An overview of the topological recursion

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 Title An overview of the topological recursion Title of Series Physique mathematique des nombres Hurwitz pour debutants Number of Parts 6 Author Eynard, Bertrand 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 10.5446/17047 (DOI) Publisher Institut des Hautes Études Scientifiques (IHÉS) Release Date 2014 Language English

 Subject Area Mathematics Abstract The "topological recursion" defines a double family of "invariants" W associated to a "spectral curve" (which we shall define). The invariants W are meromorphic n-forms defined by a universal recursion relation on |\chi|=2g-2+n, the initial terms W and W being the canonical 1-form and 2-form on the spectral curve. Those invariants have fascinating mathematical properties, they are "symplectic invariants" (invariants under some symplectic transformations of the spectral curve), they are almost modular forms, they satisfy Hirota-like equations, they satisfy some form-cycle duality deformation relations (generalization of Seiberg-Witten), they are stable under many singular limits, and enjoy many other fascinating properties... Moreover, specializations of those invariants recover many known invariants, including Hurwitz numbers to which this conference is dedicated (see M. Kazarian' lecture), intersection numbers, Gromov-Witten invariants, numbers of maps (Tutte's enumeration of maps), or asymptotics of random matrices expectation values. And since very recently, it is conjectured that they also include knot polynomials (Jones, HOMFLY, super polynomials...), which provides an extension of the volume conjecture. We shall present a few examples and mention how these invariants were first discovered in random matrix theory, and then observed or conjectured in many other areas of maths and physics.
Category of being Network topology Prisoner's dilemma Multiplication sign Equation Family Recursion
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is like a glorious retreat it would also find all positive and but for her merchandise you and you have a and on what you don't have such an expansion for everybody but it's a form of very large just of of murals you have such an expulsion under question 0 which exists in chooses was how to computes to conclude negotiations so let's assume that you have such an expulsion Alcan computer questions on 0 or so you're not and interesting interest the partition function itself but you are also interested in expectation values of the spectrum of watches the video over Vinod individual perspective that's distributor and are 1 the spectrum is mostly and put into the reserve on some of our eye of 1 of our ex-minister and I were overrun dies of and in the news of and so what is the statistical distribution of this quantity you see that it would assume we are exactly on the spectrum so that's where user information with respect to a dysfunctional on denouement to compute it's not an expulsion went older refined but it did like and bans some functions white it is a sum of and so it's not very astonishing but they have like to 1 In 1 of and pens some would have I would have written the next correction is in and to remind us once again that goes by and it isn't because of and then the felt correction Over the corrections with and 3 and so on and 1 minutes to the bill would you want Alex on the day and the questions what the question was how can you compute was 1 of those functions on the sequence of functions once you can buy for high operation functions will brandishing function is to take a product of reserve also what they procured alters or to say whether it is but it's just a technical things which is the answer is defined as an endpoint correlation function on again still to observe how we did such large and 110 gives like and to a tremendous and this is not so obvious but but what you observed and then again goes by even balls of an but today on what you want to compute no obelisk or was good Haitians the bluejeans so people are interested in competing was coefficients the answer is in the literature of machismo and there has been many methods to stop trying to computers was coefficients the 1st show them what only did 0 1 a W 0 once so which just it's of the trace of a result it was already known by people like you know based on it .period the very beginning of Rhona Mitra said so it was known from the very beginning and it's very complete it's Windows examples then the two-point function 1st correction to a F 1 of the partition function on some days people were able to which we have to have 3 and 4 on the right was computed Morris case-by-case and some of them stays in 95 ontological focused unlike in co-produced and injuries and 2 in principle computer every patient but it wasn't good reason which was read Monday opponents and for instance they were able to run it only in the 2nd when it together with Britain and potential for a switch was not returning the union also away 1 of the general structure was notes from industry then the started to be able to find generates portions for a two-point function on Form if 1 but over works and that's that's so in 2004 the new the and was the paper by a symbol of the 104 miles off on some flaky and make our minds of what we uh 0 stories to different methods but so versions used Alonzo constraints and to find a relationship among but the region's I road through be questions which is overrated to the constraints but did but so we were able to find a ocean for prescriptions on the Swedish and looked very little sort it was noted that 1 the only difference is that the denominator was not this 1
it was only 1 term would spend they too because we were standing on the high-purity good days or visit was meant as an integrated a trial stones that good generalization was to do that and this is what we we did with checkoff on all but a more fundamental we understood that the former now which can generalize to Armatrix names is when you
