Fields Medalist: Andrei Okunkow
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Title 
Fields Medalist: Andrei Okunkow

Title of Series  
Number of Parts 
33

Author 

License 
CC Attribution 3.0 Germany:
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. 
DOI  
Publisher 
Instituto de Ciencias Matemáticas (ICMAT)

Release Date 
2006

Language 
English

Content Metadata
Subject Area  
Abstract 
Lecture of Andrei Okunkow, Fields medallist 2006.

00:00
Mathematics
Fields Medal
Observational study
State of matter
Position operator
00:51
Geometry
Area
Series (mathematics)
Randomization
Length
Direction (geometry)
Counting
Routing
Student's ttest
Sequence
Bilinear form
Theory
Power (physics)
Connected space
Concordance (publishing)
Goodness of fit
Wellformed formula
Condition number
03:04
Point (geometry)
Algebraic curve
MasterGleichung
Building
Musical ensemble
Drop (liquid)
Student's ttest
Parameter (computer programming)
Heat transfer
Mereology
Number
Explosion
Protein folding
4 (number)
Goodness of fit
Manysorted logic
Energy level
Liquid
Condition number
Covering space
Spacetime
Surface
Prisoner's dilemma
Curve
3 (number)
Variable (mathematics)
Local Group
Degree (graph theory)
Order (biology)
Mathematical singularity
Cycle (graph theory)
Pressure
Matching (graph theory)
09:44
Complex (psychology)
Musical ensemble
Variety (linguistics)
Euler angles
Multiplication sign
Real number
Parameter (computer programming)
Drop (liquid)
Food energy
Theory
Number
Mathematics
Goodness of fit
Energy level
Social class
Area
Covering space
Addition
Surface
Forcing (mathematics)
Curve
Algebraic structure
Counting
Independence (probability theory)
Mathematical physics
Price index
Set (mathematics)
Limit (category theory)
Sphere
Hausdorff dimension
Dependent and independent variables
Right angle
Identical particles
Resultant
Local ring
14:38
Randomization
Group action
Correspondence (mathematics)
Perspective (visual)
Explosion
Group representation
Produktraum
Hill differential equation
Descriptive statistics
Social class
Spacetime
Theory of relativity
Product (category theory)
Curve
Basis (linear algebra)
Infinity
Orbit
Relative risk
Lattice (order)
Graph coloring
Order (biology)
Figurate number
Cycle (graph theory)
Arithmetic progression
Embargo
Directed graph
Point (geometry)
Maxima and minima
Characteristic polynomial
Rule of inference
Number
Frequency
4 (number)
Goodness of fit
Term (mathematics)
Symmetric matrix
Units of measurement
Focus (optics)
Surface
Prisoner's dilemma
Neighbourhood (graph theory)
Exponentiation
Physical law
Model theory
Counting
Line (geometry)
Set (mathematics)
Complex number
Local Group
Formal power series
Medical physics
Network topology
Universe (mathematics)
Optics
Table (information)
Resolvent formalism
Musical ensemble
Multiplication sign
Direction (geometry)
Complete metric space
Parameter (computer programming)
Mereology
Mathematics
Manysorted logic
Cuboid
Supremum
Flag
Perimeter
Covering space
Process (computing)
Generating set of a group
Moment (mathematics)
3 (number)
Variable (mathematics)
Bilinear form
Functional (mathematics)
Time domain
Connected space
Degree (graph theory)
Proof theory
Hausdorff dimension
Normal (geometry)
Right angle
Parametrische Erregung
Sinc function
Resultant
Fundamental theorem of algebra
Ocean current
Presentation of a group
Divisor
Heat transfer
Theory
Power (physics)
Natural number
Interface (chemistry)
Ideal (ethics)
Genetic programming
Subtraction
Condition number
Addition
Multiplication
Conservation of energy
Projective plane
Element (mathematics)
Analytic set
Incidence algebra
Voting
Commutator
Logic
Dependent and independent variables
Object (grammar)
Pressure
00:03
auto moon stuff Maine everyone bad I'm very pleased to introduce Andre concourse who is 1 the 4 winners of the Fields Medal for a 2006 cocoa of obtained his doctorate in mathematics from Moscow State in 1995 he has held positions at the Russian Academy of Sciences the Institute
00:31
for Advanced Study in Princeton University of Chicago In Mr. California Berkeley and is currently a professor at Princeton University who has won many awards prior to the Fields Medal most recently the European Mathematical Society Prize in 2004 of cocoa
00:53
is a problem solver of great breadth power and originality as in the case of most great problem solvers the main weapon in his arsenal has a mastery of calm company tolerates but you 1st as a student in Moscow in the late 1990 is a connection was established between comminatory on the 1 hand and particularly around problem of increasing subsidies of increasing step sequences of random mutations and random edits series on the other hand the scope of this connection was an extended greatly In the form of a con carne J. J it was this conjecture the conclave was the 1st to resolve and he did so in spectacular fashion that they needed to resolve the conjecture but get beautiful it's national on Route while company ran the Magic's theory are connected from detail calmness also plays a central role in the course of the work together with Richard on the statistical a mechanical problem of melting QB crystals in and not another area in which it at Concorde has made fundamental contributions that the area is a new editor of algebraic geometry and this is a subject of can't counting under appropriate conditions farming on direction of Whitman's worker can't concept which is where a Kong Copan Can't Hurry found that have obtained the particular extraordinary and beautiful new formula To make the count new situation again from the tourists who has a key role photo get good OK thank you thank Bursik a for the
