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2/3 Mathematical Physics of Hurwitz numbers

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so we have a right to think through much yesterday I have spoken to the courage and the very old and was beautiful political incursions subjects as I told you will have many striking similarities there is Nice space of solutions that will be nice group of services and income balls and so on and now similarities and also striking the people working in the area who presented the results in such a way that from outside would be but not be able to play so I will present my own version of the politically caution is actually equivalent to the standard 1 and the well I don't think this is my my version is better anyway fortunate to have a chance to become the case for instance yesterday demand but the caution fulfilled its numbers and the and was given after she spoke you're able to reconstruct some not cut some of his numbers from from the recursion so these kind of recursion appeared to be Maddox models and 1 of the 1st version of this recursion appeared to the papal Marilyn Monroe and an example of that papal to mothers models of another front and chair of its it happens you goal eruptions that disappeared and no it's often referred to in the and then we will be granted to In the caution saw b trying to draw during the political recursion just like these few minds so I don't think that I want to tell you that this nite I try to modify my call and it was completely after all it was completely broken so that I will be the only half of my computer experiments at achieve the last bomb doesn't walk at the moment but the we just did initial partition British works pretty well so what's into political protection so we we have made progress the data as compatible data related to problems connected to a single generating serious called the potential partition functions for the coefficients the amount of coefficients is the same as the amount of her all possible partitions so all this data collected from human race shares they have to several examples like or is serious written considers potential oil and also but the audience and forms for and they will many examples from and but the political discussion is a kind of bridge produces a coefficient of this 1 by 1 using some of their television viewing is as important this procedure but the contract and the caution after to goes not so far this year the function of the One Stop formal parameter religious schools which is responsible for the generals as for the party just who genius to undergo of dignity and so I do spoke Computing 1 by 1 in by of induction J and M 1 would use of force ,comma discussed the general accused of some of the 1st example filled with what to do and people belong and explain later the source of this spring this year you to the gym and the former huge yeah yeah there's sold subscription what do have to computer is not as a function of what is differential the addition of partial so is considered this differential the majors this combination of partial damages you just don't get materials used the financial officer went to jail for justice news as a new independent variable as a whole symbol In but emphasized that had treated just F-16 I will do all that the different ways just excited CSI office that apply for details such functions you John life do which told of
the function of the small bridges and has a son Paul for a partial derivatives the Times so this amounts to an amount the formal linear combination of Excite handling of excised the model but also because this amount as the amount of the river spoke this course unity also the data which is you you so I consider you really residue new CSI you I call hear them buyers of the scheme because I don't want you to look at this later there expressed interest some of the policy and also by the projection of 4 this could be done for any function concussion that In implied here but not what what actually is used for the discussion of the following day to said that the the little space at the summit it is a clear structure as of show us how it works we have this discussion on the future also that data so that when very very isn't this what they did not waiting to mold is just the combination of the 2 stocks I offer the basis of the new space and this is the linear combination of his these coefficients depending on the so you can see that genetic point of the space to be so for me it will be a point of view but these coefficients raised depend on the way but anyway could considers the coefficients of the functions of the let him in when 2 :colon the Justice yesterday and I think let my interests like getting all these potential the only hope of for some of the key now just use it to change his anyone you originally IT and also need to understand that a magical shifts of oranges just need is particle .period of despair some fixed the act of the things that I have supported building should be inevitable part of the initial date of Russian and I know from where the conscience of the people here on black this apparent function the just 1 and lost 1 thank you the so how supported the Ed Sullivan made the call at this point of this coefficient depends a conceives of customer differentiate respect perimeter and then multiplied by CSI multiplicative structure in each of these here have .period means that multiplication Kansas brother age hearing but multiple abuse this will move brigades straight section and also some tensions and emotional and conservative and dimension of the problem arose immediately in the example of how it works so