replace the stunned by this difference rated twisted for the but it and then in 2007 with which all powers said OK let's study this equation this regression equation by itself in the party of any relationship between the matrix mingled on the most of these properties will for instance prevent it's always did some conciliatory but it does
some of the southern endurance properties our said questions related to which could disillusioned and so on so we knew we started to reduce from Massenet's coterie of integration and this is what worries altered to because the Petrobras Georgia right on a number of surprises but just when we finished that physicists manual when in fact we started to write a paper in 2006 and I was already talking about with my new so he rebuts wasted he promises something as before but money you will realize that this rejection was also confident ,comma within months but at that moment it was thought that ministers were and at least 2 million for my Egypt using this chance serial more about that uh but said but sending 1st assuming that the chance Sunseri was equivalent to a matrix model which was of reforms sought by the departure fishing was a very strong assumption which was blocked at the border for the but take what I will go the traveling that's
uh I just want to say something about the geometrical representation Virgin metrical representation as I said what this equations written a Vatican looks
complicated that it's very easy to remember if you think fit in the graphic away
so you Cheryl pelted each other with guns here by the
picture on thrust you only get Jeanne adjusted prices represented as a teacher
representative face of with an onerous for just a picture which represents that option sometimes I write as a repentant with boundaries on sometimes with punches it's a matter of what you prefer all this picture Olmedo 0 2 which would be something we've of June 0 with 2 Belarus it's or it's also assume with 2 punches but various Tonight Show represented just by a straight line between 2 between the X next to which appeals here let me repeat
what it ours what it's nearly
a pair of polls it's more the Belafonte would be that it would have 3 independent variables 1 2 this 3 cancel so somehow battalions of 2 independent variable and it corresponds to saying that it's a pair of policy but where you have we moved to the legs 1 sometimes we couldn't do short in handling the silver so it's like various 1 bothering but which is changed just a picture very often which would be repealed the desert liner with over 300 optics depending on the 1 of my old Desouza Okura and it would be very nice to find an extra interpretation of that but from what does not know the phones it's only in Munich to remember that expression just through the nite mnemonic forward to remember the question so that's show how it works in practice for competition but in practice for competition it's a all 1 1st there are different ways of writing the questions says so British immigration so ivory were presented with things with Bonner is on somehow
it stays but it says that you won't want to obtain his office of ginger with and onerous you wouldn't say you start from the 1st monitoring on go out somewhere but when you get out there short on much remains is either of us face so is either connected minutes of genes she minus 1 that's just 1 more moderate or give a possiblity when you remove short is that you get something disconnected then you have some Jews here was the tuition this year age from prime summons a of the number of words here and that the number of forces that picture number of boundaries Wisconsin and on our way to write it is when you were presented with punches 1 say that
carries only that straight line made by 300 not takes on new to to puncture all of this is the disconnected case all of this is very modest when it and so this is not just a ways of a plant in that equation that again it's only cruise Fresno geometry and but for moment I believe there should be a centimeter behind them but it is not not right so let me show you how to do this on computer every issue to after should the effigy remember to compute the FTC what you have to do is take it all on the once or something with synergy on 1 1 1 puncher but on the contrary we will dysfunction 5 which was know by derivative of as your 1 means you integrate if the jurors due on July vitamins to cheat on the defensive just 1 this is only a special case of all of the digital migration veteran questions in general issue of women did she and then into the quarter to did she had just 1 where have we would fight 1 of her legs integrate the debate tomatoes 2 achievements and decided she so this is true for every and positive and so in fighting this case is just a case and costs Europe 1 resulted in with boundaries it just means that it should data the function with and press 1 bomber is on disk on 1 of the boundaries divide between the ministers immense and when you get this suffers we've only and moderate so it is just a nomadic way it works right so let's do some examples so if you want to compute only does your only does your 3 so it's something with 3 3 patrols Charles often ponderous industry position at the authority this recursion acceptance of this some of two-term so effect is over to this brought to and that some prisoners dominant but cultural freedoms existence that so what do we do vote this would there's this