03:05
introduction and I will always remember the summer of 98 of the 1st met in the office and Koran and new did the preference of your work with with the bike and you have the order among the solve anything that grew out of that Proprinter won't kind of thing of of it written about today and I of course all of our protest from of this Congress have numerous knew the bet a new rebel thinks the thank the organizers for butter particularly like the thing professors Billy Owens but wants were Rozel August technical issue of how could the bulk of set up but I'd like to play the on mission history and what the animation so what the federation illustrated the mentor dramatic that I bet it if I'd take it did liquor turned 1 of us might also that this was not of so if a 3rd Beijing general points of the planned be well for us putin a rut Russia and the rest of the pathogen of 0 maybe parameterized bite drop rest clutching someone public variables and cubic begins of its occur from
04:35
degrees 3 and be discovered by prisoners he answered by chose a general points on the plant there will be 12 rushed out to bid for that the new bills points are so wife was sober got to go back thank God the be a good illustration with introduction of the kind of her accounting problems that will be what the lecture stuck if I think crazy over a degree Kerr degrees 30 in the just Apollo level degrees 3 and bearable flexible I'd still be my other and if I am but there's another pubic passes through what the best throw point the winners reasons so if good will cut down the demands the wall of the source but if if I were part of the condition but did that 80 up the wine like a big I will be the want around her right leg will be perfect ball of the foot the group's report left to the group's report warmweather abroad should serve as did the band of the on the eve of the stripper Susumu off so what's changing shares the kitchen off so if if Javier we get the rate equation if it with that tickle there with the red curve and of which said she intended to get the blue sun out for general public spilled of tea assume we get the most pubic and the and has just what culprits numbers of folk like of surface of a bonus but there will be 12 vessel built was for which we get the hell out of the singularity what we went through branch of Intersect transfers and that the global instead of being generals want her to get to observe a cover and parameterized body by Russell Funchal swagger so does and will be internal problem Dole with 12 complex relative to prod the Ridgewood with as others this explained was illustrations by the 3rd 12 wrestled with the new baby points the place and should also did not as before the few does not work make a knife or problem for all but the subject of the flesh now will be and this is not that this is not a purely theoretical book 1st and it's in back in white and some other things about being buried at some point I will have to have the actual find attributed it to be fresh water from 3 point of it it's a problem which is full of are sold billions of liquidity went up mainly instead of studying and services will build cantankerous international trips space regret where work for the sort of person plan will move we will at a curve space more generally of threedimensional now it the proper lecture is a new image of John corrosive what kind of what what is the kind of pressure that will be it song before that smooth preserve the before and for example for the purposes Of the lecture if enough to prove or in the case by experts of the dessert this is already very interesting and reflects song with the degree of the car and most us Comair such cars set a genetic condition of the 4 big through for rich enough about 4 . Miguel about the 3rd for some when general cycle in fold fee and so of course we would work with like the Met they B a mob of concerns of report on the cover with the mother of the freedoms that we have a store of some there's some demands on God would serve well hot on call parameters the curve of students and the good the bad and would like to oppose cement just enough genetic conditions so that we expect finest makers satisfy the Sobel homemade boat an example of a book of the same spirit that have the most urgent advice if I went to the 3rd again rational curves big budget is of like to be set for life that is what you do you do it would commence yourself arrest occurred from for life it is in space depends on just by writing about Russell wrestler purpose something confirmed by bristled the 5 you'll see the goal the art 23 profits and it's not 23 with the us 3 copies of the calls point and the point is a good match the revived the 4th vendor points that would like to