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knows for the actual competition you've lost restraints so this is a matter of constraints because of the strong constraints fall on the left side to him that the facial appearance which involves partial derivatives and also sometimes 2nd partial nudity and also I don't the factorial future the officials said almost all of the year except for for cases and equal to 1 1 and while the out of some connection yesterday this circumstance for the explanation of this generating function here are for the functions of the year to appear here 2nd apart from the other brother of bottled and also the another extension of period the unit's expansion also implies that they should here this fall upon the age anyway and this is the well-known Minnesota Orchestra and or written consent potential no the following treated all these aggressions together in a single mom falling inquiry you a new model X news for what will ax and some of all these equations all question with this fact experts at a flower and plus 1 to play by less than that of the circulation the happened that is using this to right the question is Nice company so for instance was terrible safely summer the storm if some of this stuff future Europe the expression which is exactly function researchers this 1 so this summer will appeal if some after a shift of imports from Japan the same sort of summing up drawing this coefficient adopted what I do buy you here directions you yeah the
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thinking so because donations holes for all June and except for some initials various which for jiggle to 1 and all but 1 and you hope to hear about all the things which are initial jostle Holocaust coffins will be given explicitly in a different way explained later so so what do I play claim that for all particle attended the general from France's of just followed by a formal manipulation recalled to present them with different for years this matter equation for this because of 1st questions just relation of the political percussion and these are just the same relations that
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1 which sparked fears that is formed in the United States because it is an hour and a hearing is the function of these initial function which is of course the consumers it was not the sort of all these devices somehow the see In interest of justice the inventor of the device
the blast was not medical device here have more points good coming from the the and you have just points to have had lost points here .period here if you would like it was excellent and would going we could you here's a point in price from extra costs In front of the money cyclists at what some extra classes dependable numbers are your old article to heroes of the year is also good thing that the formation of written in these parameters so you're right for the initial but I'm the really it is for automatic article 2 0 ahead the concessions but about artists change agreed to resolve the question of fuel the solution of this linear regression schools coefficient is just exponential disappearing for articles you have to be contention that to fight this way so I hear here it's not the creation of jobs of not knowing what to expect but don't the function itself is usually the Jones from behind this way in this case and the creation of the pair of on the board during the year of the To me in the space of parameters know to change potential so it can no longer be occur in the space of our parameters in the store hold potential the going to
dysfunctional also and in the political percussion the same source it the slightly strange were using so-called "quotation mark lost 4 the majority of the formative years already and the local gene and also I use same drama say what this club clusters for years From my point of view a lot last transformers just leave it is more views of the space of around In the wearable In other words about these according to a more fuel efficient models you Papa and here they just take the same explanation of its support for but the scale the 2 of them both play and divided by 21 1 pictorial they're just linear spaces and being isomorphism of the spaces so if you want serious candidate presented to the left side of the entrance a dozen :colon that their coefficients the 2nd form by the way could be applied both boys affirmed that it is because of the
