connected them and so X is the Skype's also that the polling Kennedy Axel PKK excess he was decay prime nexus of an excess is firm and it connects the 2 points on the of the people of the sector capital Aleksandr Benny if this case happened this situation happened then necessarily the action must be an Indiana into which could use the element of and costs which could use the action must be the same Katie 1 paper so this is the area where it easier version of what the generated posted to the definition of Fairfield during the featuring Pompton dynasty a 4 I'm so
13:14
it the issue here is to characterize them and points of the scale of the stock was so then the 1st the arraignment of last year's says that the tackling of points of and costs is going on because really and that to the category of stopped early on the isomorphic that do not really a subgroup of humor I added blasts in you you will explain it this is the positive part of and injecting more visible wondering what happened happened that day should and even appointment which is described in this former smart metering and toss sets of amendments all the sector which is at what I call capital X before and now I call it to be adopted at all but which acts and trust that this is going to be countless images them actually positive all from the top ordered by the subgroup of and that the addition of In interviews and Peachblossom is provided by this formula so we should take to point unit h blasts the addition expressing an exprime is given by the action of Cape Escape Brimer owns for arriving disease so that they entered the store condition satisfied so this makes sense because the capillary speed and satisfy the 2nd condition that we saw in a previous life I then that what happened happened that day age the union the introducing union of some groups each of which is office building seeming to above the so valiantly classes which is due Donna by then taking the at the same synchronization 1 obtain so in nature and is that all quarterly order a group which this the statement referred to so in ancient is a positive factor which is a similar group and the same arguably was described by is provided to me by assigning a point that some scientists said that together with the when an action of and cost effectiveness Peachblossom because the statement that inspirational beside sense that the notorious subgroup of fuels the 2nd this line explaining how to interpret the results that the agency has some global fuel in terms of unique amending that is provided by these markets so not is that became prime and Kariya referring exactly 2 these the case it kind of future the end of the year this is something of a British of the procedures the implementing horses so prominently the same number of rational this is an occasion of holds the results of the at the start the year this is so yes I will put the new and a matter .period when the fact that I have to that thinks so much stature she from this thoughtless otherwise that Domini signatories would have provided by the action of costs it will completely just recently the 2nd part of the statement says that there there is a canonical by ejection of sex between Ponting and Casas walking glasses of pointing the top ended the number of quotient of the finite and there's and model the actions he took restaurants in the the office How is it final whether it is defined by associating it with .period I liked him this guy here and then so and then and in fact that the undead aimed at interfering the this formula and is obtained by it's a uniquely associated optimism much as a uniquely associated with 1 of these aging Huckabee's pH overstatement that money is killing HA HA is in fact the age of the so this and this general but some groups of Q each of them is a source at was unique and is yes and unique up to and yet at the actor arson which is even here and the definition of the ancient is given as the collection of national so now after there anytime secured it seems the afterward that means means that there he's using about the and then at the at the place P saying this and then and is going to be video if this page contains all the power of although I said if he doesn't then there will be a point to wear safety to the miners new worries scenestealing ancient people reminds me reminds 1 that is not any more endangered than which applies to the advance the other .period without distinction people to the milk so then and this is the definition of the young which is not anything his life but in fact the form where he and the statement that the requirement here that makes the description of a visible and I'll carry you attempt to define term there was a case that a few minutes ago and in a way we wanted state the ruble fountain mafias of the bonds of 10 thousand arising from the end of my office summoned process but 1 that I wouldn't presentation of the prime since so many people in the cities and we introduced a sort of stature Schaefer over this over this on top of us and we introduced this but what is this chief nothing back except as they said that when an option event also so impractical and if this is an example of achieving the topless and marks news out of the peak say my stature that our people using the topical geometry actually public enjoyment of people pence to use mostly on markets and is that the maximum time marks would be the same by substituting zeal that so what 1 that has a school changes the munitions In the classical description of the SME Andijan becomes the maximum of 2 elements and the product becomes conditions and this is a sheaf of on the underside of the and costs Jerry and the even the action for example element minus infinitive and tossed aside and minus infinity fixed by the action of an gossip and and the maximum between and among those think is an accepted some then that only if she felt we a defined the action of of those and house acts which states that in the DOS acts on the markets and buy from being used in the wall of his which I was the idea of sending an element there and can also sync K to need for the