Merken

# Symplectic field theory and its applications

#### Automatisierte Medienanalyse

## Diese automatischen Videoanalysen setzt das TIB|AV-Portal ein:

**Szenenerkennung**—

**Shot Boundary Detection**segmentiert das Video anhand von Bildmerkmalen. Ein daraus erzeugtes visuelles Inhaltsverzeichnis gibt einen schnellen Überblick über den Inhalt des Videos und bietet einen zielgenauen Zugriff.

**Texterkennung**–

**Intelligent Character Recognition**erfasst, indexiert und macht geschriebene Sprache (zum Beispiel Text auf Folien) durchsuchbar.

**Spracherkennung**–

**Speech to Text**notiert die gesprochene Sprache im Video in Form eines Transkripts, das durchsuchbar ist.

**Bilderkennung**–

**Visual Concept Detection**indexiert das Bewegtbild mit fachspezifischen und fächerübergreifenden visuellen Konzepten (zum Beispiel Landschaft, Fassadendetail, technische Zeichnung, Computeranimation oder Vorlesung).

**Verschlagwortung**–

**Named Entity Recognition**beschreibt die einzelnen Videosegmente mit semantisch verknüpften Sachbegriffen. Synonyme oder Unterbegriffe von eingegebenen Suchbegriffen können dadurch automatisch mitgesucht werden, was die Treffermenge erweitert.

Erkannte Entitäten

Sprachtranskript

00:00

Ladies and gentlemen it is my honor and my great pleasure to introduce decor forget their very generous with completion national treasure got his Ph.D. 1972 remain grad nasty bidders will begin under the supervision of Let me retire told of his dissertation woes singularities of mapping Nash a took kit

00:26

Officer position at 6 feet being there Camira public after a difficult period from months summer tonight to 1987 It was allowed 3 rate from the USSR a United States of America in 1987 visited mother was Sciences Research Institute Imus are in 1988 enjoying the mathematics department of Stanford University 1989 where he has been ever seen he now chairs the bottom of the present area researcher gesture Judge Merrick Victor topology the discipline that rule from the contested Deborah months ticket geometry underwent in the last 30 years

01:08

Under the influence of many people particularly Hyampom off but also Because of the Porsche from article physics Simplex job 3 really appeared As a geometry when your kind emit more clearly shows freed icon of aging all 18 on Nevada he assumed Among and then was fully established by Stern William Hamilton with Carnival contributions by dark winter could be in the 2nd part of the 19th century and the local content of the theory was completely uncovered the beauty of the series praised by Fiji's signed his introduction of real mathematics of the 19th century but . its usefulness the emergence of quantum mechanics in 1920 gave a major impetus for food developments of the theory and shoulders relevance for a wide area reputation The shift toward global subjecting geometry do some more time 1st major step was taken by Eugenio cannot be in the 1960 use but it is my Hyampom turned things around somewhat later by exhibiting completely new rigidity properties of automotive them simply manifold conjecture by got me back down over number fixed point of simply Dakota more reserves Also in Royal Dutch guess started to be interested in Greece Problems in 1979 and time Conley lanes and approved solved most conjecture posters further important evidence on due to the directed Andreas floor

02:44

Dutch I guess big started a very fruitful collaboration with for 1995 she presented a new version of the nominee mental series he developed for reasons 19 99 thousand abortion offer and given tough These lectures gosh I guess would pose where Subjected field interpretations stands today Yushan measure