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precipitously the fall the advises by users with simple if you use the right side of lost for started here reviewed by the exponent of thought small are on the same as part of my family so update Of this serious issues that could it's possible there where have the numbers you're the space which did all right and although I can say this is just the Houston the old enough conservative from the scale of the coefficient the case .period Inc basic veterans X coordinates in order to update my I want to buy multiplied by a suitable model year was inside the Federation of the Blind has operated the lives of so obvious but modernized some of the other branches in Rector from the reference site to just looks realize reference lop off form but in the lessons that you should you do Strange talked of put the fusion and you do I will speak about what they mean by ability and with it if you wish story playing the usual good photographs riches part the
borrower's you hear in the this could spawn tho before minus 1 or 2 line the poll this includes 4 of the last 1 With reference to which responds except I'm here so that these are units the In the Lord have balls so please these years spun off Of the closest homages to pursue this does the same as before this as a space of their functions it's but the song it was just coordinates deployment of spares about now it's not coordinated just made fun of the character which is slated up space in the space of promoters years and also the precautions taken were required .period the trust of the view that the Utah and it is equal to according to my attention something like CSI why which is to explore it's also some information of than of the functions extended its incantations initiate forks just same With the relations with relations they work some these implants percussion a game users usually if you take a few days ago this Dr. Johnson jeered agency then you obtain this because a procedure to recover the
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certain spectral cure for the structural from this incursion is twofold longer Lambert cure for use a slightly my station is so different from those used to total of viewer was floated shoes of variables so I used that this is a landmark draw I use Gordon assistance that the critical point of the progression to the next slide is the origin so if you expand the it's what the synthetic squirt was cooler full climbers when you toss the plus 1 force 4 1 said something like this and inclusion the exchange's privileges of protection the the program takes double Digital coverage so there is the a Jewish new chose to points out that many homes in this notice how some bite my this is slightly misleading attention because has nothing to do with the complex configurations however is used to provide the papers devoted to this guy percussion let me introduce an old coordinates his new by these equations for this notation of Asmara physical to minus as for this is Arturo and this is
how the functions while other is coordinate becomes just a squirrel book if you look carefully at a cost of 4 Nova ignorant and then have that it depends only on the all components of all of this function life so you can freely modifies the competition them not participating consider corruption the there was a sense focus there is a huge variety of persimmon adjust the change the spectacle for His produces does the same percussion few modified it the composition of the gusher vision Villamizar said so I did the slumber ,comma just as a job a for the origins if you write this way is a terrible
isn't like stands as a global coordinator a fine coordinate on this land but the question you're still a drop of the covers origin so you just hours sitting in computing coefficients unit only 1 part of the the computer also do would for this or blocked the I the heading mysterious the relative their share of the bayou In my from auditions by just lost here to functions for the 1st quarter this by the coefficients the 2nd 1 is viewed by the duty which affords or partial bottles chords idle for 1 the couched in terms of the special character of the problem the next but just to make the case for the focus 1 of the stranger the kind of identity and I use the reference being if you think that this is a family that at this remote corner of the career of this 1 I observed slew of strange but part of the guys from Mathematical Institute Institute in soil this is exactly that this language is foremost from this paper this paper is I think the chorus numbers this is the political discussions you have to have a disco officials which appear here it slightly different from the other related to the subject of our talks deals is as simple as expansion of government functions of state and Victoria there is no standard formula something like it was a part right and then there are connection to and simplistic expansion which you here forget about this is your moment but this is In I mean if not not exactly political to the theory goes furious appears to have the asymptotic credits in terms of the synthetic
functions and city informally people a borrower and the lender society observed for which is close to what was used in the book Duma wanted all of the above on the stock you have your own you as