09:46
the ship with the skirt and on the count of this'll behind of the get a class competition somewhat harder and 12 Butler will discuss before soap a half an hour course this this kind of competition go of there would be a into a but they also interest reinforced by by the relevant such numbers of recently acquired in mathematical physics and it's not because they individual number of for it but was much more important they the structure of the culture of the numbers displayed so what wove cost compared go 100 what is this room is of interest agreement instructed think the where would what what's more interested improper exotic above but some the that of some going structural about the but also Walker Cup and structure appears extremely respondents with the resort of time 2 expand from the start but then Weiss if I some area but the problem the release of around the instructor will will submit all the start of the mothers about I received can be found inside the problem before the birth only mile limit of its peers with talked about what they say about the brand
11:23
image of the structure here is extremely rich and so it's a lot of the princess right so why we're interested in person 3 4 the way the revolt of distinguished for rights of results and 1 of them was the of by the end of the threedimensional the critical critical that it's critical for if you like wakeup call parameters occur fraudulent agreeing to it in bright that big band of expected to mention that this it was a good number of parameters also known as modulate but both on the seals of the it it bears all the data would whether you have a threefold of something the matter less or bigger so what's vessel but their 4th this expect dimensional 1st of doing the but independent of the entered growth was definitive wherein the smaller than and the case was a dimension hot remember when we when which would have the animated work force that's all relative to the June drop but their jails was Ursula going up in the metals doubledigit and independent of the jitters so before it can translate this From what will the Farmwood would approach the mathematics where the definition of what to do with me but for index and that liberal either bitter ways to describe 1st and go what some of of the recover cover and attitude of the Beirut that was there big enough struck remains surface so but I hope that's not confusing for you've ever interchangeable use real and complex picture about old all of the theory that I'm going to talk about the old or conjecture for that matter the old hold 4 public sphere of the complex's Muslim variety but some of users of real picture just 4 was itself so it with a curve in curve baby by privatization but this the David Baker remains the and from the ads for example arrest for me to do but the thrust of privatization of the of Big Three of year amount of text or it may be described by the players and the other with described the and what occurs this is just a few minutes on local charge Miss what is north of it all possible occurred or possible Poland the advantage discovered it up you don't look for some minimal set of occurred just think them all and this With the culture of all levels of energy performed for its alleged in the riverfront in that court charter as about the global optical coproducer and and all of this is why we have fought well to
14:40
recover from Niger Madrid future couldn't think of a better picture of the woods yet explain later 1 of the the represented now the source of the danger their practical would for for example if I'm actually refined if I to drop judges just just for the purposes of preparing this book I have to draw some from 1st and about either by doing privatizations in Maple said what vs. Deridder grazing will be fit in with the war and of us is the figure fell carried over from beer From mathematical its point of view this is the 1st perspective the strength their respect for both would be the of the world was and proper duty from about so this is the 3rd Virginia words of problems with facing new conservators somewhat simplified what built on dramatic simplified competition their wares from the point of view on was really well but finished in the car as defined by prison you should think of this source of bought the villages those of the right to pressure from the perspective and a big perspective their different things what it called the growing theory the recognized read the fundamental contribution of Rome with the subject the other theories much nearer and it's somewhat more bold the things that mixup several special expert are modeled after the Gulf of fear of surfaces and they made the 1st day of the 1st the 1st road did result theory were obtained by Richard Thomas interfaces are written on the direction of so Oracle the bulk of the now 1st metabolites smoothbore became Kansas discover the by either parameterization or reason and and of course if you if you if you're wanting