Wallcrossing and geometry at infinity of Betti moduli spaces
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Title 
Wallcrossing and geometry at infinity of Betti moduli spaces

Title of Series  
Number of Parts 
3

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 
2013

Language 
English

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Subject Area  
Abstract 
Linear algebraic differential equation (in one variable) depending on a small parameter produces a spectral curve, which is a point in the base of a Hitchin integrable system. Gaiotto, Moore and Neitzke discovered a remarkable structure on the Hitchin base, consisting in certain integer numbers (BPS counting) associated with cycles on the spectral curves, and satisfying universal wallcrossing constraint at hypersurfaces of discontinuity. For a generic spectral curve the wallcrossing structure leads to a preferred coordinate system on the Betti moduli space (a.k.a. the character variety, or the moduli space of monodromy data). I'll speak about interpretation of BPS counting as trees on the Hitchin base, about generalized Strebel differentials and associated quivers, and how one can effectively calculate BPS counting using algebraic curves in Betti moduli spaces.

00:00
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Fundamental theorem of algebra
02:05
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Fundamental theorem of algebra
Universelle Algebra
Multiplication
Polynomial
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Infinity
Parameter (computer programming)
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Entire function
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RandelementeMethode
Betti number
Social class
Resultant
05:00
Spacetime
Group action
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Analogy
Monodromiegruppe
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Hill differential equation
Right angle
Thermal conductivity
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Divisor
Real number
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Infinity
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Number
Wave
Frequency
4 (number)
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Homomorphismus
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Transzendente Zahl
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14:48
Spacetime
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Fiber
Maxima and minima
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21:59
Axiom of choice
WKBMethode
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36:29
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37:36
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45:09
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48:08
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54:14
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56:32
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57:30
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1:03:28
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1:06:04
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1:09:37
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1:11:33
12 (number)
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Überdruck
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1:13:46
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1:14:59
Area
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Hadamard, Jacques
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00:03
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02:10
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04:47
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05:01
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13:03
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14:49
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15:18
so but it's it's a lot less the last bomb puncture Glenn will be plenty of and then in the case of the day yet so just what once more .period within the international agenda without knowing that he was not known how long it was of covering companies along the eastern end of the you have to be able you are to have ceased I thinks that it's fixed parameters that could set on fire and it's a is a function of a lot of Corsican where a anyone anyone is as well yesterday at the Freemen of such things cancel this 1 important since here in case of and where my function so what kind of would function and it's mission functions in years of age but here if you overlook where age is this Alsace sector stopped dropping and to get some kind of ambiguity so get fiveminute function of each buyer that all only considers function all over the 4th of July at such important pointed in America Acacio lead you get some ambiguity rotating Katie bar that all think it's actually they're just beginning of Earth title studied but many people this conviction but but there is asking the jurors to higherorder perinatal differential equations after sold off work which afford not before the public of crap order and potential proficiency with minimal social credit agreed that kind of 2 parameters here and then they get a remarkable maps to get colorful plastic from complex numbers to work centralization of authority to explain and Fisher called Rusman and plaster righteous and Zipper address completely similar stories it's you consider psychically ordered collections of metals in highdimensional space what can focus 5 epicenter nemesis President and possum person and emissions space is a properties of all of them rich product 2nd order I'm on 0 and considers the chance so it's kind of a basic example of cholesterol right to refer which people study in very simple sentences appears in amplitudes very pretending commitment to its assistance as soon as the mill basics cluster right here the rest