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numbers I that this year so that I pulled this coefficient enumerators and also in the rest of the In has Coulter Missouri what they labeled the Library of thickens and committed differences and they gave me this reference to his religion because of the the to hold on to his death from the but I don't know of course so I think that the the issue is my example and now ready to if you the more general forwards accounts the Commerce moralists all the cases you have to buy their own we still have time probably will start in the definition of the problem you know
I give this because it's going to affiliated looks like so I just think that if you just 1 ways forget the youth of this followed the repeated many many times have you principle of the whole of this almost 2 years before the according to according the the general principle of the new ideas come along because people believe stopped the belief this book because comes a new generation of additional full discretion when it works for them the people of the U.S. this year by the way it does also before the before I go further than the they're play a little bit of this especially closely and fall that is the strength of the nation good in all of this the utility of the call for you but this is Bryant formerly the falling for it is the hope of your but you in office that he will the mark this financial mutual combines drawings of different nature so this is 1 of this is a point of space so I Nevada to do you the more you're going to compute the dance of this expansion about different wages as they belong to different spices I don't like to pull them together about the furious you've got balls include the good consideration is what good does correspond to the presentation of W 0 for where is it so so if you will compared with the bulk of initiative and that this is his 4th of the Colonel what do you want to log into the continue consideration was the the right thing to make it was metaphor so might the formal as it appears in the Bible all the related to you should go .period someone alive Is it it's painful to watch some extra jobs so you can combine these the transformative who did all this time former leaders "quotation mark defined the former is hero don't and that this job include will be included but I still prefer not to do this for me Holly you this year told steals your there not such jumps well I think is about these someone 1 of 8 x I did race but the letter the existing of case it is the concierge and led the drive to compute built lofty what is built of so far but I missed a drop of this is a belt of the alleged infiltration can build of 2 some modification of the 0 . what do you Air bridges will last long the Victorian with the power of the Times India the wonderful or it was the duty of you if you your CSI stop for a while is a global cell phone and the 0 2 feature so if you have a therefore it will be by definition this is 6 I just come so of the come then you can rent the England this 1 . 4 4 this kind of thing because it's should been like this you works for the potential what I do you want to call it the serious side to keep the 4 20 I of Europe this so now we played a little bit these examples I think that your idea the the initial so now I you down the condition of the political precautions foreign start to 1st of all started some it is a fine dimensional community will also review and also acute business product which is rare for a move multiplication which is due by the functions so is 1 of the very little is known "quotation mark at 4 but I thought at the time for dimension of this spring In all my previous examples age was just the one-dimensional and the loyal considerable difficulties the typical example support signed the premier cells of which has been submitted for offered them so when of which I it wants to use them some multiplication like the fight square musical for the this is for the rest automatically but it's not the 1st of all the use of your place you want to the new awareness is proportional to the I don't remember well 1 the I don't remember the conventions prefer some may think variables which purport stop like you and also and also that it reduce the arches of regions this article built up please it is the 3rd part of the impetus for the advice of whatever this from expanding the base and that officials of the French all of this this is 1 of the typical examples in the case which responds to the precaution of friends and around them how it appears to practical is it most papers response to that at least get some or all of the Church of the 4 them all right but that happens in the petitions users who have so far as to the source Of the unity of the physical .period some Lodi so detention of capital of the so it's the convention than all the built-up Isaac equal to 1 is not the physically meaningful a typical example is called knowledge and call you go moldering cost some congressmen defaulted this is the way forward appears in Quantum ,comma 4 minutes ills the fix for once and for all considers that the formation of the initial date of political caution and therefore Minnesota but also known the deformed fetus at once and for all the next step is to consider the algebra the place used my examples age this is this spice of bouncy as you no 1 variable discussions I I hope for the sprays of water