to the quarter the plot will the band where the music written or perimeter there said whether it's also the complementary but this new approach by the new differ very and what kind of degenerate called it a lot orders for a vote for the purposes of universal John to renewed through a lot balls From to map medical physics 1 of the authors of both object but allow the vary and what is called the gesture of will will look very different from the prospective both McGoldrick Imperial bomb their self since we're the general public is what natural appears unit of general object make contributions to members answers just small sovereign there is a result of the addition of the authors of the so what about points whatever points for the workers what what what what kind of generation of what a lot wrong and what they wrote 1st of all there's bigbudget right so book what In in in the space parametritis all possible optical possible resources from Warburg recalled the Joyce based and what are the points and was appointed wanderlust base In addition the night's most person I think X also so good but they don't know what we are melt is bestowed the prefers prefers transfer of Berberis flag is that of the symbols of over performed with registrant 3rd on source I want possibly notable Parizeau now with with with whole Norfolk acts and both or sovereignty have another resident in privatization for burst their the image of a former identified 2 object that differ by the if it so decides so that differ by rapper which is reasonable domain which is what I do which of the 2 threat of medical would represent a possible problems dominant than by the research funded through wanted technical points here want there's for so says reconsider objects assertion this joke everyone in it has support the group and will call for a promoter there so that they don't and Brit and ended in the technical this year there should be no infinitesimal but the you may want to serve God also while I can join connect the pictures that is somewhat more vital to allow disconnected so the for the description of a mobile were back a before the description of do want the modular what kind of logic by along with the with a possibly Oprah where the nub of backs no now From the point of their crazy this is the 1st described by risible object namely some local charge we will look at all all of them but Bennett 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summit somewhat and and somewhat reluctant solve them through tribute ever bonds which of any 1 of them sit Thanks for the 3rd time the hope you can remove them so forgive multiple about everybody below Everybody and everybody should know there will be already automatically do so once we remove or so sub if Faber said for part of in their jailed by blew them there all the affair will represent the yeah others the staircase curve like this just because they're appears for red Aretha occurs forever just over lovable discover what individually and of the above the curve light and the government of food I think from the picture it's clear that if it if it instead of Poland will be available at almost fear where both them because they thought it would be a list of the old every box represent 3 possible export exponent of excellence and both both which are not Idyllwild form of visitors muscle petition blacks so there is expired the particular pressures 1st of all to do an example of an 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of the weather's but there's a philosophical difference but also just like June the number of tourists will come on it is our conjecture that that they remained the main certified you that I like to discuss here because there was a change variables that those of exotic growth returned well but analysts and so it will be more of the trip ruled there was ruled takes have are fearful some airport for the is and what will they do a analysts expect the collect some of the others Robert rip but should go way back but 1 the 1st lights but could but at if booked for the sup up what airport With would take some very restricts the degree of the curve and the fact that the thoughts of collector of this for example me think signed appoints journal of no will words but worth so with food Tranghese 34 Butts was 30 the greatest but the jury and what role the rule of thumb overall generous so some or all possible will take the growing power of Djindjic 1st meeting In some instances of that most of the points out that the argument there isn't full what's called the generated by the honorable just the thought of mother of significance and the exponent by which we do where the 21 stop deplorable but what is important here is that as I say the fearful for the situation 1st triple the transit name they expect the Council of course of degree just like independent of the gym with us why we are able to move the middle of if the number the condition of had their both were dependent on the main point of the the and and also but the technical point above the rim with talk of did resume bolstered no 1 goal of Thomas said the same thing