meaning section which is described by multiplying I endangered by actually just 1 commenter 2nd because there is not by chance that the Fed and the idea that I care the algebra underlined in the store .period and it is With the stagnant himself instantly stature and importance in my structures so they of characteristic 1 the sense I said the Union Xpress exit 1 have that so the reason is that good and in the previous slide so we have acted .period there was uniquely up to buy some of his characterized but a Dr. New Group of Q so this talk alone and is reflected here so in the in the statute which is unimportant so there is a kind of connection between and notion of iron importance in my stature and the and action awareness so it's not a case that that we and the indeed the geometry which represents in that class basis which is a space the characteristic zeal now is described by the level of the origin Vice I'd importance in my stature and the definition of the enigmatic excited it's here it's like when 1 a scheme and the stretcher Schaefer the scheme is substituted by the topples the such as the of the group and by a selected and Schaefer on distal claws which provides the station of the out Morpheus and analysts say that in view of the Of the statement I made them again so here we are in the description of the enigmatic side here From then on the
22:38
next day at work and the stocks Of the statue Schaefer and so and and the assimilating statue Xerox is compatible with the action of an and another stacks of the stocks of the achieve when the following Sturgell my fees so if I look at the stock of the starches chief at the following of missed which is connected to mediate onetoone with this subgroup of Q H after 2 years and insists that it cannot legally as an office with the stock is canonical some officers to the scene I feel that age remarks and it's like a by conceded in 8 should teach us how abstract and analysts no 1 knows who but the subgroup of fuel from the end and and then associated with the corresponding similar structure which is adding minus infinity make a variation of the conditions rather than Plassmeyer access and the multiplication becomes blast so what happened in that people are a ones manner and the stock of dispatcher she felt his eyes isomorphic of Ziemer said and the .period associated with these the order and subgroup of Q z cornerstones 2 1 and then there finite and that which is in fact made by 1 1 1 and deadly please and the reason is that if you remember the form without it's clear from what we have considered this point here so that the 1 1 1 1 1 evening everywhere corresponds to the point that Pete at Dutch associated the disease well then all what happened about the last they say it's the best describes the space which is which has some of classical point that the remaining points of which are associated to subgroup of Q and wonders will profusely ancient they soccer after you might think of obtained by specialization and I made it to the exact space education going from pH shipped to PC PC is the unit point NOS that and no plastic .period them to have some and there's not a lot of these but the more interesting and this collection so not the spectacle using 1 and so now in use Sept . 1 and the field that finite field rescue which is on the basis of the geometry companies can be it is claimed by this being the case and I feel that the 0 1 in which 1 plus 1 is 1 because it will mean blasts as the maximum between 2 when it is clear that this is closely modeled on deal different from 1 it's having to be going on in the window multiplicative identity different from the point of its appointed only 2 elements in this thing and we we saying that cannot these 1 meaning X expressedsec square equal access so tonight important and completion of each of the demand the definition of categories and being it's amended them so now that the arsenal like in the case of finite fear that when 1 considers finite towers of finite fine finite field extension of a given finite feels that here and there is no finite field extension the first one of the the first one that either the important wondering what we're going to consider Imax class which is the multiplicative version of Adam said so then because of the multiplicative visual landmarks is defined by law of the sector zeal in Feni the marks says Osama and that costs of multiplication the 2nd operation to remember that Alumax said without glacier so here is the moody to emotional found lots is a suitable this version of how maxim is suitable for the description of the family of the other morphism of maxim and the fixing the so nothing at the finite extension as I said in the course of amending the Marxist this is not the usual emergency maximize sending the local minus infinity and want to see so if 1 think of pride wind pattern with the geometry of facts acres of of pine complete could refer to the country's complete then should do should be very very few global sections only the constant so if 1 computer development section of the estoppel Wilson a number section from the structure like a such a sheaf of the shape we fixed the marks from the balls and this is the general definition of Belmont section for in top of steel this is not the methods even minus infinity so it's isomorphic to be so it's not not like likewise without and went for a complete could finite in Fallujah group of the other sections and used to the constant sq pursuing this case RFQ as I said that place might be and this is the 2nd here and now that then put in them what happened over the years if we extend this callous if we pass throughout marks so if we look at the point of the talk was about the only at marks when the minds of their enigmatic side all Annapolis marks appealed states that easing demonizing Moffett is isomorphic to Donald quotient which is the space that could have some ice the call as fast as the space and then assumes than in previous work at and but Muluzi after losses on loans in the end that the action of accross that on the on the side corresponds to the action of the from