of the I think it's all the things that things will listening in this case habitats kind of threw generalizations of people OK so largest pension fund is the creation of a resurgence Brussels as what is the general framework supposed that a lot of Rakoci and the call Norfolk and have some parameter space forces but most of which will be just opened still some small radius Epsilon and consider cold bundle of this product and now all were supposed to get my connection long fibers and fix it the richest man Norfolk both variables and has just poll mandated by are equal to 0 now certain that get really feminine no bundles on his mom connections only that there have been certain qualities .period it's a government permit space it should contain component debacle pursue it's got to convince her to collect 1 doubts could contain some as a matter and she had just audible as it and other composers can have other local audibles and principal unconfined by the use of believed that it was not I consider constant familiar but I think consider product simply in principle and saying the EU yeah visitors and realizing In the end and yesterday some some other CCL immediately yes yes you can have this golf and offences in more than a good this conforms people here also confer follows a component the then principle also can also occur to a that would eventually bar but it just wasn't listed in good condition that get affirmative bundles of Islam American in connection with a defined on voyage biological presumably would vote will usually have some connection and all our forces not bonuses connection Kansas traces of 1 Rommel's asparagus data which can imagine an act congressional bill seeks to consider some solutions decaying consumed directions and so on and so get funneled require his bid modernist space and I think we find that there are a problem rising now and not not now we affirmed that the risk of connections his muse introducing Rajasthan curse debate committed by and for the connections somebody want to cooperate some entity services at 10 months of the year manner not enough that is a function on all space of all local systems see "quotation mark near but not now because the article local system dependent on the system they will call the notorious for that yeah it's going to be its huge complicate algebra conversations Florida officials but now have for each Egypt bombing of particle local systems so that we can evaluated here and the function of the parameters about and it is expanding its interim lowercase it's sexual functionally not on age bobbled when the universal ,comma depends on the bridge of OK so surrogate and therefore may be universal power puncher discloses that make him on MySpace and then this company directed to check such issues arresting dysfunction to any right so sold Walker approach 0 is in your face then functional run almost exponentially exactly because this production has questionable yet and is
22:01
a the conjecture is the subject say this function is Gold and functions and I think that's all subject was essentially the main example in all this conjecture that essential questions parameters just so's this small a defunct rules introduced by the current so what does that mean that get the function although there may be no so ,comma qualities and the whole world is Bob and I tried to make up lost on form between the indecipherable because he operas 0 and Tintoretto from some . 2 0 and as a country integrated the integrated prompt some past linked with your some barge Europe a strict policy on the part of 1 no no no no but in this case it's on the 1st In this case its 1st positive or none at serious and would add to to this the claims of this function of which bars are eclectic score minus some constant we after it's not other porous here now and then Nussle said fills functions call Sergeant if you make the slope was transformed into that function has endlessly intimation what does mean the slump was so strong as this is the defined as some demeanor gets some convergence but was bombed and the conjectures this accountable which in reality it's everywhere dance said it considered arbitrary past which doesn't calls set which generate busses a functional damage be continued for the sports yes yes or no the bullets and you're kind of this is a basic example which we have here he felt obliged to call formalism was a case of harmonic oscillator 1 gets sense the falling function the best but but but but but but but but but but but but but but but but but but you have it considers this function and the claim that the if integrate and in all but 1 which bars and so if we integrate probable for explores oneself slated diverse 0 maybe 10 per province .period Group Plc was infinity considers this function this slow process it's welldefined defined and into a right of playing with limits analytic on universal ,comma 469 Cminus prompted by just now posits that the basic example for certain function this it used to be His discrete yeah yeah that was founded national known as this is exceptional said but it is that in this case in this case at the of our some Frank 1 be assembled Francona in in general says exceptions that this summer will find a trend but because it's a 50 50 strikes until the evidence in this good 1 almost all milk ?question mark universal covering because appointed does it consider arbitrary branch should do is to have no Summerchase near but if you're Brownback you'll see gains in its English is here to listen to that deaths the projection yet but if it is considered a kind of a romance surface international surfacing regicide similar those separated from which other but about on the projection that evidence here earlier he users will have to buy assets of the beautiful objects into was studied by Andrew Morrison to account and also get such a sink and size understand that