rule against our world possible all Joseph bitterness of a very small part of the defined but what is welldefined Cold the court characteristic which is 1 1 2 her with generally defined by right on the edge of the Cold War the characteristic of welldefined if above the bogus and more generating partial with with Burma with 2 Burwood from Jim or a but the plight of the of prefers and course the before a precipitous on the adventure mentioned this but this award more complicated than presented here and there there's there is just a defined the skull How did the cover of entered the generating function when very very serious shared mission customer was with the what's called fundamental glass and have been developed by by of found vacant but they can draw with situation and bound by Richard Bove above the subject of his rigid the search of the brutal fundamental above the law but there is inherited Stewart crucial dimension but fearful doesn't those work so far so now we are we have the generated West the function again before Brazil the girl with the jitters I defined by all the figures because of her subdued and where the body the 21 the same thing with with all the doors it's instead of through you region food would the cotton finale but not conjecture and Circuit judge proposed the public years ago emotionally native about but nearby is that while this fight there is little not recalled there's there's a veritable censure bearable Muslim name with fury might affect financial oil riches of remember will being very impressed reads Inc a line in the in the Russell under book do best wrestled to buy it is 1 of the most beautiful forms matter because the combined folded brought mathematical powerful such as want to read said some Pope Pius missing but Brewer got some others some of them before the October south of Susan thereby photo auto suburb took knew what will 1st ready what because the the fight there were defined as formal but what was learned with the formal 3rd with no discussion of convergence and and so does the statement What Cheer weird brick the statement about the battle of the same penalty by different points and then do you think a little bit about what does the statement of their responses the speaker analytic of different points would comply embargoes on their motorbike implies that with the sponsors like the rest of us and tho To do so and this is bubble for both of us are for the purpose of the storm but there's a general set of their just along the lines of the but marginal said so the book I'd like to to report on recent progress that we did together was with emotionally a blonde robe under of approved the conjecture for a door fearful and particularly differed so what their supporters authority therefore this is the 1 which evolves rector of the because of his that was not norm for example the old called on just the 3 space River just failed every of the Court of by complex number clearly that what was known as a reporter was killed through any other point of the of course of those form open orbit in order to the productive space would be an an example of an odd like 2 of the worthless larger electorate Kirkwood go over big song not approved with all of the essentials of the group and the dues as does the proof 1 what reached it was fed up considered what's called relative risk a web of royalty theory about before or into the new curves mutated points or other curves and pointless through stores for curve commute but device was equivalent of bust middle serve the growth could be new budget topological research however if you have a surface of supposed fearful of how a fearful of that inside of report with them that's a surface and other careful be incident or not the service forms of topological reasons what we we we ask yourself whether the intersection occurs with a multiplicity fears that the riches of both goes to the situation where the Carpenter said the surface and troops points instance landed and so there's multiple want attached to the true point of what with long and want points of multiple and also way what we may what with both the countries of the points of prescribed the White In terms of the pointer researchers would like the wireless 5th or partial bilocation was the enrichment of the theory of just say while I'd like to be in the middle of the 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visionaries will be discussed tomorrow but anywhere there is aware there's there's a there's a certain sense in which I can take lifted rigidity in a the cost of the repressed it would made out of here's a thought because trucks and despicable the basis of which are With the kind of tripled I was in tow and move on from Sept said but there will be 4 0 buzzword effects of such a just and active analyzed however fizzles separate for what just before a World Vision advantage serve but the colors but what this is really are the artists into a relative for the whole nite illustrated by or in the case were prepared facts which of the more the heart of the trees soap what's the birth of the birth symbol is the shorthand for secular purpose for found and the particular curve count would be beautiful and that take care which is the product of their project of and if it's for a caller told is just the most of us the and I have this at this point is origin 0 0 0 the 3rd with reporters at the door the origin summit of the car that I called others the they cordoned excess and their relatives of the 3 West prescribed tend to completion of resolve which is an example of a curve that lies please some neighborhood of the recording Texas and Stuyvesant painted ordinary points or course professionals want what before they covered rural school with a petition that the petitioner 30 the problem the public sector multiple terrible with because of simple . 