being used hello the single and the size of amorphous missile it .period then as in underwear geometry is characterized so heir following the final some fielding in the classic adventure is this guy saying I have a lot but between the assets that innocent baby use the it's the populace the old fool sheets over the Singleton and aromatics to 1 us all so then it's it's the fine by assigning to call upon and that a component that which is given by the point here In the 2nd component of bad given by I'm not a majority we will look at the university and I'll so it's like kids looking at the stock at of all at declined to say which Renault to be at age maxim for some a subgroup of Q 2 and Max blossom and this is a lock on morphism came in the previous talk we heard so this is a and Morpheus in this case of similar fields so then the description of the spines when be characterized by looking and the image of the land and the Rangers on these s blasts shriek when that 1st of all the Rangers 1 cases when the Rangers of this lockout mafias and is completely contained in the In these other points in fact of the popular so that would be In sign onetoone correspondence sent by the previously we know in and that class of finite underclass is In the middle portion then there is the 2nd case that when the range of the P Sharon Chabon is not totally contains some containing be so go outside and in this case certainly what you get up to a democratization of HSH crime "quotation mark Longview view from you in the range of different from the the entertainer thinking more and aunt once available cute but in fact there at subgroup of art and the association he earned his association with map it then which of his duties described by if a and then which in the case of the finite there it Asan finite and there and that the UN number 2 it land that HA which is in fact that it is something of our officiating was a subgroup of so then that accordingly to the composition of the number of cautioned that into parts and the number of pushing you at that it's the composers into passes by looking for most of the finite and there's and then to the events which are not finite To the cart without immediate component different from 0 1 and the distinction between it's something before and subgroup of France 1 subgroup which have contained Q r subgroup nothing link you to the conditioning areas such as we saw before so now that high in the
32:40
sky the Eichmann excited when somebody came in and I passed the distinction of the map of the Mofaz deploy take that I mentioned at the beginning so this this is a particularly important 1 because it connects a classical scheme at seekers populace to toward incitement side and it is provided by he uniquely determined by a few font also created some officers of pollen now and then and Costa Rican and toss union 0 this the beginning I said sometimes and later in the park Williams and zeal so in the law itself and the unions and nonnegative future because that yes that is so then the earmarked in office metamorphosed applied in that online by a few from depressed clad flowing enviable customer categories from the small capital with a single object and and say Look analysis to Schieffelin spends it so it is as it is needed if I defined what is news chief of respect uh which is the manager of the unique element that and all adopted in the captain and so I take that Skandia's chief that 1 think what the data incidents political minds and not between the points of the as applied here it's a primary national primary and so it .period here In terms of the 1st deal and we so it is that it's a sector with an action often cross so then the energy of the definition of state accounts mapping P tool added to the positive factor of being some uh and once a loop of Cuba which I did that then the noted by HP and it's like a year to as the got it's like localizing being so taking I have an additional of 2 integers and the denominator see all possible powers of P and of the numerator we haven't edges so that the on the the genetic point here is not to deceive so HP's of this spectacle example of around 1 thousand rubles queue as before is going to be an age attached to 1 and then it people In the end that turns out which under the HA pieces can hear like kind forward but the and attached to the spectacle of some group of Q when you see only at 1 time or the power of please leave icing on the please P now the and this must banish because you have all possible power of speech and the other places and there's no additional and you put 1 so this is the corresponding events in this case and that the FAA the definition of the stock in view of this Sept is the intimacy the stock of these Schaefer and the point P because it is yearly and amendment of sex with an action is this guy like this might assume I do play H plus the positive part of each week the sections then you have to implement the handled the action of the Internet also means she's on the section this so this section and even by maps from you as you enjoy shifting to the core product for repeal of each group blasts so that the the the stock of the German this section at the different from the only for finitely many people knew and the action of friends cost on on this section is this guy this formal so an absolute oxide by acting on the germs of side at beach this is the leading candidate to win this classical scheme aspects even with the stature Schaefer and getting excited so be it we sort of freeing go to gadget that leading 2 different awards characteristic zeal 1 is in characteristic one's mind is not the point and there just aren't as a common to the tune of highsided went lake that provides a unified framework from sheaves of community dreams like carefully instance the stature Schaefer spends the and that's pretty images of 0 here's mocks not once I the Bremer Jones maximum which is the 1st sheaf of for this topic and now asking
37:34