have persisted this means supported make to forward to think about as I said this is all make mistakes made in this mathematicians like mine ranch enemies then there's some kind of federal mistaken in moving people farm and so on so this really that this is subject should be reworked it to guess that sits at the conjecture so that all will example this this the gum function that I to prove that might work for someone with some of these analyzes of the of many I have a choice of yards already area known as the "quotation mark policies on the this was your idea that neither it's again for America's subject and I think it's a good thing the information the circuits murkier have also visit recession that money who most attended but I think you mentioned as the 1st she hasn't come from the far weightier yet and I think this whole crossing structured scandal was a frame product understand the Solar Temple ginger forces subject "quotation mark or at least not as this 1 kind of work thicken modest achievement with 3 important thing because of all crossing business gives it for any function on vitamin space and for in generically you can expect it in exactly say what is the right course and ship it is it's community my it's already interval I think yes so or now again just can't seem to repeat that would and was still talking about Soviet have equation Independence Hall parameter and that it was the 1st of the ball is in the limit object is not there but those connection but its use as a cremated school kids bundle to get their homework a bundle but instead of connection to get 1 form this deficiency in an amorphous connections would cost 1 formats and both were hold if a connection and it depends small prompted some local coordinates assumed that the tests the 1st of the poll bar and because it is skittishness it h bar interest and its illdefined auditing the limit is Hicksville that's on farmers and amorphous involved both were all the volatile and there is a huge field do suspect spectral cure which ended known by Sigma and namely this bottle condemned subjects that if you have times character the is an affair on form that operator of a prosperous and uncle ,comma spectrum and scale contractors spectral will be skilled so the whole thing nature understood as a subset of local dungeon space and the cart and then you know arises .period when of places the trajectory that that sounds somewhat onedimensional somewhere I can look up 100 spaces occur and what does it mean and kind of real example again just will all speak about this with potential should encourage potential resignation age body squares Aqil Passumpsic in our just replace anybody would be survivable W yeah so that's Colgate's spectral Noble is coordinating cut up into contention I this but medical
30:40
and no might get ability to stop so goal to draw within that's all so what is the control system a game consider but he model features a bundle this the 2 vectorbundles field also got some constraints and .period and then we can forget about it the because social spectral so the goal that if we have bundled and get a suspect aircraft and then projection for more specifics about some and insects as long as they suspect processes are always urge that it stop the burial rose but it's always has a metal structure of a fine Nepal's space a find space or completes the essentially the spectral coffees section of some 1 bundle of space for possible sections in contention by its leaders they also get a map from all 1 0 manifold to another and but I was going to the most important part of the problem descendant of its services complicated stuff but there is a generic .period generic His bundle is a very simple objects it's just speckled and the line bundles spectrograph you Eigen space crews .period was returned from someone bundle and you a rule will all this projection is it's necessary forget line bundle consider prospects for the spectrograph was signed for land to spectacle the you have this guide some kind of coffin Cottonton bundle the activity and would make a nice scarf incompatible looked as sober I'm afraid covering cos original cover yet and the fiber the sink its noncyclical Jacobean or you might expect will cover costs of you should consider all possible and bundles on spectral some sort degree not and invigorating conceptually algebraic intervals systems was a modest piece of Hicks bundles appropriate conditions there is other breaks eclectic and it's it's fiber to General Pervez said in writing Texas Lagrangian right here is the presence of ritualistic structure yes yes sort I'm not going to just sit formerly the thinks there but the questions all parameters but where have Hugues bundles of the limited some dramatically but it's the taste of family because they're like Andrew Grove speaking about some special feminists of connection with the scandal applied to at a true of a refinement of the creation of any default parameter so if you have some of the questions obtainable small parameter then 1 can do the following the on and the 1st to some kind of universal commission would again find ways to end the violence but if you have a a N and Commissioner won't understand some firming of accretion small parameter medical Silpaarcha 1 introduce a kind of Earth Summit some mn Ingemar studied mainly in the Valley has made his Italy yet I have a question the Pentagon yet the equation consider questioned binnacle small parameter or I think all of sudden death like Michigan and separate services graduates some unison and so scandals regimented framework here's a falling so for each age on me all it can consider some familiar off basis depending on parameters there so for many parameter is nonzero this modest space is modest spaces off the other rate differential equation all bundles his connection and and that's what school there are modest basic