the serious work in and you can multiply multiple multiply using multiplication as of this spring the becomes it began the report also directed for this spread due by the following the formal so if you dig 8 x to the borrower can do what the physical demands 1 quarter of the year this case is a the planning of a and B at times the coefficient some extra coefficients regions president and the shriveled his father taught to plus 1 some because of this property it's skews future players can sign the negative side but there a more inward and white you have to learn to work with them the following is a due thank you you get a possible the boss was labeled as eurozone Booker plus 1 plus 1 different buyers I made his substitution my substitutions that affect people for the same and that it is primitive of these the primitive difference defined up to recall some of the constant doubled contributed residue the power to define the the basis of the schismatic working them the next fall and the spring the thereby away by the various this if you this was a vector for without Runkle produced many commendable resistors basis 1 of the possible of awareness of the following so user the uh bestowing Texas the but your case really which is is something new times lyrics to the power game To the minus column for the Fort Portal you would expect new can this stuff disaster this want them to keep 1 so if you smell it that so the burden because the sheer neurons for 1 dimension of the spread and came from 0 2 so if you take the playing with him reactors the same investors to get 1 up to 5 0 and all other cases where you yes there is not presentation of the data using what love for my cousin played G so I what please stay the part of the picture for real so Space View it is the 1st is just a part of this the moment I have not they plan to use for the caution because all of these can so it can be used for any for a year the fees that is the next year or the year sources note it's important the reason festival this is just the opening and the coordinates of space consisting of all around .period opening of 1 or more I know and by definition always organizers of 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space complimented players and all sorts of use the coordinated protests of 0 Algeria's according to spend it was you before for which could consist of money but not all of it so here we use which have chosen the way this CSI all 4 she overheard you always have which makes also there is a basis here which is also due police monitors but the bread and butter furious battles heroes of do not at this point the decision the difference between these 2 measures mutual what additional article last struck vertical so far although the sponsor the belongs to the so this is president of the would you be so you here None of analysts city the subways so claimed here on clay this opera 0 is assuming a single and all 4 rounds for all the barriers which he said the 1 thing that you know you can use different measures but not for a moment the business here and the was due to the spot but respect the differences of race that actually In just the before you T some of also some Utah some practical 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thing that I remember was leaving it to fix you on what you do for the child Church of it 1 support you ate he is a continuous Gold thank you we have to this year 1 this is because of the falling for some the people it's all so Excel for excited the boss functions therefore of multiply you have to to be still more often don't function of fuel increases that a assault would be above the law Of the functions but is getting greater and greater Fourier carefully defined 2 founded and later joined this contribute the Commission due to the human I will speak more about that for the of the initial data but now from this year so long it was just applied directly to the because all of these Church of also contains the definition of you 1 1 and you 0 the venue but applies this discussion you find your June for all Jews there for this you Aegean it is universe the 2nd statement is the falling so the the quality of this year's Eugene In uses itself this is the claim that the display on knew that there are only 5 men job here on final this summer's final action on the fundamental nature John and each individual coefficients Of this expansion is putting on to on for each gene of a heavily funded in real terms so there you for the for the conditional the point of his narratives it could it is a difference these properties depend heavily on defense some space is Lagrangian immoral this condition is the initial conditions also used where much of the proof of this condition of this property if you just but slightly initial convention conditions that this property for for a stranger to the British stopped all books were sure but the to the profit from difficult but this is so far as to use caution could be applied for any for initial conditions because Yanukovich saw it is the 1st of the 2nd landowners doesn't use it hundreds of property of but the Serbs properties in the property this is crucial since all this implies that you're going to recover have