description of the skin side as I send the skating side go when the previous years and 1 of the biggest says that there after and if I consider the point of art class monks of this domestic excited then I get there it won't go 1 correspondence between these numbers quotient in the Atlantic side and that they're just passing to the conceded the point of and last month said is not there sufficient these these new ones we were not happy about this process so we're looking for that couples whose collection of pointed right away without extending passing to twohourplus marks will provide the air it set up in which the collection of clients I immediately in onetoone correspondence with reasonable caution this escaping side this can cited it is not as easy as it is unrepentant about any topic but is not as easy as the previous 1 in the sense that the BOJ is not more basic um topology we use before the end themselves and noise I said is provided in dramatic and the destruction of this novel caution so we have to the finest site 1st and then go on to another category we use to define the the it's the militancy here and there they have detected the object in the cabinet I mean abounded the opening rebels was in the end the inside and sealing infinity and the Mafia's men between them 2 objects such as the skyline and cost action of ankle should be some forms of music is given by all and then saying can house which maps In the 1st there opening cannot only got to the 2nd 1 this information is no fan the otherwise it's the same thing soviet that the on these open 2nd this dealing feeding uses nuclear apology between users and there is that jumping indeed Minnesota where the use of the complete ecology and there is also heavily on turned in the category than consider the collection followed and called residences for the definition of the season and fool only income so this these out called of the union of a midnight meeting about the only I opening new meaning and the
40:11
and the composition states that came in fact got an apology on the capital C 1st statement and the 2nd statement says that the chief of of the chief over the Cyprus top of is canonical isomorphic to the capital the feel an that part of the colossus off and it and consequent iron sheets and 0 infinity so then you seeming to join on innocence because over and the affinity there is looking and appointed to those of the jump off the penis of disappointed because apologies and defined before was the trigger apology so then this big jump on 1 side that would bring them interesting and somewhat more difficult interpretation of the points in the topless but on the other side we should be back To give us a lighterweight distraction that really and we had to and work over in the crypt previous aside light passing 2 points the of Annapolis month so the skin side down but information is beside the scene with the content apology genocide which had just this kind and the scanning top concert is the category of sheets of any sign or equivalently in view of the previous position and also provided that the action of the on the feeding
41:39
but at the end of this year says that in fact then as before 1 look at 1 study points of news on the stock was the category of points of the stopper submits a bomb concealed and then I would there would be a statement that when this block is not the 1st case policy the same as the capital of defined costs which is not about the points of the 1st day of the enigmatic signed a final the 2nd is that when you look at the point and support different from Museum which is canonical agreement into the category of France won some global so the points that we saw in the previous statement for the enigmatic psyched up to passing to those bonds of aid the final Annapolis marks so Indian this steel the goal was achieved in the sense that we immediately we have found that the collection of pollen season onetoone correspondence With the bubble caution here as a consequence there tonight because I joined rejection of sex between the eyes of morphism funds of this topples the bonds of the enigmatic goal posts the SinoAmerican last month except after extending and the number of pollution so soviet as I said we pay a price because the populists and government offices more sophisticated someone difficult to understand from the point of view of the study of points that would pay is that and the results in Santa Monica on as before and it
43:14
would be a inspection chief attached to this mystical was and that there if we simply extend the statute sheaf of Xerox's twohourplus marks and then and then import that encourages impossible use the stature touching the pencil product known as this is not quite as Schaefer anymore in his 2nd topless because it's not indicates case that a she freezer Schaefer so what happened is that the definition Of Schaefer is obtained starting with this same Houston Wyoming will which is simply an extension of scoutmaster from Xerox collapsed last month said an to induce format and then a localized this that we have to localize this is gadget and this would be the stalk of the of the she's so there's little transformer allowed 1 this kind is this enlightening indicates what is it that when the men are in fact gender given on 1 a subgroup of art agent had Indiana maintain that this so proud of the it is the maximum that we can do this definition description in general where I take each marks said this is that you don't polygon innocently as a new polygon to Is the comic style of the unifying risingmany warrants IX Jerry White J a a minuscule where annexation would generate its appointed the panel discussion .period in age costs and so the neutral polygon in factories can uniquely determined when function marks land Jenkins that's why G went on the internet and Elenore making up lost some of its new can the sky but this kind of stock attendants look and consider the ring of comics piecewise defined continues functions even Fini and sloping ancient and financial many singling out this .period West operations when this functions than the confrontation says that it is being used as a product that according it's in fact isomorphic Can't by means of the sending the new gone to the corresponding function and end tool the the similarities are each of convex piecewise defined continues to except for is this is the