was the famous foot connection but to aid you want to see this altering in assist descriptions bundles has connections and and the limited and issued the 0 considered by most of his connection with on forms it's going from much reflect from a full break so the so Solid and he said the only if any of the no 1 can if you have a mean accretion the pinnacle so parameter that there is only 1 thing yeah but but the question the results of the balloting indigenous I think this the the president will have none us not 1 single family authority in this year's labor is exactly that all until the even in kind of nice addition will be of break from the old requiring In the end the exchange of the money he was not here not not Moses who is now he said that he will not know the Higgs is the claims 1 can construct some affirmative holds )right parenthesis the pinnacle of parameters while also failed to break a leg said at 8 am 0 is more of a huge let's
36:32
opening connections the resulting singularities and a major box modeling of vectorbundles his so fibers accounts said 0 I the same but does Europe have different forever on principle so
36:52
that this family of connections and that but the knowledge when then we describe all commissions this position of mayor points and Johnson gratis can you from Europe at Brussels itself requests can legally depend on each bar it also get this the picture and the gracious all parameter of command center just homomorphic section of this family whose roots inconsolable exceptions for each Barry rights immigration before anybody could pursue a right not equation but buttons connection now so it's kind of genetic information what equations for parameter just repeat what they said but not all
37:38
of the is all interest thinks is certain functions come come from because this competition cowriter muscles require writers on space is the same as bait to Mordor space which is representation fundamental rope and made modest basis it wouldn't a small parameters here because of its subdued by some questions into the coefficients which explained to you us that slogan is the same space sources that we get in nonlinear ,comma connection under the bundle which has small the displays which have been discovered connection the said that as a connection exit have not moment remaining mineral case which is expenses some of his might due to now and then we can locally to realize this connection so all section will be no complicated to certain functions necessary so was kind of different over extraction different connections that can present gives algebraic functions Is this a surgeon function OK
38:46
yes or no knowledge L some brief eerie waters what is the sole crossing could think that number because and return but the future vehicular MySpace optional for the reader to transmit it the there still so that the losers basal Hitchin interval system is so fine space and it can't do that all the talk through what kind of nice spectral which osmosis but sometimes speckled processing the and in the course of the performance indiscriminate local switches to cover surface in that the the basis a In the offender to space with medium body write some explicit question in the scabrous surface has completely Korbel cigarette as it was also possible singularities and it has complicated fundamental come a compliment that aren't on the complement of recovery room spectral office most there beget a local system of flat assistance is still some old rules but cooker and the spectacle of could be the compartment Grisham has bowls and most intimidating so too is the selectors has a bear pay intersection benefits could be degenerate and that was some sources you really want form on the Cup unbundled gives away it was STS and who has the most of his was better correspond .period you on the basis on the head of the Federation of change in view there is no history is of the the also Milanovic consider open part 2 at the polls is the center of course they also can change it changes now is William them considerably from what is probably the last major cannot consider what property Parton H 1 does stay the same year direct now they are so good that confuses religion experts spectral curse and then 1 can restrict because perspective process canonical form on good times and bundle gift 1 former coffee and begins a functional on the lettuce you can integrate formal went in cycle so Linda function for electors to see are always in the 0 about is that the image of this matter is filled exactly since its analytical system a yes .period through the slop last of 4 generations on this is the only 1 I think it's moment which collapsed in the from exact statements that now but now I want to see some Schiavo waters all crossing sinks is also watching the 2 more next year says it because there are some road some nice numbers of soft whistles geometry which source to it .period alternative discrimination tend to point and schools colleges should get some integer numbers should reach the that jumpsuits something along some holes as a decisive all wasn't formula that the souls of all sexual the has also depends on also should introduce face this week it's it's much better with the Devils members that will spot a can of forgetting to rate features yeah up now to where we want interpret 6 is a full inquiry that had product was cold a base and uh here are long considered 1 of my mind indiscriminately now and here we get some real could dimension 1 local namely we have to do have special there's a year many you have point on the way of on interval system and on the basis of the vector of this decaying events with Obama is on 0 or something special happened then made it through the draw .period it here in the 2 cities argument over this complex number they also get some who complicated could I mention what think which can be sort of