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# Where are we 100 years after Shannon?

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why what and then unwaveringly on and that the basic the the the idea of the of the panel was more or less to discuss about your thought about new mathematical theories but within your feels that you think we should invest on From industry perspective if you have to be forgoing that what I did rapidly for their audience I went I wanted there to things I did this is a look at what we call basically the important mathematical problems uh that were imposed in the last century by Gilberto as you know there was a 20 3 .period problems of Hilbert in the last century and then I looked at what where and which will by the way shape all the mathematical research around the 20th century for people are interested in that as you know many people try to 2 2 at least to some of the ground during the 20th century it turns out that in 1998 less so In couple of years ago there was also the will to define with word 20 Hilbert problems of the 24 centuries so I think it was that the Mathematical Union of mathematicians who asked us males to to to put into place what he thought were basically the most important problems that we should solve within this century so it was "quotation mark I was quite surprised to see that many of the problem in some of these are the problems that are there are in fact problems which are quite useful for our ICT business basically so these are the problems and I went into looking exactly the PDF he

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wrote just take a look at you

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added if you can see and this is also may be an honor it's a change in the mathematical the restructuring of of of the things that doing so the romance hypothesis came as as before the contend the Poincare conjecture is still there has not changed then there's problems of complexity coming in which I think are are very important for us says you know algorithmic people where we're trying to find some solutions with low complexity so those people equal and peace still is is there at least but there there's also so here In integers eurozone putting him only was 1 variable which from my point of view we have still failed in

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urgent need but maybe there we

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were in high bounce for the often curves I encourage you to look at them but so what another thing which

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is quite surprising is that these problems are also quite understandable and you can take a bit of time for research engineers which is not the case of the things that found in the Hilbert problems so for some reason I don't know of the level of mathematics the industry has increased or there's a charity case is something that is readable and recent trends of understanding what they're talking about the solution isn't it is isn't there is another city in question but at least we will understand where the guys are aiming for the infinite list of a number of Republican breathless solicit mechanics uh which also was not a big interest for us distribution board of .period wanted to sphere there are some applications I can spend on time but not here where we can find some application of this conjecture by but the introduction of dynamics in economic theory which is also

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something very important in terms of the disposal is a practical problem for people looking at the Columbia stuff but then and and things as you can see here extend the mathematical model of general equilibrium .period to include price adjustments it's the 1st time I conceded that it was the strong conjectures or some problems are put into place like that where there is a practical meetings where price adjustments are there leader programming problems the issue for us as we all know still for industry in in in trying to solve some optimization and here you can see the the policy will tunnel over the real numbers which decided the feasibility of their system of inequality the X hired and be some quite surprised that that the at least then the closing them up I'll finish all this one-dimensional that dynamics generally hyperbole centralizes of the former of the phone rings the the philosophy is not Hilbert system problems still there nor the tractor netted Stokes equations still there at that still there but at least that the big issue solving polynomial equations eliminated the Jacoby conjecture solving putting on equations begins here and I can use all the guns and Rural Valley complex immigration unknown be found approximately during the averaging pulling you time with the uniform of yet to know that these in recent years there's been a lot of of of work on this and they found some solution on average I think there's a couple of solutions now but not limited to miss the point of view but on a probabilistic point of view for solving these things is inarguable work these last year and 1 which is also a very interesting is the fact that also all artificial intelligence exchange entities that are basically in the kingdom would be called the most important problems of this century with respect to what is the limits of intelligence so how this can be solved but it's interesting to see that there is a will to look at the limits of all the intelligence were putting also devices interact terms of the text so what the game I would have poverty this this 1st presentation here was used to show you that other than the fact that but I would