45:43
potential product of this connection of fraud in the in terms of the new trampling on and then the stature sheaf of of this topless in the final by localizing there the agency because in fact now rather than H 1 1 Kedzie because there we are extending skyline from the structure sheaf of the domestic side to off marks and many the fully rebounded overnight this kind the section of this she felt so for open landed a collection of the sections on no major acquisitions maps a from major 11 flummoxed and this section at Comex piecewise defined continues functional major wins loops using the action is provided by the FBI useful and and then it through
46:41
the years the fumigation I look at the stock of foresaw the dealer says that if I consider appointing pose and associated where once available of our ancient the stock and at this point equal pH is the simmering on each of germs no of I'm not smiling comics piecewise defined continuous function with little children age and yes so in the case of the abstract and once a group of our H and really we will consider the source said .period would support in the so in this led Beijing upset slammed socalled Group of our electric blue agency of source at that point would support in the home in the stock at this point is described by disseminating H. costar marks a source at the monstrous construction to this industry automobiles the distinction of the the stock and there are these attention that aren't paying attention that not enough to consider the extension of cattle that are more she of the chief the marks for the enigmatic side wants to be much more carefully because in this set chiefs and not the finite sets inaction most of his career years in the review
48:01
the use of the word because it's this talk the sole yes
48:09
and this is the "quotation mark response to deal before that when we look at the stalker definition of this year OK
48:19
so then the definition of the skin side there is the 4th this Karen Koppel although which we fix this structure Schaefer that I just the skies and in this case at the like minute and a half view on it as identities pulp was landmarks the blasts in the sense that the the statue Schiesher lock Ali structures were an actress marks and if you
48:51
look at the end of which gives the final viewpoint on his own this time the pontiff skating side says that and even if we look at the point of the skin side of Annapolis Max and this is not collection of points of the Of the use scope of the side of the right of the skating site and tourism by injection of sets and then there is a canonical rejection from the skating cited were getting many scientists out of life getting zeal in the media industry attainment and costs in London denies for the final by ejection of the PLO some of the city the skating cycling I have thus marks of all the points of the domestic side of progress marks the end of the tunnel cautioned that we know where we looking to study using
49:47
could get catch then the remaining practice here it's about the initiation of connected by lines of hearing from for the incentive skating site Anderson then known this such Schieffer has added new stature so immediately and you can look kind demanding so there is an amending of the stature she Fellini the extent meager prison amending of the section in a major way this emission of fraction of all make me as a standard users in view of the new statute between pause for technical reasons over the institutions of the enigmatic of the skating side technicalities you will what is behind this back carries and is because this is noted the from unions acts so on the on Arkansas in this framework of surmise that much so then is amending Mets complex piecewise defined continues functioning the in field of piecewise define continues functions with those of the year and the complexity not because it's not worth holding Andean the natural action of costs sheaf fractures and defines a sheaf of similar I feel this getting so from now on it's like a sort of generally generalizing the period of decadent rises because now you have a sheaf of function functioning she fractions in this context that and
51:28
so then and suppose you become upon on the stalled which corresponds to a subgroup of violence then you can't their German of this office of Solano that in the stock and say efforts the German then there is the definition of war and an offer of news German as a H plusminus each Weirich crossing minus its service carrier by nearly that is so imaginative going the that idea you have to have mind the new Portugal on the point of view it's so these are a fine a piecewise continuous function you look here at 1 point in which you some from the slopes of different and so then at age class and each minus needs you it said that the the slopes from the guidance of from the left and was also the 1st because there is a singularity and point that I'm not going get the functional managers and the vanishing is described by his friends and OK so now this plant it's about the statement made at the beginning that that the intervention of the prior that is that the 9th it on the 3rd floor the action in either 1 of these use of these sites so then and this is something that we don't see a dispensing because inspect C was the only place we don't see the orbit of the USA so will gain in pursuing this approach with the sites and the Mexican skating is that now you can't see how the action of the the from being out of the 4 wheels on the sides act on Boeing's so safe suppose peas in here as a nationally the and conceded some space of points of the skin side CPE which had Mississippi it's a collection of points to win the property that each of these Pontius onetoone correspondence Windows and window sometimes wind up with the camp 1 constant after the open and which is isomorphic at 1 of these HP and this guy befalling the process of getting the definition of each part .period apparently yes so HP outdoors and