a collection of kind of stocks erased in just the usual playing deepening continuously on .period the disk was if you fix disk that you should get 5 financial comfortable subset although or circle sometimes dense and to you replace with .period encircled by recent good yeah on in real life it's yeah that's citizen entrenched understand what's the condemns them into the different religions means so it's all about or what and explain the 2nd of the Avery nice exemplary don't have this circuit can focus finer picture but the of the yes yes it's it's that think What is this stocks they and begins next year and explained that what this will cost structure the game and the set of the if you cross all should serve to grossing the Wilson on change of transformation some Torres women some domain and Torres but and the centreright associations some kind of bizarre way I've developed earlier uh concentrate on Tuesday it's an overrated sexual X formal posts used on the Net of its formerly it's computer formerly of and public and the main constraints make small preserved in the composition is trivial sorts in the explained the soldiers along with 3 and what a
45:12
basic things to say about this but noon crossing the 1st full and as of this focusing constraints so powerful it's some cyclical 0 Kurdish acquistion of flight connections and the the funeral was business numbers for some point on the base and all the actress so message the integer numbers too users is and by some kind of phonetic intonation can recall collegiate everywhere it's like the analytic functions and it's determined by Taylor expansion so this is going to stop its analog of delayed specialist .period year rococo today different .period the effect is the problems that was up to many anonymous who don't know what to do unjust so it's over says something about kind of nice to see dramatically later "quotation mark Nelson and the next important pointed if consider this point on this product this 1 and 2
46:21
as a base it's not like a novel which could the configuration .period the 6 Gujarat and is and you get the coordinate system on better model space New Year's some corner of the consensus so he hadn't fights locally Altman you don't know really much what conversion to some domain in Torres and and go across the walls escorted system changed by what was focused interests relationship that's what's explains associativity was a constrained because students but and there was a rumor really nice things as I moved in this product of domains says a serene normal spend freely because demonstration don't have evolves and discordant system should be algebraic kind of biracial coordinate system the essentially in this case it's there you get a minute of the Taurus but your yard said Tillman written word especially some contains a skillful partridges algebraic tosses electorate Florida all but she contracted Egypt and the multiple functions will be to Stalter or Laurent Bonomo I can make man into Sosa and as important since its men of this number vanishing causes some In the quality image suggests it's all based on some kind of joke trusted emission call they are completely different I think it says the it is that what was going ,comma that the letters let's suppose it's Kansas trips to seek numbers meant that they're
48:11
so that's the kind of digital points as threedimensional space next 2 plan and undersea fear and resent those who claims that 1 of the cycle to 0 in some neighborhood goes a colonel that a rough picture and its related to a kind of come the interests of convergence of O Holy could understand parts used confided convergence
48:41
in all this is business and finally the those it's going from the most beautiful but here is that so absent a remarkable but a set of functions all owners a bit too modest pace which form basis solvable functions as a billion group it's for a integers antitrust some nice basis like temperature when animals were big digitization chip shop in animals and risible peace and which Escobar intersection generous close group but this is a set of this is the basis is a good living beside abstract set and now knowledge we have our game .period totals of all the sets except Bill bidding to fight elects and then there are under consideration nice for some projects because the issue strict with this His affirmatively commissions by among other amendments this a dysfunctional will have a gross which you can afford expectantly "quotation mark beak is interjects in what is nice but if you can imagine it .period all different .period so have different roles it is American said because the good demand from both largest to real number C and generated so being inclusion so be union depend to integers and that means that if you consider linear combinations of this fall control basis and want to start is the order song on 1 end on a 1 1 home the term of the senior Commission will dominate this is the best value for the invasion of Iraq as total the small rate in it was yeah it belongs Arabia it depends on the radio in areas hoses was from yes yes has accepted this stuff yeah and as a son run can intrinsically resulted even understanding quarters for women doesn't somewhat of what what is it what is the meaning of walls it's uh it's best I 450 were new .period on the basis of the considered you get a lot of research and functions as a sudden functions have fewer stocks erased because of their long sudden race to meet our system that killed jump for 1 contribution to another at all possible stock so all possible nerve function from British form for all the assets completely intrinsic definition all that but that is not not dissolved basis because it all possible functions as a claim that considered linear combinations of those divisions over here and not all possible combinations basis expression traces here Herbert Wilkins who