gym so as to truly huge uses differential for instance you can use them better form I what is important is also believed that 42 because differential function that can occur the function of of optical some of the examples of a convention before 4 in the form of accomplishment and potential this constant force holders 0 the purpose that we cannot assume that the soul of therefore session this summer break to recover the constant jumping on the cold here capital that this potential as many as it was proper to someone obviously look a the way so-called by so-called dual equation which said if you will defenestrated it all literature observers from Geneva to condition imposed problem because we're deficient ones so here are this is Jr -minus close by G so this call we already defined formed and little to do this year so it's all hold for the villages of well is defined this is going to hold together humanistic wanted the door jeez you in the same way so defiance In defiance of the company might be here to John mind soldiers who assumes this month in this isn't but the initial here reported here for would you mind to box and positive 0 0 0 2 0 0 1 2 0 0 2 and also want you're all of this year the no properties for the potential the Royal discussed :colon on the variation of the Lagrangian plans so long as there is a quantification sympathetic consideration of whether to on you because you tomorrow I'll will discuss his dependence on the choice of what to buy the knowledge in mentioned several on the property that's why we fall on the way but to what extent the Church of the day is important for the 1st probative of the different Utah leaves per shift all durables social aggression that all of the combination you might and to minus the offer was made so a different churches of EPA useful just shift of the timber will absorb the fact you the the death of the weighting functions the shift of the terrible says the Community tool there is a currency store the differences of the 2 at the center of the property this this is what happens if the troops a different ways drew different tiers of on the basis yeah war tho case findings if you look at his formula no it was meaning that the actual children of the business is not involved so this falls so so this constituted is all the there is a formal functions well defined and the the Bernardino of the terms of the baby the what you're the feeling in the event but developed a local officials to new diffuser coordinate so there's that particles just as the presence of the political coordinate system on fears of new defense bases but if you just consider the a formal functions so well defined on the and even is not too that's not the depend on the on the nature of anyways but more more all takes expansion of this function of origin expert so .period what problem I some of the functions that was a defined but In the what this is a space and we don't know how to expand this functions origin but not politics but this is the point of view when he had different shades of Utah but shift of foreign so this condition conditions on the community that if you change the terms their good responding footage of the functions of all defined the shift of the government and the direction of these notes is well-defined operations the function I think it's putting on his direction some of the children who knew that this potential has the burden meaning the it's essentially as determined by a Lagrangian point of essential part of the definition of the potential plan and all although think it's that just the coefficient which are used in them for the political interests of communities at the end of this the meaning of this actually is unique determined by then there the property of its creation the specter and also in the view of this I feel wall 2 hours thinking much b question no I think but to postpone the creation of the next book is the next stop will be mostly devoted to Huish huge amount of new different applications of foreign firms give and very few places not I think people want to believe that political leaders written so you're speaking on the eve of the Office of talking to kids Griffin's cautioned that these are the ones you want for varies from here's here because of what used to be that of the you won't it its close all the political clout of the you think that people be 1 or to times in 2 the fact that the rest of people over years and also professionals from different religions or what he said he had have the effect of general book few
Transfinite Induktion
Quelle <Physik>
Dualitätstheorie
Vektorpotenzial
Mengentheoretische Topologie
Momentenproblem
Statistische Schlussweise
Formale Potenzreihe
Relation <Mathematik>
Gruppenkeim
Zahlenbereich
Rekursivität
Bilinearform
Raum-Zeit
Gerichteter Graph
Wärmeausdehnung
Arithmetische Folge
Ausdruck <Logik>
Kommutativgesetz
Zustandssumme
Modelltheorie
Kontraktion <Mathematik>
Basisvektor
Lineares Funktional
Parametersystem
Materialisation <Physik>
Axonometrie
Ähnlichkeitsgeometrie
Kombinator
Partielle Differentiation
Partitionsfunktion
Gruppenoperation
Dualraum
Assoziativgesetz
Flächeninhalt
Forcing
Rechter Winkel
Koeffizient
Rekursive Funktion
Algebraische Struktur