picture in this picture just means you might supply the weights associated to each leg so serious that day and is yours the Z Bar X 1 I'm sorry please only deserved to so just take the product the Wallstreet things on integrated optics integrate things I think the residue of branch at and you have a number of grass tensions with spread weights of the edge integrated at all of officers on the gives you exactly what is written so just limited quake but is very convenient is a nice this product is that in fact there is a signatory to zooms and if I lost 2 quantities so which reporters often residue when you reach reprieve for something to grow at the same venue in here so you could just say it is twice but 1 when you computer this new animal wonderful on the 1 1 so what's this rejection means is exactly that but is this picture so I'll use it they could take year throughout Windows Europe 2 so here again you think the product of whites associated to a Roland edge corresponds to a day this non-Arab edge corresponds to a when is your too I think this product integrates source at the branch of texts and that this media 1 1 this is just a rating of the integration rights let's do
not complicated example it's
contradictory as to which she want contradict to what you have to divide by 2 minutes to G which as many as 1 half example multiplied by 5 so this is this red dots means Friday at of this is only down to 1 soldiers to 1 with a 1 country but is still needed to 1 the plight Egyptian to 1 and was a sum of 2 downstairs here in what was obtained budget was a K some only down some the giant
that some on India 1 1 on the media when 1 another time which was only got 1 too and
this is just what you think about this but this was the only guy 1 1 we have already completed this year so let's replaces all media 1 1 but his brother you and for this 1 again which I computed by so this is what we don't want to which should be computed by the from so Soviet media 1 1 advocated by the grass on the want to wages British again so what this introduces a number of and then you have 0 0 meters 0 3 Ontario only Jesuit-run 1 1 why don't we deserve 3 I replaced it but his graft there will be factor too on only down 1 1 here prison but his brother and serve your media 0 through into big I just replacing to remember very distressed so we have to it is just some of those 3 graphs if class means you take for product of so to each edge so if it is our old recession today if there's no narrowed associated take just take a product or ban on Denver is used and the justices but remembering which although computers things so it means this residues was computed us then this 1 on hearing that brought this residues complete Mendes 1 than this 1 so you have to be careful about job over news that you to again control although residues and also the old all of our roles with great to remember this was written in the Russian which the interested persons and its importance in which older you take residues because because well boss Atkinson .period soldier although of competing residues doesn't it so 1 so it just went so this is just the way this is just the value of those brass become secretion so for me it's much simpler to remember Wallstreet graphs for F 2 were overrun or this and on the so you have arisen said the undefined but there is just this so this is just the most just enumerated in the way of writing but in fact it is very useful because most of the and you can prove a very easy to prove gratitude performances the symmetry all over this usually light equations ovaries prove gratitude on also developed an eye for men's and it comes out very easily congressional wins so so it's not only pneumatic tubes that actually really useful when you want to Incredibles is the same political appointments for trilogy work no U.S. itself or its president you have to take a sum of all critique of the good it is also wanted to know about the nature of issue over an efficient and the critical points you have this year an the reason is and raises various here it would never let and guns In this means and to a fault on this trip but you can also say that he and importance of the sum of on and it's only when the core of some resistance substantive the move to so OK so I what they notion that finish the so sorry for his watch so we know what it so I just
want to prisons vary for his some of the properties in a known very well defined way but just to give you an idea of what it was the 1st property which is not written here but which is extremely important as that is I already mentioned is that
although her rejection does not cubes a treaty in all its arguments the ones instigated the default for sold the 1st seems to play a different but in fact you prove attrition but that the result is always intrigued conferences the refuge's representation is very useful
to do things it's it's really it's very easy from 1 varies but promised to take steps but I think it is from graphical positions so on and so this is not to abuse at all or that it's going to produce some even under 0 3 only 0 3 remember officers ones too is a 3 it was a residue
of chaos C 1 0 the only day 0 2 officers in the 2 meters 0 2 of the 3 what we need to talk to what does look of symmetry but computed from the refinery this is always
right so this is not the reduced but this is happening this is an informal property over ways all of this would not be where the what a number of properties whose injected barrels wanted to be want to share this military proved this isn't proved false specialties but the
idea is issue what if you have this excellent was so it
means you have the care of somehow immersed into the square persistently 1 to square their current Austin too 1 of circuitous crosses square or whatever that's why there is a very nice properties that issue making it safe for us as a rotation in the square you the notion of branch points over the zeros objects on bonds Robert entrances that John McEnroe and so when you make auditions for instance to you challenge excellent y or and if you do a retention made payable to the areas will be totally different and so on the competition the looks totally different but when you contribute fetches the said so they are unchanged when you do that and it is but then 1 proof is that they charges this is the example of the lumber here if you forget that some of the excesses of the graduates now so and so what do I mean by that is what when both sides are always the center of his conviction then villagers greenside 1 of our social and so that's what they said it's proved on Monday when the car is really IG break Swiss Re proved larger break so you mean I mean involves Exxon widening on both excellent to have branched out and then it is Sonatrach it proved on inducted so for instance it is not proving the case correspond to cobalt 1 bit of song all true or even a uniform ,comma fruit and it does not apply Fogel freedom because does not apply at home but in the form of freedom we believe that it is reducing the treaty but it is not approved by this proof sold for in fact we are trying to draw is approved for 900 case but said its help and fulfillment we have not succeeded another property is well that's you produced this way always some modular forms but by uniforms and in went around with respect to so when discovered that some genes