there's some hope of Q the and then we each act being is in 0 is when 1 of the wives so the schematic and he should take all of these CPU dissolve itself and in this on its own merits not to the image of the landmark taken here and this collection of army itself fact it's a some space of the points of the scanning signed and the bonds of this can sign up to the point of the domestic side it is squarely state government if Cartesian and so this collection of belonging of the from being in email costs the finds new special status and explicit way just to see the extension of scholar of Baker spends the in the area so this is not an analogy to the scheme and 1 obtained by extending the skyline of France scheme and I expected to too then the chairman of the guardian of the Director Jennifer sq so there has ascended this the distinction is because he was not visible in inspectors EU how long the PUC only Peter only when you move to an 2 extension and expansion of student you would see the action and from his actions and the lobby but in this case there is provided by industries
55:26
so now what the 17 that each of these CPA the acolyte care they corresponds to what classically would be an elliptic curve and then and canceled and the next statement said it's about the size of the it's about a certain topic which is a definition of monochrome monitors ingrained in his in his book which so then what I'm not actually it's a statement in which the government in analog form with only the on the on the undisclosed new went unclaimed and desire on topic and curves by the way currents so of the final round similar stature and importance in the structures and there will claim that they have claimed corresponds to a curves in the classical context because an elliptical in classical context is described by the quotient of costs a model Q to busy in this case the current work will be added and seem would have at last costs model between us so so then the women rocket that will receive the aid have will have meaning it's different from the classic and 1 because the beginning of and end of the year as a result in the morning to during this context is only a number so then the manner in which sending out cross past the CPA in you susceptible radicalize morphism From the the promotion and activist last month PC to seek the then what we do is a CPF downloaded so some space of being skating cycle in which nearly Saskatchewan sheets so we pull back mustaches chief inspector to CP tool and this portion and that's what we call it that will be so in is that she fell on the squash into section of piecewise defined convex function with sloping each week for 5 minutes at the end and so on and so on then downloaded definition of the of the Schaffel quotients undefined before P then 1 can prove that they had almost section that has eluded the alarm in the order and uses this Phoenicians so it's feeling that defined before pulling back into the courtroom and I realize alike in the classical context that can be recognized a sanction from the CP and through saying it should have Of the bundle of page so more their age which is a subgroup of Fatah installing a in the ties of upstart which the and each small each and the nature its impact unity of the country analyzes brokers and the newly offered advisable CPAs this finite sum I I'm going to beat faster so I would this could topple the the
58:27
material so that PM says that if I'd be tapenade lies along the it's all beautiful beans actions then the name zeal and also CAT II of the United means you can use them up to which she is defined by looking at the whole possible so or is a under each piece of land and some of the evidence not sending to which promoted minus 1 each piece
58:58
so then if no beginning on Monday nights and zeal life and that's also the image of Kai would be my kind you and then these principles so then there is the notion of Magical beam from Cordova and morphism Of the Jacoby and this could lead the modernlooking minus 1 C and then in
59:23
fact and there is a definition of what classically we consider tendencies chief of the almost section attached to an adviser but over the courtesy isn't exact in Ireland with a classical definition of what makes the geological and them before each of years for section of the year and this is reason what's the on penalizing found the marks of the padic normal feature that as long as the peas so then
59:57
and when they said 1 conceded in fact have a suitable notion on dimension of these margin was that the differences between this case and the classic case it is needed again because the agency agency would in the classic and context would be a vector spaces feel that I feel that in this case it isn't there is no mental space an email and this is a margins in the margins it's said my in factor so that 1 has to implement the accord and definition for mentioned in this case we to correct this possible this definition provided that in fact 1 proves this is a topological they mentioned classic politically mention provides and 1 proves that this limit is going that indeed it is
1:00:44
finite it coincided with the beginning of the late myself eliminated which is to it policy so positively lies the gates at least recent negative and therefore more than I alluded before and monarch formula is as this Cajun so you see it's like an elliptic case because at the time limit and the rise of history is not present so you have good this for so long and so so
1:01:17