allegedly said that was the basis of the interest the company yeah Boyd said he was going on and I know because I was going to do they understand quotas for winter wizard both on and off solar ,comma computer differential questions can immediately see the variables in its is a subtle expressions jumps the behavior yeah but no but now the sinks modest perceptible It's kind of cynical Drake the it's called its local writers has some important element In practice for this and and the U.S. mainland somewhere in the the low for the area my Moreno 0 yeah yeah I know there is a fork it's rooms the losses ahead of the game the outnumber courses celebrities that is not compact yeah yeah it's his competitive occasion and for Dominion confusion on Azam's but is another such forum for Chris Fussell the political divide all components to the meeting also sits in a really and alcohol break Torres and there is a complications tickets out of booked vacation particle uh difficult toss to conclude trade in different ways by different polygons castles in the singlestory here so can start complications there and now we know what we need is investigation unit before identical Norfolk Neb from from a punctured discontinuous Secour let's sinister colorful punctured disk still there my old required to transcendental met I consider small various small circle fritters are so get cough off and I want to say calls Anderson Korzhakov look like but authorities and command Boston and feeding them ,comma pokerfaced confirmed here for told bullets in lives of the was the major who he said that he is not about Dickinson registers at the industry can you get kind of that kind of smallstock which depends so Pompton intervention will travel somewhere around future that's all I know is completely shrink it can really ask Rozel Christian Holt behave like it because space no compact and as a glance
54:15
at the moon as the slope so consider very small riders who considers this in the bar parameter is sold and on complications a claim this is a slope trails only knew onedimensional structure all the confusion in the wisest infinity and the Legislative Yuan seeking to chain of onedimensional it depends on the cation yeah that's sorted draw here it's going hit on the left is or will be rightists and from each of politics in real picture which is drawn by is the sub symbols can threedimensional space it's complicated by some twodimensional surfaces without completes surfaces intersect books and Carson themselves and eventually points that can competition occasional when he drove and then this and this is my circle will still socalled but why draws among different colors the and on the same color if you look at carefully vessels a circle with a drone work and of great and and Danny kind of threat basis is already here yeah but now this great pieces water very tiny pieces here but erect pieces will be very long along the US it's kind of small things became legend Lessing became smaller yeah ML
55:45
nearzero dimensional Mendes Cisneros small beginnings can make engaged Red different coordinates to Sears properly indifferent .period Collins because take lot of front of complex coordinates and builder of public finances the places added yes until it straight would the improvement comes on its behalf William like stall see us he's article and revenue dollars the diplomat from October To America's space and the initial circle will be sudden edits no
56:34
but no at 11 had we use is up to you the reader discretion get a cough which travels the wrong several onedimensional and you get the kind of losing jinxing still be degenerative to cover reunion of city wants I have to get
57:10
simplicity ones and at infinity NGO my cell copper assistance according to the chain of secure so degenerative Decker the amount you know what we can do is intended to cover so let's
57:33
consider some small neighborhood of this university once what we get some Chino from the richest of the Wildrick origins and is
57:43
usually much as somebody I of recorded has some possible structure is is more modest basis so that all have apostles structure so that formal schemes formal warranty which is the than I a mentioned but it's kind of middle middle infant is a neighborhood of New York University 1 these levels possible structure which finishes and some justification song and New Age .period broken it looks like neighborhood formal neighborhood were onedimensional starting in Tora clarity Wisconsin possible structure as what's locally completely is the standard object and there was examined as young as 7 among approved the full Inc the assurance of if consider obstruct this formal for some lowerrated issues for all possible where tissues informal neighborhood of cheating over there the CP 1 responsible structure the modest pace of such thinks His unobstructed truths infinite dimensional find space but it has been working there the head of the usual complement of flaming each component of what is going on now considered the formation of kind of boric while he usually avoids the man at nite and I consider going of this form former neighborhood sinks Atkinson of require formal varieties which are formal neighborhood of change said he was loaded onto a little information you love designer arguing you don't change a secure sponsors all parameters but kind of men considered high Taylor proficiency courses include get some freedom to them the States they said they had to assume that they will not a transfer so that they're kind of normal crossing site called Magic will exert coordinate coordinate line but to coordinate with the judges underlined the need to do is less than doesn't like open it looks like you couldn't line cynical to coordinate plants and animals also the glands of Mordor space that that kind of thing is just so they could not branches and have a look at the