03:08

So how

03:23

Of course it does what Doesn't work on so they team As Some have mentioned that some Prodi which initiated 2 years ago a a defender the poor and it's not You're 5 from being completed a lot of people contributed road just Building based in the occasion of the and this is of course not completely and that Below the people will look forward to working too simplistic conceded that can they created there were very relevant and I will not give their names because I definitely forget someone so what That is It is Some kind Being in press corps subjected to so complaints in Germany is Germany All not degenerate Keating had been biting him for like a kid in German German estimates for so Semitic for him at least 1 bears the signature but the kitchen at form with unique and the the differential form always candidate in this form And the old and the importance of distinctive about form is in the context of complex structure But if you think about it Even the event of space and convicted territory only listening and dimensional space and think about the babies as A complex for for Senate to take it for granted My imaginative part of the standard permission from so Lickteig manifold is a manifold locally modeled on the air After this special form and because that would be the with fear that many of them not just on the genetic of differential before and very important again later is Based the consider making journal Former together this complex that And in this case On the almost home extracted man complex expected on engine by the surface and that this is a compatible Simply for what Relate to chat the same way is the standard make a performance standard on the structure Relate to each other again So It's important and the very crucial for them For Ford called a development that almost extracted you only get all the plan Compatible and this is Jane moral as this is the kind of convexity should adjacent contractable choice but uh On the other hand if you ever GAA Always was Find the combined elements warning that mice slurry or so A big seek manifold unlike the cause of the 1st glance look like peddled 3 Miami The medieval methods for more amenable but unlike you my Make it meant for a huge group of more than a call to let As well This is probably due to the fact that You who visited some semantic for together and then and left 1 over Do and that is pretty medical and and my 1 or both of the stipulation due Such a fugitive So the group In the 3 dimensional case and make a lot of sympathy for just performance and the German that's a German German area preserving sorry but I did mentioned this is radically different from the group of some of them for really brought by an amazing closed this year the Polar due to the continued of the group is Progress of Group of the group of William during of Spanish so as Aziz's again created fundamental TNT Open the and make things so Soviet city algebra 0 4 0 of group consists of simply declared the field and this is just a cruel this is vector field The shares this Rogers said If you contact later for closed form an especially you would like to have that they consider the case and that the dual for what is it that the end then this functionalist called Milt Diana responding that field called mobility and that our and will by the simplex gradient of each and AT going so in the bag book orders of course ever within all oldest analytical form for a From the rebellion backed the field And the burning patient differential for the floor of this form be don't mind Richard equal could go to the gym So for AT compatible woman candidates Victor gradient just uh They are Very important obstacles that elect Sanchez said This may have the on Danish and Matilde site dimension can be Just stop And and in the context that evicted tonight by the property of the new were multiply By J. that injured they become almost over so there a dentist who most important example of Lagrangian manifold money they could then Bonneville and put them bond lamented that the canonical eclectic extract