Lineare Abbildung
Punkt
Mengentheoretische Topologie
Hausdorff-Dimension
Formale Potenzreihe
Relation <Mathematik>
Familie <Mathematik>
Rekursivität
Raum-Zeit
Computeranimation
Eins
Arithmetischer Ausdruck
Algebraische Struktur
Multiplikation
Differential
Kommutativgesetz
Modelltheorie
Gerade
Verschiebungsoperator
Lineares Funktional
Axonometrie
Gebäude <Mathematik>
Kombinator
Partielle Differentiation
Frequenz
Umfang
Linearisierung
Arithmetisches Mittel
Assoziativgesetz
Koeffizient
Residuum
Mereologie
Basisvektor
Garbentheorie
Projektive Ebene
Energieerhaltung
Algebraische Struktur
Lineares Funktional
Vektorpotenzial
Numerische Mathematik
Mengentheoretische Topologie
Relation <Mathematik>
Rekursivität
Element <Mathematik>
Vektorpotenzial
Menge
Computeranimation
Radikal <Mathematik>
Vorlesung/Konferenz
Zusammenhängender Graph
Projektive Ebene
Virasoro-Algebra
Algebraische Struktur
Inklusion <Mathematik>
Einfach zusammenhängender Raum
Lineares Funktional
Nebenbedingung
Vektorpotenzial
Teilbarkeit
Gleichungssystem
Partielle Differentiation
Frequenz
Computeranimation
Richtung
Arithmetischer Ausdruck
Wärmeausdehnung
Einheit <Mathematik>
Zirkulation <Strömungsmechanik>
Sortierte Logik
Primzahlzwillinge
Statistische Analyse
Virasoro-Algebra
Modelltheorie
Wärmeausdehnung
Maßerweiterung
Gleichungssystem
Verschiebungsoperator
Lineares Funktional
Grothendieck-Topologie
Teilbarkeit
Besprechung/Interview
Biprodukt
Computeranimation
Übergang
Gruppe <Mathematik>
Koeffizient
Differentialgleichungssystem
Mereologie
Virasoro-Algebra
Gleichungssystem
Prozess <Physik>
Teilbarkeit
Gruppenoperation
Besprechung/Interview
Bilinearform
Biprodukt
Extrempunkt
Wärmeausdehnung
Einheit <Mathematik>
Einheit <Mathematik>
Gruppe <Mathematik>
Mereologie
Körper <Physik>
Gleichungssystem
Subtraktion
Gewichtete Summe
Bilinearform
Term
Division
Computeranimation
Multiplikation
Arithmetischer Ausdruck
Vier
Vorlesung/Konferenz
Virasoro-Algebra
Tropfen
Gleichungssystem
Normalvektor
Bilinearform
Oval
Teilbarkeit
Einfach zusammenhängender Raum
Strömungsrichtung
Biprodukt
Teilbarkeit
Entscheidungstheorie
Druckverlauf
Minimalgrad
Rechter Winkel
Mereologie
Äquivalenzklasse
Klasse <Mathematik>
Mengentheoretische Topologie
Relativitätstheorie
Relation <Mathematik>
Einfach zusammenhängender Raum
Gleichungssystem
Rekursivität
Bilinearform
Gerichteter Graph
Division
Computeranimation
Koeffizient
Volumen
Virasoro-Algebra
Gleichungssystem
Leistung <Physik>
Bilinearform
Quelle <Physik>
Nebenbedingung
Theorem
Klasse <Mathematik>
Vektorpotenzial
Punkt
Polynom
Wasserdampftafel
Klasse <Mathematik>
Relation <Mathematik>
Unrundheit
Rekursivität
Mathematische Logik
Richtung
Wärmeausdehnung
Volumen
Vorlesung/Konferenz
Virasoro-Algebra
Modelltheorie
Gerade
Gleichungssystem
Bilinearform
Verschiebungsoperator
Lineares Funktional
Äquivalenzklasse
Grothendieck-Topologie
Numerische Mathematik
Relativitätstheorie
Frequenz
Variable
Reihe
Funktion <Mathematik>
Rechter Winkel
Mereologie
Explosion <Stochastik>
Resultante
Impuls
Theorem
Vektorpotenzial
Klasse <Mathematik>
Polynom
Relation <Mathematik>
Bilinearform
Computeranimation
Temperaturstrahlung
Variable
Wärmeausdehnung
Volumen
Substitution
Verschiebungsoperator
Bilinearform
Verschiebungsoperator
Lineares Funktional
Parametersystem
Äquivalenzklasse
Variable
Reihe
Minimalgrad
Funktion <Mathematik>
Rechter Winkel
Sortierte Logik
Koeffizient
Energieerhaltung
Umwandlungsenthalpie
Verschiebungsoperator
Lineares Funktional
Theorem
Klasse <Mathematik>
Polynom
Sterbeziffer
Klasse <Mathematik>
Rekursivität
Term
Variable
Division
Richtung
Reihe
Wärmeausdehnung
Funktion <Mathematik>
Flächentheorie
Koeffizient
Volumen
Garbentheorie
Explosion <Stochastik>
Gleichungssystem
Geometrie
Verschiebungsoperator
Superstringtheorie
Resultante
Klasse <Mathematik>
Vektorpotenzial
Prozess <Physik>
Punkt
Momentenproblem
Bernoullische Zahl
Formale Potenzreihe
Gruppenkeim
Mathematik
Rekursivität
Computeranimation
Arithmetischer Ausdruck
Fahne <Mathematik>
Ausdruck <Logik>
Verschiebungsoperator
Lineares Funktional
Parametersystem
Zentrische Streckung
Numerische Mathematik
Trägheitsmoment
Teilbarkeit
Rechenschieber
Forcing
Funktion <Mathematik>
ARCH-Prozess
Rechter Winkel
Koeffizient
Zahlenbereich
Faserbündel
Koordinaten
Faserbündel
Hausdorff-Dimension
Wasserdampftafel
Klasse <Mathematik>
Gruppenoperation
Zahlenbereich
Bilinearform
Term
Ausdruck <Logik>
Zusammenhängender Graph
Modelltheorie
Zehn
Gleichungssystem
Logarithmus
Einfach zusammenhängender Raum
Schlussregel
Physikalisches System
Vektorpotenzial
Minimalgrad
Mereologie
Differentialgleichungssystem
Basisvektor
Parametersystem
Wärmeausdehnung
Lineares Funktional
Klasse <Mathematik>
Stellenring
Zahlenbereich
Bilinearform
Kombinatorische Analysis
Frequenz
Raum-Zeit
Sortierte Logik
Ausdruck <Logik>
Zahlenbereich
Garbentheorie
Zusammenhängender Graph
Modelltheorie
Differential
Faserbündel
Klasse <Mathematik>
Theorem
Prozess <Physik>
Punkt
Mengentheoretische Topologie
Bernoullische Zahl
Klasse <Mathematik>
Zahlenbereich
Rekursivität
Transformation <Mathematik>
Bilinearform
Nichtlinearer Operator
Raum-Zeit
Gerichteter Graph
Computeranimation
Unterraum
Lineare Regression
Inhalt <Mathematik>
Modelltheorie
Integraloperator
Zentrische Streckung
