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Wall-crossing and geometry at infinity of Betti moduli spaces

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she so the time has come and and the key In last 2 and a half OK so you speak about acquitted double-crossing condemned have continued to make modest basis which are expenditures but space its name choral section I think introduced to mathematics it's character rightist space of representational fundamental rule was 6 all the hassle my talk will be have a lot of the intersection this contributors and drew up the Miss ended in the but help put kind of different perspective the chief chocolatey no we know use Apple more than the good here OK so let's consider their creations say so I'll talk about gracious useful parameter and there which ended in Ordway detail and times institutional by age bar blocking you know the sort of political chaos that followed status as the candidate OK secretions regular similarities to have further outlets his several complex number sent several mattresses as American right the differential equations which in and that provided functions which has stressed all the polls Bantariza circuitous registers OK so we get to the end of the most important thing to put H bar it is further ordered heritage and so and now this equation has someone under a which holds a pencil age by now what is what is modern you
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in a minute that's all 1 can hot right coordinates insists that had modest space just foliage just because he wanted to considers the base vector so that have poured into 1 0 0 1 is any right to questions at which further prove it to his physical too 1 the presented fix fix but it's 6 assume number 1 song but that next on his list is long and also refreshed so that for some unknown parameters and if you look on this substitute to this equation used to get to nontrivial equation that some pretty simple algebraic surface doing to creations for wearables know what detestable this on differential equations not really for a moment I just simply separate plant was to be equal to what look at this the differential equation it banned pets two-dimensional space of solution because it's a kind of wonderment and amended and given by Britain didn't dinner .period and in the space of solution want to have 5 directives and Victory II until the some function citizen the submission of anything 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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 five-minute 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 higher-order 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 high-dimensional 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
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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 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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
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
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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 single-story 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 poker-faced 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 small-stock 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
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 one-dimensional structure all the confusion in the wisest infinity and the Legislative Yuan seeking to chain of one-dimensional 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 three-dimensional space it's complicated by some two-dimensional 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
near-zero 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
but no at 11 had we use is up to you the reader discretion get a cough which travels the wrong several one-dimensional and you get the kind of losing jinxing still be degenerative to cover reunion of city wants I have to get
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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
and modeled by shifts so get detailed to itself which should punctured doors this the 1st and
Subtraktion
Komplexe Darstellung
Fächer <Mathematik>
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Gruppe <Mathematik>
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Geradenbündel
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Teilmenge
Funktion <Mathematik>
Mathematikerin
Vektorraumbündel
Phasenumwandlung
Körper <Physik>
Projektive Ebene
Garbentheorie
Restklasse
Sterbeziffer
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Trajektorie <Mathematik>
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Harmonischer Oszillator
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Differentialgleichungssystem
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Einfach zusammenhängender Raum
Trennungsaxiom
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Objekt <Kategorie>
Modallogik
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Flächeninhalt
Higgs-Mechanismus
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Rangstatistik
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Einfach zusammenhängender Raum
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Punkt
Quader
Ortsoperator
Familie <Mathematik>
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Singularität <Mathematik>
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Vektorraumbündel
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Wurzel <Mathematik>
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Kategorie <Mathematik>
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Singularität <Mathematik>
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Restklasse
Analysis
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Eins
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Varietät <Mathematik>
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Varietät <Mathematik>
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Kategorie <Mathematik>
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Raum-Zeit
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Prozess <Physik>
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Metadaten

Formale Metadaten

Titel Wall-crossing and geometry at infinity of Betti moduli spaces
Serientitel 3eme seminaire Itzykson Wall-crossing in Hitchin integrable systems
Anzahl der Teile 3
Autor Kontsevich, Maxim
Lizenz CC-Namensnennung 3.0 Unported:
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DOI 10.5446/16453
Herausgeber Institut des Hautes Études Scientifiques (IHÉS)
Erscheinungsjahr 2013
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik
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 wall-crossing constraint at hypersurfaces of discontinuity. For a generic spectral curve the wall-crossing 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.

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