09:40

As well as differential is famous for being killed and Section or if you like and even on the course For this section particularly if you have a Differential functions in exact form is Drive you that I will be with function is Lagrangian and on the other hand if you consider simply manifold with them what was then a draft in the productivity they can make former former on 1 of my most of them the draft of the Lagrangian and its oldest and the important Victor German then When you have a 10 months before and then Lagrangian manifold looks like good out of the automation and another system of course they look like they're are beautiful from sold This is because of this huge group of more than it's very difficult to find to convey beyond some of course because but the what it's in there and then a class of compatible with that man and that the clause is Molitor glass Although eclectic form is also in it but it 1st forum for loser Beginning 80 if nothing else was long essentially what some minor things and this further The Ronald Reagan Introduced flew more thinker As the tool for finding more settled Recent lexicon that will discuss this today Subs Let me but is about the plume met with almost quantity When the Fed last weekend as easy to talk about The more met with was composed manifold as In this Citizens for in just a differential called in your map But this Unfortunately it if you if you load the dimensional source manifold failed to mention that it doesn't that this is a highly over 3rd and never having Solutions genetic look so it's at That the miracle of the Christian immigration in the Group bookcase encouraging mention solos but as well Band The then and by the way this is almost gone extracting coal on the England Argument is that they the same This he just come form that In this case you have a look at it as a system as the Edmonton at exactly the same degree of freedom of practical Norfolk may have entered bulky and they pulled what occurred this case also J. also Jake along what they want to develop and like should because it doesn't Take much sent Because you on the phone with injured title fight to the this end of terminal edition If a motor where he and the schools and is appropriate under conditions that it exist them and Its principal single the same as the of bar It does Ripken applies then the called CDA and understood that Besides I sound you define model is a civil war water could be fined but finite dimensional manifold Dorotea's or before And algebraic German text but gave visitors They just don't sell But a Aziz's again of course Saying thing but it is extremely serious so his physical coolant of a worldwide and introduction Almost all of the treacherous to both matches that like You get a much more freedom of acting says called end another big German onto debate genital it take that as to how we can achieve that but he added that hope that you can ever a Almost as The freedom of the topology is chairman of the Senate But unfortunately it's not who I think he is Almost but not quite and in some cases indeed you can achieve the society and just forget about the button that gave it to infect too and that the class of fuel in talking about somewhat generally accommodations and more perfectly but I will not rule this But that is a huge step a line of Michael berated him off qualifier and scores devoted a lot of Building appropriate foundation for this But it so Local As they said in the non general cases find But If you want to get global Adelphia need cover the back end He is a stand of 1 of the major result was ruined by nonprofit ruled that there full Uganda Through similar is out at the end of the famous Clothes and the amount of composed provoked vacation or Does the space of But there is a big deal Get on the end of the The new about them and stay difficult to control this so that the role of subjected format Come south of unity in this born so Let me get the call to think about the amount the case so according the lower implementation here you can't talk about the among such as this might want the same as that about 4 For this condition

15:59

It is the same as hyperbolic may take on on the surface This condition Saturday and the stability condition described a just ensure that have cut their voting on this thing and then So there a competitor against Amount of the stained by nodal surfaces and they looked like a union of toe cast in Reported interpretation and the division means thinking loaded it will so the stability condition that they have the justices fight forever to comport grow come back here with the same but the difference this stability conditions be acidified quantum competence of God which I Sometimes called Is the band of flight Modification of remove compact so this is that we make a this phenomenon bobbing 0 4 60 of that doesn't exist in this case and took about 3 months and That separated the role of Objective for Mr. area but the point is that this Compatible deal on that day the famous any meaning means that I'm just integral or simply for And because for of that depend only on the home allergic Alaska over the net of the and so the new Our considered more vicar Molitor class you don't have to be worried about control of the same rule in that his body weight problem is about Lagrangian manifold So what Of the findings that then will morph occurred here with the began April called extract compatible with the woman then Victim but defied Based on what they could do with GE if he wants class Can be viewed the cycle as a kind of similar Indiana each model is based on just more of which is kind of Much more much simpler object and it's the political And the compactness theorem into a more underclass Of this cycle remain unchanged than Mandla J. wild Keeping them by visitors today Therefore because old G-8 and from what not again and we get A physical remorse Is just the latest let me give examples of that Application and this Area is and somewhat in the formative years and is so Let's Baker said called simply cannot problem it's from cold About so let that hinted that based in our 40 Corsican been would the kind mentioned by the 1st known to their 1st In a minute period dimension for consider ball and Copley is a small hole And that idea of this quality Smaller than that of the ball and the but that thank you thank don't 10 those to We to put this by saying they had thought it would be a bowl of this fall And this is a clear that it's not possible for revises forcible so what to bar that in this set as the End Then what At because old called extracts Here the following property the ball is just who for a standard wanted it and PET spent an author near Our her near the value of the remaining part of Factory Lane stand by And because this is power All the context there should be because It is comic book gold to sets can easily poke prescribe almost compote structure you on someplace and just continue to extend elsewhere The condition that it compatible with They did for So what do not make a Lagrangian cylinder in this place just 1 like attendance even seem to get this End of the that Model is based Diaz is 1 my point Is not not so received before the war of course This led leg cylinder with deal by led Lagrangian and you get this kind of our room of conveyance this site has one-dimensional family of this Lagrangian and this cycle black Then the need for Don't expect for a GATT have such removal of and This family together they form some kind of 1st stage this Lagrangian Lagrangian and when the bull by passing through the called it some woman has In the exists and moving war and so that for and some are meant to have a is being run again and its center said it on 1 of the flag and all of this will and then this month we can look at them The area on Monday can begin Computer