then just to collect and I I don't have the time to do through inside a machine in the case of migrant workers say there are just a few words here so Anthony I mentioned at the beginning of this construction hiring characteristic 1 so the Irene importance in my structure expectancy it's a gadget characteristic the likewise standard the class based of the number of caution so we know there is no ban on July 10 the connection between disease and the the news I said at the beginning so in order to gain a unique bottom structure characteristic free and then only Faulkner told USA said the construction which have very the use of force and known anyone known to bite the bullet apology with and we filled to the construction of sounded so any of these categories in fact I think that the coalescing mining center and Seline says a certain construction in a of geometry in that behalf provided that in the passing recent past the period when odds they for each of these in his stature and my stature inmates the fatefully if I consider for example the knowledge and disseminating standard faithfully as a subcategory of the controversy so be assumed tightening so under the closing alone project that we also meant died some which have more of exotic form of 100 expansion and the 1 that talked about it so then we knew Sept . 180 conceded I stature Schaefer for example in all respects and so when 1 is similar to toward the interpreted the stature Schaefer structure sheaf of misogyny going this way and this is a unifying point of view In order to remove the characteristic Bassolino tool and I want to talk about the characteristic of P Cantonese conceals a characteristic 1 that black like unique salsa legend categorical structure at the bottom which is characteristic free and there which provides the the possible definition of absolute Paduano unsuitable I think it's the opinions of on and have and go to the end of that you think the 2nd 1st 1 is on the scene 1 of the good news is that the wishes of the resistance civilians would that was the only way to find the system this is already I that just before 1 of them all it could afford under under anonymously you know what August
1:04:46
and the other thing was the news that the Member of the Order of this Solar for or whom you from there this is the very survived the of clashes for the the CEO of the U.S. was full of violence and questioning yesterday had Indiana and now if you want to consider the dental product that which is you can define for losing my stature me in general will be and so this that's why we passed through a new stature new stature like a hen moving from marine go to where the used Inc and then when you have a new structure but this thing is then it helps not only end up .period but as I said also at the moment that when you want to the find for example we have Keeley of correspondence and even talk about this on such product of the domestic side In the end so this correspondent impractical for the news correspondents salute from the unions in this for this type of conduct the underside product that they do not behave when they are not going to want to use my it's because they SMI structure so that's why we use systematically in that I condition not development about their being the freebies correspondence also introduced actions of the new statue is like twilight that badly behaving before being used on Anderson because of the freedom of being 1 of the lawyers for the government to watch the situation that as not suggesting last year news this is unique for the scholarly alleviate Monaco's swing south of keenly myself talking on and off the bed and that they for the last 5 years the last 3 variable factors facetoface debate over the half of the year the varies on the city's thanking the construction of the world the saucepans analogous to the world of the bears price for the year all the Bill the into very from buying group that there is a need for it but said only October social rank bosses have Arkansas where we are and what they say is that the longer sentence he has softened as OK that's 500 Europe fury very bad reviews that I wanted know who will get the alliance that read Pride and DNA and should you have to have a lot of things would have been higher than his review that campus which is much and wish you all the things that is low Ministry of Religion in its final group I love you are here is because of you and the PGA will be devoted to the dangers of local Cambodia Development came about because of all those things that are and what we found is that with our construction as reactions were planted in the search for the little ones because he was leading to calls for the last 2 years after the end of the day right directly from the original including all the time and again that was once you start like we gonna say it wasn't said tool bottomslapping was reported in the 1st stage of the investigation of the period prior to you won't have taken no in the West the extent of getting confused and exhausted .period point was to understand that went into hiding commenting on the fact that in the fight against the whole conditions on June the calls only for the time on it's the strategy in this area what I want to say that we a greater the reason is that the real problem is that all the policies that we will be back before the end of the world this fall will go on sale in the House and Senate to knock over the last year that of the people there thank you all the of those things that the originality of all machines that I do this morning I was and that was the reason for the Fed that would face of provisions that would be interesting to look at the business end of the century the the executives of the 2 presidents and hold for a ceremony to patients in the cities that there almost machine which is right at the end of our of the context the of existence of this is 1 of the things that you have the floor of the old rule from all your life you want know that along the lines of the European Union and get of good things ,comma explanation all of the little rainfall not University's School of the development and use of serious the fact of life as we know very well with the rest of world was Gillette usually means that the President of the rocket is all there is to be welcomed by the soldiers was so sensitive the disposal of the envisaged in the this is an idea the failure of short of what the content of the question of what happens to so this is not the answer to the station this a technical questions related to what used community 1 of this year this to you but I can say is that the Department for the good of the country and this was 1 of the people who want to see this is I I thank them