34 of the petition there's a petition but 1 and your habits since the bubble point so put forward here and here I was my attempt of the drawings of the multiplicity of above there's of triple computer so what Bush and just put repeat the same thing that both verdicts represent the ball rolled off Paris which are your neighborhood of all the union recording Texas was the subject matter the Lutheran Infiniti them up that was a big reported by the superstitions and without being very 1st composed electorate which of what weird bold vital North so so both ends of a bucket by more Corsica and from of the source of if you don't molds and that they will not be numbers but the Belarus and the waterways 2 0 0 promos ring Rodrigo more drinkable point which is nothing but they just to Thresher function and interfere with what they wanted 3 in Toronto but if it is just that element of the Feldman it is just an element of the Leon to wrote story as ours the 3 parameters Of the period so what we're really is approach but not to the global correspondence between 2 variants of or for global careful with factor approved because individual cases of this prisoner and local actually met Annabella whether this would provide about procedure called but told the trend is not a motive in principle but rather practical so it's so inventor the soul searching for linear differential provisions brushed off into the Madonna so what it is some of the 3rd but this is a greater share of the source of this occurs in the Russian Far another someone listen 1st Lofoten the of the what do they do that old competition it in I thought like you have to compute the individual numbers like 104 of such a of every number but still but you get the whole generating function by Rutherford Vermont now burst of the did this point would be measurable amid the PRESENT approved through F the flesh for will without part or both to both or both but I should say the table for like formal fight hope will will discover From hoping the elect worker for most of I can't west of both Will Vogel will discover things out of their way and what because it's really bandits about mathematical competition and also was bottles cable just also of through through something beyond the form and what before author of the report the goal this the 3rd special this is the 1st of those decays went well when your for right up to be old recorded over the this noble spirit album with the adults and and the Jews there brought the specialized do something called topological something called topological border for what if a bus doesn't but the Goa give the probe of the public Roddick's form the ghosts but with the problem Herbert it was striking inside 1st conducted by got Clem in involved the number of us 3rd well but this since the job figures Furcal and a lot of the people the beautiful coveted because of the way the topological forum with authors of the journalists and injured 50 or so but like to prepare them Ford so far short of the of the conjecture and was just 1 example of the kind of pressure was so what I'm hoping for is the better representation understand the article triple but and some other opted for serial rolled abroad but is is this is Bob a poem Pugh repose risk officer Russell washing and she wanted to do and depends on 3 British for their country classes and symmetrical or any of the other country From Petroleum of from the petitioner current representations it and I'm certain of the others they're very soon will have a better understanding of come the world representation terrific natural basaltic both remote hoping to make progress along the lines of wide other triple to join and pretend 5th there's the goal just just registered something still missing something of something that I got here who is Becker conjecture that the verdict could be Apollo so was the focus of the dozen for it all from the fear of would develop because of the F role trip we can only approve the threshold functioning with both cycle from the moment the body but all along with them but is just what the example or quite things the thing phenomenon that sort of thing for more of going around what of 1st was just as of the with various there's more the court conjecture bears In Search of a weather was so any algebraic fearful which the portal relative but of course to wide open the dismal the birth of the world's 4th