21:40

At the intersection of the feasible of more Inside ideas in because These will watching these abound like engine manifold and therefore It Keep it just as they said If that The band simply invented the depends on the regulars A Lagrangian it's difficult awhile or by and was end I can consider this area Looking at the wall itself and the ball The book this And the extraction society ever cooked passing the template of the center and at what was then that the perimeter iniquity over this Should be bigger than about where to get it Growth but then so is this Not only do they regulating mitigated by he the bank of break information contained in girls and saw that the could this summer Let's consider those subjected combative from the start I think people who the let's think about this problem the glasses some differential for on moment and then this can physically motivated not the defines that could relate that just pulling back these the model is based on what they got their wish The 1st might 2nd at center and integrating over or around so Uh soon forget I just said before the vote him but is 0 this is it And then we would like some kind generating function for older could relate to It takes basis and the call Molitor and not just to talk about Who Molitor thinks the bases with J and And then they did it defy any any home Molitor class can be expanded as bases this confusion Monday and called us Geibig and just do not distinguish between deed And this Mojica so this valuable forms All of this For the basis for knowledge and uses the broke even but then shall function for call for all could relate to that exist formally committed it's important that day that he has agreed Both the same grade followed better bridging could keep that then we get this thinkers and each competence even greater than the semantic expressions of and If you look back expansion in the variable get all clearly for the meaning of related as the very simple did just that if you consider more Do The political Molitor class then It is It was explained Don't often legal yesterday would be counting accounted allomorphic fur coat Sound Subject of it in the list Conditional offer that is taking some might want to 3rd don't cycles So also again a bit further including so-called descendant the variable If you don't No we probably will not be able to learn from my talks not just what I just want to say that You go further and the The but Incident In indecent more because Imposing some restriction on jets sophomore guard his and it said Traditionally that The way and But the important thing is that you will you did this to grow them but then began the depend indicating they instead of trying a visual dimension of so June hero But All of this Expansion with called pressure over most of the attention And foreign For the case of seek don't let's take just stand the basis of a pool of this wine and the two-dimensional formal for the radical world class To Just projected flat the stand in the way of the Cold and consider this function would 1st Variable could of the theater wanted to heal and only things a lot this month we the ball and and so on

26:19

They gave and have very simple enumerated meaning that it wasn't yes The dog is number of rational got home given greedy and in the competent in the projected played by Kate Once the general It have standard number references to go through The boys get by 1 lands at the end Biogen was because the relation between a number of points the good he did not define Anthony End What I would do little to discourage some kind of Jimmy data generated by That filthy rich in explains that talk computing fucked This is a Today A name that means they couldn't procedure that From Kuhn said For computing this number bye I will some another 1 This Others also infect clause toward a queen of impotence and thereby prevent them from running biking so that the following consider this is a dimensional space over there should beware of formal 4 years you just can't think about this as a formal hoops in Space of and Accordance I to the and the bed just 28 confusion on expenditure Subs Notice that not constant 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said Mulino dribbled out at and the sale of generating system of integral but I want So when the algebra over whether they should be in What is it added more legit but of course there is Much more There's scant Komodo beat that while and that is much more structure and count Extract a chilled computable invented the problem so there is below the work now Getting the political and variant ideal a future for infants The idea that into The political manifold and do some kind of canonical data construction but engine bundle union potential bond or end And then he'll Stuyvesant take invariant variant of this and in many cases they turned out to be far from the political on the prince's citizen I just mentioned live and work On knowledge In their knowledge but that have a lot of work to do here So there is this And cat and more or them a constructing relative which is calf constructed more growth with not only 10 puncture but also his and They later listing the bulletin glass technology and that is what rule for plan After bar Lecture Cabinet-level plaster mold you speak about this today And so there is A team There is a certain procedural coaching effective surgery It shows that later with serious data collection Spencer and not have to be able to compute plans 1 kind toe to developers isn't the sort of real shed light the series and there is a connection between the deposed from Over and over 50 years as a kind of some work Jim demand Warren here and a The revelations tropical German Businesses some of tropical German is that another very much related to the duration of the assisted euthanasia and notify