it's 0 Maduro respect with the institution of the vengeance yeah yeah but so it's a soldier majorities executive Desue would you like to so I don't want to extend this is this is a property which you can Primerica from uninfected
for but 1 of the Russian for this gives you an extremely approved the is always it's so everything which subsidizes recursion we always had said the and this should is their I wonder if we don't really know what's majority meaningful fashion authorities but what it is to be explored wanted what integral beauties again his notes free proved displayed on a case-by-case for cellphones .period and families of spectral skills but it is
believed that the budget should hold in a very very generous said informal spectrograph for instance very softly and with illegal method proved that works for kitchen light spectra goes of what we formed to each insistence on we are working on the wrong end which consistent so we can prove it it's the provision that we suppressed its for long 2 and that's the issue taken all of a series of images make this series won over a sort which vaulted to humans to while this is about the function of something to Boston 1 of the the future
of the the what it I don't fall to me to be true to explain that to . several natural traces of coordinates the corresponding so if you have had you break function as neuromorphic functions here the coordinates with the Evo coefficient of energetic part flaunts function in each board
on that would correspond to the teachings of 2 component 2000 I mean basically gets out of its which it or for
systems it would be natural for me that is issuance of cauldrons of cheese which is it's me not to go foreign indigent but so the idea is that the WGA and while the W donated shares with satisfy some the timing of the phone on the Nunavut In the procuring editions mineral such relations should be satisfied and it is not approved in general on this is strongly related to the notion of quantum calves about but there is no general proof various formal apologies that is proved so on visited 1 ministers proved his Quentin orbited the present through cellphone again and it's really specialization of this was God's on of soap Castle killed a very important property which there I would like to say that to become or is about to take 2
imagine that you have a family of spectral Cos so you have on very which opponents sometime 1 thousand could be assumption of maturity on the major indexes 1 at a certain value of was to see a critical time the car becomes the generated desert coast instead of having to functional so that it doesn't ongoing function in surviving the
punishment for instance you can have a at this very special value when you are not that it
was just the world when you already did it away from the was deceived by the guest is resolved and you have something like that on what we saw Syria cannot free Computervision but here again competitive G as a function of his time on your today Georgia's has 2 main assisted to some power you can compute verdicts today villages as the administration to Sumbawa answers the question so edgy with lodged with 2 minutes to subdue some bore which is always proportionate administration on so To assistant about appropriate but were up and 50 hasn't it and what is that needs America's 2nd it is also the energy of some carved on that golf is just blowup of a security so so if you so am not very rule rigorous way to write it is that the units of energy of St is the energy of a unit of US what and but wasn't interested this is the idea the idea is that this the effigies under the omitted Shenzhen but also integrated but Orville mutagens new commute which taken in its section on this matter this is an extremely useful purpose .period there many many overall nice properties but I don't have time to explain to our relationships with send with and equations is 1 of the additional missions which I electrical from I duty which some people corner of special geometry properties of 1 it's a different mission questions I think you're going to talk about but were and that's all there is no real nice properties and why you know you're going also to talk about Vernon Chris Young the formalism ahead Georgia browse our sold there but they don't want to favor Nelson a treaty which you can also extend that to all noncompetitive spectral cuffs so you can where there is a notion of committed
girls were excellent don't commit any more but you can apply this formalism unwarranted works the same way and it's entrees Morrison property I don't want to to guru to