Lineares Funktional
Parametersystem
Logarithmus
Einfach zusammenhängender Raum
Isomorphismus
Vektorraum
Vektorpotenzial
Funktion <Mathematik>
Koeffizient
Zahlenbereich
Parametersystem
Isomorphismus
Klumpenstichprobe
Differential
Theorem
Mengentheoretische Topologie
Numerische Mathematik
Formale Potenzreihe
Rekursivität
Vektorpotenzial
Isomorphismus
Nichtlinearer Operator
Kombinatorische Gruppentheorie
Differentialoperator
Frequenz
Raum-Zeit
Computeranimation
Unterraum
Negative Zahl
Multiplikation
Algebraische Struktur
Isomorphismus
Integraloperator
Normalspannung
Differential
Theorem
Mengentheoretische Topologie
Zahlenbereich
Rekursivität
Bilinearform
Nichtlinearer Operator
Raum-Zeit
Computeranimation
Unterraum
Wärmeausdehnung
Einheit <Mathematik>
Spieltheorie
Modelltheorie
Integraloperator
Gleichungssystem
Gerade
Inklusion <Mathematik>
Lineares Funktional
Zentrische Streckung
Grothendieck-Topologie
Exponent
Güte der Anpassung
Relativitätstheorie
Vektorpotenzial
E-Funktion
Grundrechenart
Koeffizient
Mereologie
Differentialgleichungssystem
Isomorphismus
Total <Mathematik>
Punkt
Mengentheoretische Topologie
Klasse <Mathematik>
Zahlenbereich
Gleichungssystem
Rekursivität
Computeranimation
Variable
Zahlensystem
Wärmeausdehnung
Arithmetische Folge
Zusammenhängender Graph
Delisches Problem
Integraloperator
Geometrie
Inklusion <Mathematik>
Optimierung
Konfigurationsraum
Auswahlaxiom
Gleichungssystem
Normalvektor
Logarithmus
Geometrische Quantisierung
Zahlzeichen
Gleitendes Mittel
Rechenschieber
Reihe
Kritischer Punkt
Lemma <Logik>
Funktion <Mathematik>
Forcing
Sortierte Logik
Zahlenbereich
Term
Prozess <Physik>
Momentenproblem
Familie <Mathematik>
Zahlenbereich
Rekursivität
Term
Asymptote
Physikalische Theorie
Computeranimation
Ausdruck <Logik>
Überlagerung <Mathematik>
Wärmeausdehnung
Einheit <Mathematik>
Zustandsgröße
Konstante
Nichtunterscheidbarkeit
Zusammenhängender Graph
Integraloperator
Tropfen
Normalvektor
Einfach zusammenhängender Raum
Lineares Funktional
Datumsgrenze
Mathematik
Geometrische Quantisierung
Partielle Differentiation
Hochdruck
Fokalpunkt
Gruppenoperation
Reihe
Quadratische Gleichung
Lemma <Logik>
Funktion <Mathematik>
Rechter Winkel
Koeffizient
Mereologie
Wärmeausdehnung
Koordinaten
Varietät <Mathematik>
Standardabweichung
Reihe
Schiefe
Lineares Funktional
Subtraktion
Vier
Abzählen
Zahlenbereich
Rekursivität
Gruppenoperation
Quelle <Physik>
Stereometrie
TVD-Verfahren
Impuls
Vektorpotenzial
Punkt
Prozess <Physik>
Momentenproblem
Natürliche Zahl
Gleichungssystem
Kartesische Koordinaten
Gesetz <Physik>
Gerichteter Graph
Raum-Zeit
Eins
Richtung
ARCH-Prozess
Wechselsprung
Gruppe <Mathematik>
Stützpunkt <Mathematik>
Vorlesung/Konferenz
Substitution
Tropfen
Auswahlaxiom
Einflussgröße
Feuchteleitung
Verschiebungsoperator
Nichtlinearer Operator
Addition
Lineares Funktional
Parametersystem
Kategorie <Mathematik>
Schiefe Wahrscheinlichkeitsverteilung
Gebäude <Mathematik>
Güte der Anpassung
Gewichtung
Quantifizierung
Endlich erzeugte Gruppe
Biprodukt
Frequenz
Ereignishorizont
Entscheidungstheorie
Konstante
Arithmetisches Mittel
Forcing
Sortierte Logik
Beweistheorie
Konditionszahl
Koeffizient
Dualitätstheorie
Explosion <Stochastik>
Stetig differenzierbare Funktion
Subtraktion
Total <Mathematik>
Hausdorff-Dimension
Wasserdampftafel
Gruppenoperation
Abgeschlossene Menge
Unrundheit
Anfangswertproblem
Transformation <Mathematik>
Bilinearform
Kombinatorische Gruppentheorie
Term
Ausdruck <Logik>
Differential
Algebraische Struktur
Variable
Multiplikation
Spieltheorie
Reelle Zahl
Endogene Variable
Quantisierung <Physik>
Diffusor
Maßerweiterung
Grundraum
Leistung <Physik>
Fundamentalsatz der Algebra
Mathematik
Kombinator
Physikalisches System
Vektorraum
Quadratischer Raum
Quadratzahl
Symplektische Mannigfaltigkeit
Offene Menge
Residuum
Basisvektor
Mereologie
Wärmeausdehnung
Lie-Gruppe

Metadaten

Formale Metadaten

Titel 2/3 Mathematical Physics of Hurwitz numbers
Serientitel Physique mathematique des nombres Hurwitz pour debutants
Anzahl der Teile 6
Autor Kazarian, Maxim
Lizenz CC-Namensnennung 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/16424
Herausgeber Institut des Hautes Études Scientifiques (IHÉS)
Erscheinungsjahr 2014
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik
Abstract Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge number of relations represented in the form of partial differential equations for their generating function. This includes equations of the KP hierarchy, Virasoro-type constraints, Chekhov-Eynard-Orantin-type recursion and others. Only a few of these relations can be derived from elementary combinatorics of permutations. All other relations follow from a deep relationship of Hurwitz numbers with moduli spaces of curves, Gromov-Witten invariants, matrix models, integrable systems and other domains of mathematics which are often referred to as `mathematical physics'. When discussing Hurwitz numbers in the talks, we consider them, thereby, as a sufficiently elementary but highly nontrivial model of all mentioned theories where all computations can be fulfilled completely, and all formulated relations can be checked explicitly in computer experiments.

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