00:00

Vervollständigung <Mathematik>

Sterbeziffer

Mathematik

Ortsoperator

Schlussregel

Kombinatorische Gruppentheorie

Frequenz

Computeranimation

Topologie

Singularität <Mathematik>

Flächeninhalt

Minimum

Geometrie

00:47

Impuls

Prozess <Physik>

Punkt

Mathematik

Kategorie <Mathematik>

Theoretische Physik

Reihe

Zahlenbereich

Quantenmechanik

Physikalische Theorie

Computeranimation

Feld <Physik>

Simplexverfahren

Flächeninhalt

Reelle Zahl

Mereologie

Inhalt <Mathematik>

Einflussgröße

Geometrie

03:08

Hausdorff-Dimension

Konvexer Körper

Besprechung/Interview

Gruppenkeim

Element <Mathematik>

Komplex <Algebra>

Raum-Zeit

Computeranimation

Gradient

Äußere Differentialform

Vektorfeld

Feld <Physik>

Struktur <Mathematik>

Topologische Mannigfaltigkeit

Auswahlaxiom

Schätzwert

Fundamentalsatz der Algebra

Grothendieck-Topologie

Kategorie <Mathematik>

Physikalischer Effekt

Eindeutigkeit

Gebäude <Mathematik>

Ereignishorizont

Simplexverfahren

Quadratischer Raum

Universelle Algebra

Polarisation

Flächeninhalt

Symplektische Mannigfaltigkeit

Offene Menge

Mereologie

Ordnung <Mathematik>

Differentialtopologie

Standardabweichung

09:40

Resultante

Abstimmung <Frequenz>

Punkt

Gruppenkeim

Familie <Mathematik>

Kartesische Koordinaten

Baumechanik

Gerichteter Graph

Eins

Fahne <Mathematik>

Gruppe <Mathematik>

Theorem

Radikal <Mathematik>

TOE

Vorlesung/Konferenz

Gerade

Parametersystem

Lineares Funktional

Grothendieck-Topologie

Kategorie <Mathematik>

Gebäude <Mathematik>

Ähnlichkeitsgeometrie

Biprodukt

Frequenz

Arithmetisches Mittel

Universelle Algebra

Menge

Kompakter Raum

Konditionszahl

Garbentheorie

Differentialtopologie

Stetig differenzierbare Funktion

Kreiszylinder

Stabilitätstheorie <Logik>

Subtraktion

Gewicht <Mathematik>

Wasserdampftafel

Hausdorff-Dimension

Klasse <Mathematik>

Division

Topologie

Freiheitsgrad

Flächentheorie

Quantisierung <Physik>

Hyperbolische Gruppe

Modelltheorie

Struktur <Mathematik>

Topologische Mannigfaltigkeit

Leistung <Physik>

Finitismus

Schlussregel

Physikalisches System

Objekt <Kategorie>

Flächeninhalt

Symplektische Mannigfaltigkeit

Mereologie

Dreiecksfreier Graph

21:40

Distributionstheorie

Vektorpotenzial

Spiegelung <Mathematik>

Momentenproblem

Extrempunkt

Gleichungssystem

Zählen

Gesetz <Physik>

Raum-Zeit

Gradient

Richtung

Vektorfeld

Poisson-Klammer

Vorzeichen <Mathematik>

Gruppe <Mathematik>

Translation <Mathematik>

Radikal <Mathematik>

TOE

Bestimmtheitsmaß

Kontraktion <Mathematik>

Analytische Fortsetzung

Phasenumwandlung

Gerade

Krümmung

Kategorie <Mathematik>

Gebäude <Mathematik>

Güte der Anpassung

Randwert

Universelle Algebra

Menge

Rechter Winkel

Konditionszahl

Dimension 3

Ordnung <Mathematik>