moment also told fish to get 1 more branches in all in all constraints whatsoever that some infinite dimensional the infinitely many parameters In this parameters are despondent should to some of them main elected and and then there's the idea that I finding by the way the him but considered tale confusions it's good for them will consider canisters but grew by some form pop formal bosses formation yet and the source of much of his or her infant Khamenei below proficiency which are free parameters In the space of the that is modest pace of such apostles skin it's the same as small a space of all crossing solutions when you were in this picture product for Swann president be to considered neighborhood of yeah at all doses of Kansas was proper to foment condemnation if you more numbers of women go gum all gunmen in the lattice Zenit can come only political at nearby father 6 and acclaimed that's all always control all the scum explained in different ways of you gets the same formal formal scheme which is not injured algebraic yeah the assistant can during formal the different Malaysian waters all crossings and while he was still lost his allotment knows there is a fault because vinegar fit automorphism off for all the for right they're given by French was record was a function in the C algebra is the same size as the functions as a whistle get hurt if you forget to alleges while its malls and all that different someone can boost similar sings his character fields but this will be a not to cost increases his 2nd more general sense now and in the light aware of what the legal authority to monitor not it's none of the reasons because Moses all modest pieces of possible writers the Sussex department there in principle is a false stories can be generalized to result was instruction now and it allows us to focus on this as some kind of parallel regain call struck numbers or from formal scheme in our this nestled require registered Dick former neighborhoods and extend numbers yeah I principles can be done will company computerized began looking the world the only for those that I now 0 from the season can accept or medicines some completely formal way if you get arbitrator Kenneth Taylor proficiency is essentially cut by 2 pieces to get no parameters single confirmation code grew the provisions of free parameter principles on can make it to the it from with the computer problem which should be very effective until a completely different way tool local troops openly this woman customers in under talked about Spectranetics do some complicated pictures on Gaffen song here don't do anything to consider some old )right parenthesis and local commissions for bosses should get the same think hello yet the speak include new used and we didn't pull off that its did really not some kind of
1:03:29
all bunch of conjecture whole Hall 6 a related knows that this procedure for respect elections should be the same as the spirit to break procedure no epic North a total of its a really nice to have the means they have no walls yeah it's also the last topic which has described suit deep losses source can afford to discuss the budget code that no such thing Her circle incident in the kitchen base as the suit of on specific point but and this should be a bit more precise so the future system depends on the plane parameters the new incoming just sits there some kind of random number not related to to the limited not not related to the meeting Russell but so can change complex structure the car for punctures could have changed several times and the most important is the 6th time will have 1st all polls over the Higgs field you can change eigenvalues all the residues of Hicksville departures this was a bit of sample some parameter someone portends another end of the month rise aspire to freely enter and all other issues and ways in all sunk in World War arbitrarily residues of the remember recalls that spectacle has 1 form and some compact has some room punches and 1 focus residues deciduous are important process and central parameters the pessimists and then also worrisome arbitrary Zoellick Ingersoll phrases cool to moved no no and let's
1:05:33
assume that all future system said at all residues are real yes means at intervals so some forms of the items through a number Zachary purely major and the claims that for such work their future system so this summer at something in the remarkable unique .period that said it is not only know at intervals of 1 form of all Smoltz and punches say mentioned above all .period images no now sources say
1:06:06
called journalism the generalize Chiba differentials angst that even intermittent white quality but this so infected did just that were explicit rate coated the terms as foreign and you know if you assume that is all raises so real the alternatives adjustment to get them map tool Will the bill would have real part or all of the time of the central church it is element of some space and this identifies locally also discriminate my this is a main opened the mainland rule that the space the rule that the space we get on the futures contracts all their costs and and so that director fields outside of discriminatory and conjectures that's it's example continues for everywhere register so the women differential the top layer of the eye's early but commission harmonic analysis appear here but there but there some for example function which is convex also just disagreement so the grain radiant floor office functions such very plausible conjectures that's stinks exists
1:07:20