fall uh wanted to go 2 examples of reputations so now in its new mentioned some applications so I will be very sketchy we if precise definitions for instance about environmental was I wouldn't give precise definitions I just want to give you an idea on most of those things also conjectures and not everything is proved and many of those things on the prove that all but 1 example which she mounted a result is that the Pereda rejection something to do with not we not serious it's the completely totally mysterious almost nothing has proved yet but people raw Shawmut works the infects F in the 1st set and in the 1st place where it feels is by diving off from issued in 2000 I need a where he won some of the genes for say would transporting them you used to be raised no it's not say whether Jonesboro is too broad interest in obscurity have defined some variants associated to adults the past you over is 1 which could John Springer J and that it depends on lots case is not incidental Nevada virtue hundreds of pounds on an integer and is usually go Korea on Tuesday for more bombs so this is a pretty your it's been almost 2 thousand you of In a related citizens of Q of sorry necessary to cure instruments 1 sorry integers so it's a silken which is not on the boss altered to be interested in a holidays of the logic of this case when you sense a SoHo doesn't when you sent to a 2 to 1 on entry ingenuity in such a way that you will be a source and of Q so it's good new remains at 1 160 so how this behave what and it with 1 of at you find something press busy reduced some of note you to some 2 G minus 1 on that score aggression sorry sorry acute to attain this could be questioned SK of you so this agreement as minus 1 of you so there is a conjecture about estimates 1 of you which has been there for most of years which is not approved OK it's good volume conjecture so what's s minus 1 of you is it's voting conjecture it goes back catch it if you know I don't remember what that was but you know that's the recent thing is that they have some free claimed that's already estate's here they freedom and big game but all estate's are busy related to vote on the legends of at the butchery party British in reply to a certain carved on that here while serial presented few 8 militants were not 1 not so fishermen it's not good for the it's not on various notion of John variety associated to another don't want to govern these days but through direct authority of another is a cover once immigration Regent ex-wife wars like that like that Sweden question raised in excellent excellent white stated was just a
quirk of applied at a particular attraction computes was intervals of Medici she and up to you all of them to integrate all of our the
allies so orders the eyes integrate them up to you
divide by sectorial some young "quotation mark such fat 2 g prison ministry questions what good SKW the conjecture is that this computes listened takes of the transporting so as I say the and believed army is an approved this fall from improved soul and we are very far from proving rest of expulsion but uh bits you won't want to say we have aware for instance with my students frequented the data will we computed with for this not to be in the computed things up to sell power offer notes to on the matches Karen so yeah mean Dorit suffered an American agent in fact we can fruitful Torres nods and full toss notes redundant not only the transportation was the Bronx to bring but for but sold for even but not so far from improved format notes the just minus 1 has been proved by year's end here and there but not the rest of the expansion so on it's talk and mysterious why it works but it seems to us some people are already shortages works most of the recent because they go far but that so on so it's still it's legal to a of example which is you want to go through the politicians was through the politicians are or people courses ,comma but also playing politicians are you boxes in the gone off room 1 but sometimes you want the room which has called off the land 1 in that state as a chenille or did you what you want to rule which is not necessarily a square and undistorted puts boxes on the floor from from this direction before from the sky from this direction and they go to the butt of rumors I so it's a statistical physics program so it's coming problem and the awaits you put to a country aeration is just the number of boxes I also use the weight of acculturation is just that say you have a barometer of you so you have just tuned to look for a number of With Kuroda skewed more 1 so this is just how Yukon configurations so you wake every consideration by that of his young you're on In politicians on you want to compute their views the some which is what guarantee does number of freely politicians of different size but somehow this is equivalent to save you some overall or politicians with that for Due to another abduction on you won't find yes and that when the size of a room become large so which is Morris equivalent suggests takes when she was 2 1 in bowls of rescue so you want to go congestion tactics on again observe Jacinta to take schools by bottles of to work to ministry G. on won't contribute creations FG 1 Ave 1 for industry origin to bring the Internet is this is conjecture um so so we just sort when you put a lot of tubes so serious confusion with the issue tubes that when you put a very large number of then it starts to look like that and if you observe throw some regions were but there is no cure on the wars on awards here on sharing the country's you have reached the opposite wall of the room In the vocal yeah and so 1 series Shiva is a kind dissolved but she on most golf the varies annually since there is no Cuba or here and there is no and in Kingston New somehow here it's frozen it's got frozen and there is a chance which separated frozen region from where he quipped region and typical of the Arctic Circle the Arctic Circle of surprise the decreed from the frozen region viewership from home as well as on the shape of that started circle has been completed his forces versions the public unions could go from shifted the unfold but example Revay a would find it is diluted but you know what injured or what they find is discovered is the smallest of degree algebra coverages dumped onto a so on the decree derision said sizable boggles equation sold to renew old Alonso here we have a cover without a computer messages but in this make India's 1 infected slightly more subdued what's at St. I have a good news is that we did that get sentenced legislating most of them take any slice all I don't think the density of locate brought about whenever there is a Vatican edge and also was on the books since it was .period set up this happens the spectral of 1 which depends on which sliced through your true so witchdoctors Fletcher you truce which was slides bundles of survival but when you robots it's kick so you you have a family of bolstered his butt since they are related by goggles equations this means that they are order simply to get equivalent some Holly