Differentialtopologie

Faserbündel

Kreiszylinder

Stabilitätstheorie <Logik>

Folge <Mathematik>

Subtraktion

Betragsfläche

Wasserdampftafel

Klasse <Mathematik>

Diskrete Gruppe

Mathematische Logik

Variable

Algebraische Struktur

Rangstatistik

Reelle Zahl

Spieltheorie

Fächer <Mathematik>

Endogene Variable

Abschattung

Hyperbolische Gruppe

Topologische Mannigfaltigkeit

Berechenbare Funktion

Stochastische Abhängigkeit

Schlussregel

Kombinator

Gibbs-Verteilung

Umfang

Chirurgie <Mathematik>

Symplektische Mannigfaltigkeit

Wärmeausdehnung

Dimension 4

Resultante

TVD-Verfahren

Abstimmung <Frequenz>

Dissipation

Punkt

Hochdruck

Formale Potenzreihe

Kartesische Koordinaten

Element <Mathematik>

Feld <Physik>

Regulärer Graph

Nichtunterscheidbarkeit

Minimum

Stützpunkt <Mathematik>

Figurierte Zahl

Einflussgröße

Nichtlinearer Operator

Lineares Funktional

Parametersystem

Theoretische Physik

Reihe

Ähnlichkeitsgeometrie

Ideal <Mathematik>

Endlich erzeugte Gruppe

Frequenz

Teilmenge

Arithmetisches Mittel

Druckverlauf

Ganze Zahl

Evolute

Garbentheorie

Standardabweichung

Aggregatzustand

Invarianz

Hausdorff-Dimension

Gruppenoperation

Zahlenbereich

Term

Multiplikation

Kugel

Quantisierung <Physik>

Modelltheorie

Struktur <Mathematik>

Widerspruchsfreiheit

Einfach zusammenhängender Raum

Beobachtungsstudie

Mathematik

Relativitätstheorie

Orbit <Mathematik>

Dimensionsanalyse

Komplexe Mannigfaltigkeit

Physikalisches System

Integral

Objekt <Kategorie>

Flächeninhalt

Differenzkern

Mereologie

Dreiecksfreier Graph

Basisvektor

Differentialgleichungssystem

### Metadaten

#### Formale Metadaten

Titel | Symplectic field theory and its applications |

Serientitel | International Congress of Mathematicians, Madrid 2006 |

Anzahl der Teile | 33 |

Autor | Eliashberg, Yakov |

Lizenz |
CC-Namensnennung 3.0 Deutschland: 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 | 10.5446/15951 |

Herausgeber | Instituto de Ciencias Matemáticas (ICMAT) |

Erscheinungsjahr | 2006 |

Sprache | Englisch |

#### Inhaltliche Metadaten

Fachgebiet | Mathematik |

Abstract | Symplectic field theory (SFT) attempts to approach the theory of holomorphic curves in symplectic manifolds (also called Gromov-Witten theory) in the spirit of a topological field theory. This naturally leads to new algebraic structures which seems to have interesting applications and connections not only in symplectic geometry but also in other areas of mathematics, e.g. topology and integrable PDE. In this talk we sketch out the formal algebraic structure of SFT and discuss some current work towards its applications. |

Schlagwörter |
symplectic and contact manifolds J -holomorphic curves GromovWitten invariants symplectic field theory |