and in the case of a simpler system the spot differential is suspect cover the same spot in differential and this is this is very nice .period is existence fairness .period it's selected another serial Chevrolet which ended in the mention of the most famous result of Flanders that if you have any cure for respond trusts and some positive real numbers isn't but this insisting he quoted in differential this is the subject In my Garfield reunion of craft tubes is doing the images asserts it is it's it's my conjectures construed generalization of should resolve but this a different approach Castle Kansas case and kind of a good deal for putting differential some signatures not to confine shareable can't it's doesn't fall from his result that again for the skin which triggered good for erasable for any number 81 which can be sold as part of affordable system it is you can't afford to support the base the good news for anyone to diseases such all priests are real what do you mentioned that's absurd 6 simple Michigan .period but this the state has a statement that it was the owner of any any public somebody once in a while you are gone we were all interval can be on the double cover which is amended articles defined him for any of his head and he said he had a fall all put prepares to your material and in the space of Pontus composed again on the of not unknown already such as it's the Sisters of folic because she has a calf is indeed to covers on puncture injuries is automatically 0 yeah it's said insisted that gives a have just wander 1 month puncture it's there and similar run can cover crowded question it's still get or consider altering the group minimal until have still won contracts in the same sisterinlaw was used in this case against conditions can enter the to clear this is thing but 2 Intel sweetness and red conditions yeah and there
1:09:40
isn't a new fervor now the claims that if you're if you suppose at all the stripper differentials kind of nice it's so there is no don't have .period indiscriminate which is position physically stop a suitcase .period exacted tulip and it considered warranted before a differential to refresh this simple zeros there and only get an appointment with Kansas City the main in interests of animals and there's really very little holes here because exactly at the my point is you all over me as an MEP from my letters Silbert to imagine a number and more freely to beautiful the opening bid the association did just that and still win left and right amendments novels they also you automatically give donors the means remittances which injures triple differential and Germain should give some original proposition that some biracial met from 1 of important Swanson "quotation mark assistant another yes so that some of them but were shown up and look to the claims of success in some kind of small accorded to those of the subsequent career because in the previous picture Have the stars
1:11:04
formation and exported expenditures solution that various the vector as a claims that the suddenly "quotation mark school Oct aren't so be it all as a citizen legislature changes in the composition of the land locked onto an older generations was soaked and so did some nice collection of some basis the lattice and an hour from the schismatic former can construct
1:11:34
a cleaver yeah and those acclaimed that's all this clearer kind of control sold and this even where additional maps and 6 controlled was a screw or community centers and he said that you have periods is the same as the working no not to at that time the natural killer is the same as miscues he significant into genetics because you all positive pressure so the number pharaohs yes it's just wait to draw schismatic into tremendous In largest finished restore basic examples not so consider Campeche option to purchase came potential which of course was an example that were just a took reverse it crew In a versatile solutions some of this kind of difficult questions very but knows next examples really interesting to consider elliptical Jerome then there's the scurrilous history as the versions oscillation finally after many years of attempts on goal later it's such a monstrous biracial transformation which control sold all secret sources was focusing structure be thinking at the time it's true of the IOC is this he's a variety of seems wiser than when you have in the region which is really a wall that's the only way to get out of the national considerations rather version was released to the atmosphere is it's it's it's it's wanted to get our invading couple In this case it just get rescue and bedding from
1:13:41
stop foreign to them 1 of the original walls and that's
1:13:49
a long story of property in
1:13:50
this region and I think it's 1 concedes that 1 functions on your own around the victim of space to stick tolerant than animals not to do this some kind of fun this I couldn't really understand it very well now the most had sold to cover and half experimental work expatriate workforce established the only time also is made up of its kind of the simplest warning In French decomposes went into the elementary various none of the stories fault that in this case 1 Canada composed of likened composed they're different not defined compositional no no I didn't trade him going into the
1:15:10
working by Exxon and Minister slump was 3 years so it's not just you for me it was just a 2nd it is the end of the list of those who are in the area the actions of a rational manner and the U.S. and Canadian maniacal collected so it's computer refined from formal it's the only legalized go on not for foremost massacres in little although not with this it easier now that the sink is a fault if a composer signed portal myopic cycles to its interests that isn't the answer to reinvention yes it's yes it's positive show from this is that the system was forced out of among punches Sunday appointed him the freshest you considerable that as such it is a shipper differentials very simple once you consider hexagonal belts the lattice kind of and glued to process
1:16:24
and modeled by shifts so get detailed to itself which should punctured doors this the 1st and