correspond to themselves to from the old computers and efficiency thanks to boggles
equation so the conjecture which you can really the head the coordinator is that the evidence should be here to Compton made at the particular applied to those of adults cities and some hold what I would say there are some cases were misses proved it's because if I had listened to some of your politicians is of 3 politicians Morris Verwood comes as the some domestic invariants this opener come inferior for solvent until many forces which is equivalent to go Moffett and violence on somehow edges of offered and on in some way involved in the case which guru actually correspond to an enraged drainage program somehow is approved they're going to go from there when co-founders corroborate but engine order for an arbitrary trio the shape of the main this is not true proved this was the unfazed there is a branch .period here Bridgeman no more kids it's not protrude from the computer and convinced that happened at the would erode that would they just wanted to show his issue changes of that upstairs slice of the changes but to changes in the leg by simply morphism which consults lifted right for this is just an example of mediation that'll of what I want to say she worlds of at I
was just not just the number 1 recently see know is because the of you he come from merchants series becoming very very very important subject nowadays because of what's called educated conjecture which is I think military union more conjectural but I mean that's what you could buy digital but bids which say that's a good correlation functions some operate also in new vehicle from the history I don't want to explain on what this really means are very closely related to what was going on because of In the course of Bochum functions on that's on a bit so 1 thing is getting contraband imparting curator new computer than in this and needs of 1 billion reconfirmation surety bonds on such workshops which is usually written this way 1 persist through square on this say can compute was things in the units it's going to heaven and we like to computers to the enlarged Union aren't so if you want to expand but you compilation series function In 2 balls of Cuba at Celtic jobs the gains we go with powers of king would review involves of you and you would like to contribute kids on again there it is conjectural that the FDA's share Archer concluded by the 2 procedure rejection from the specter of golf on the spectral can also be 1 1 1 y square sought to use way square white square
given by US Open expression which is in fact the
euro was quoted don't surrender over dressing and don't sort in Munich for so distressing Najat also spectral carved on Winston stress ineligible and the disagreement of stress knowledge source get the speaker cover on the issue credit push for a person to meet you should get gestures correspond to the cultural expunge so this agenda conjecture that what we have good reasons to believe it's correct and
analysts way this year this program yeah yes
noncompetitive but didn't want to so the but it didn't want to look at and then there is the way to the final details in 1 committed to days such medicine when you
consider it is something which we have done before pot of Chekhov's on the region option which is here but what is
international assistance programs but we have to do this is 1 of the characters and you break but the humidity communities well but it wouldn't just
concluded that also initially the Depression-era Regulation was introduced in on indeed rose to find that out an expression of matrix lost by Jennifer expressed anger isn't so somehow it solves the problem of competing not an expression of interest on the issue of obstructed from explores the issue a played to an arbitrary carved then defines some interesting objects which could be environs of that covers on behalf of itself varied interests and fantastic mathematical properties on it to do and I think adjusts itself to be didn't just because of that but they have many applications and for instance was the fact that they conquered ,comma freedom violence for something passes of Canada also was looking story CAN END as improved but so did he was open but other foreign social rules of storage can look at it and knows it was proved that all but 2 of units it's notion is renewing a vote it's a fact that it applies to John Springer the total industry at the moment but instead and so on many of many of the interesting things to do with the or was controversial and indeed the having the general framework to do that would be very nice but also on the phone with his picture means urinals for French which
also 1 2 holds a clear here "quotation mark was going to be a long long way so as to 1 they
also called on OK and then it would come home from work I know it's full of strangers and this is really and the form of the question really is JIC which but it's and there isn't something else which is cool to perjury rejection worries you really have 1 perspective to also left but it's not the deal is due the 1st for the 1st quarter
of this year in fact this is this is for instance how we proved exploitation which we will do it twice on this also prevented birds from
already agreed time In stronghold of new regretted matches
2 the few around

Timings

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Version

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