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say that the community mathematician is working on these problems is also a is a sign that there is also some economic flavor on how we can explain these things in the next young quite surprised that these things and are now at the level of of where we also want them then they they can be used at the store the consultant problems that we have a trainer so this was back to to my questions that last the palace because I'm not here to the presentation is that in your field basically the 3 of you wear when you think of the main mathematical problems or directions we should invest where if you have some idea so I can start would you know you're going in 2 minutes later when I thought we did have some ideas on on when you know that I can I can make to 2 comments on this list with which we just saw so I mean something which from all other problems which are there 1 which is closest to some expertise is certainly the 1 on the Navier-Stokes equation because that's on a partial differential equations I do think that this is a very good problem but I'm not sure whether that's kind of the most relevant problem from the point of view fluid dynamics I think influence dynamics 1 0 1 of the issues is a better understanding of problems and for tolerance for instance it might be actually more important to understand the rout to would singularity formation orders equation rather than ruling out or constructing a solution Navier-Stokes equations so sometimes I think that kind of focusing of field on 1 particular problem is not always the right the right thing to do the 2nd remark was this side of this problem on economics which I like and I think by now and no no nobody in economics would put this up in this general equilibrium theory of Othello and you blew it is I think I mean I had some contacts with people in theoretical economics and bond is I think completely out of fashion and nobody would think of extending that to a time-dependent case people rather think of mechanism designed game theory and these are the subject so I think our input partially some of the subjects very quickly date right amid some of the subjects which male put up there I think you probably already completely dated someone should be careful careful careful so we have some new problems coming in by new helper grew up with there "quotation mark 2020 problems posed to people of this she said living with 7 problems the some 1 million told AFP Coleman's given by claimed that Institute and so I think you have to remind professors you program a contradictory measures so people simply and then you had the hots conjectural so more manageable Internet-ready and the best instrument and the conjecture number fury missing some of them have been known to look at it landowners in the pocket sitting inside those those those those problems that would diminish at that time in 1998 the couple's ones which were out there for them to find the means and I will claim any authority that might actually looking new cases you think in your field basically what are basically think the the new needs in terms of of research in mathematics to solve the new usually I mean that instead of the 2 shoulder maybe 2 items but not exactly know exactly what to with soul very quickly in the paper and there is maybe the 1 under bonds on the 2 states which has to be a generalized obviously for us for the and here in event rest and many fallen Villeneuve and flag manifold so and complex 1 but and this is 1 problem that could be very use for 2 decades the number and communication in many settings and then may be the 1 related to doesn't approximation me but not exactly this problem because In fact this is the sort of African approximation the bears now area when we wanted to address them the problem of my user according specially for example will 1 that 1 thing the 1 that doesn't become almost classical the computer for and which in fact is very amenities performance is very related to that underestimation ,comma multidimensional 11 approximation so there is also the problem of the deference alignment but not the 1 that that has been a popularized by means by history 2 fires earlier but don't get 1 on the realignment of all these variations on it and there was "quotation mark I mean among all these problems is you this is what they see then there are some of the troops and the than in some other mathematical problems that have to be solved true for some of the applications in no hurry to the 1 that we discussed was Mainland this morning for example of this problem of the solutions for year morning entered re-creations not not only solutions but especially Somerset physician principles transfer OK knew there said that the idea of you know what I want to do is basically to come up with an interactive come up from the panel is the same thing as Hilda there than in the 20th century to come up with a couple of applies mathematical problems format for engineering that we could come up with a list I think this could be a good stuff than by the engineering community where they would highlight another 20 problems of mathematical engineering that should be solved in the next year to help engineer because they're the ones which were said well pure mats at what would be applied the problems that the Dorothy's that applied mathematical tools we should switch to solve conjectures 2 2 to move forward in our dissidents here do you want Susan Lee said without the of the European problems in the user information theory it's amazing that the different channels we going understand each other asking open questions to reassert its main intelligence here is the basis of the industries the share of indistinguishable from what used to be the voices to memories to everything and the fact that plan and the fact that some of these problems this so I mean ,comma this is not 30 developed a nasty apartments and speaking the and I think it deserves it amendment use a version of it and go on to the end of a lot of problems which president later of the in the deserved to be in as important if not more into the physics is changing the world is changing so we have the means we have a new set of of questions to cut the soul within which would include questions of the very problems and so they use information that would be good example after the 2nd 1 was high-dimensional geometric so we think it's something to which starts showing up as being contested by 7 series presenting an administration which was consistency as with and so I think we lacked understanding of from the very busy questions about the change the trees the but that some of this will be questions that come from a very practical motivation of model economy ACT and physics from something physics because it something physical the topics of communication and this is so basic goes beyond what we have learned that 1 of the waves and thinking that we just you know these problems but it seems this this is a part of the year and justice and historians no makes as for the world and change at all in the last 20 years or so and so and rise in the that isn't it yeah just long commands a handful of going said about my views on information unit the is of the homes of another another problem coming from prompt hearings for example you know these are non-Chinese quantities from information theory that has a meaning equivalent including the and you know for example that the aim is to go beyond the it seemed like a like bonds and for this we need them it to consider some of the groups and some very specific groups we don't know which ones could be I mean we have some examples but we don't know which properties they have to choose 2 verified due to be some good candidates in order to build them and it's a good deal natural cold you so I didn't want to quantitatively Butterbean but please last network and network mathematics all to phrase it in terms of use of crafts or on we're still trusted network of whatever kind of religious definition but this is this is the In a sense it sensibly entity to know days of social networks of communication networks wireless network while it is also from interactions are in terms of the subjects and how is it that we readings even see the world drafted the letter setting the understanding that the mathematics of graphs and you anything that goes beyond what has been done and there is some structuring their asses itself so showing up in the work of other useful and so it seems to be absolutely and fundamentally and soul I would define this list of very interesting in the button in sort of oblivious all of the fundamentally version of all societies in the world has been changing in a very dramatic way and with mathematician don't want to to moved to address this continuing their think everybody loses their investigations and that but also the community because it means that because these things of of may become mass and but the government of President recommends that forwarded questions to him Morris then contributed a total of future underwater people in world no more difficult to isolate a single question which will be the center of the socialist yet in the 1st set of questions over and over we equity dealer channel and the and the and Andy Interfax child OK and we can put a few others of which for being front for widened from recent some results and and because the decision is made the question so if we can formalize formulated at the Internet's narrative questioned and then we did have the work and I think this is the main problems when we travel list mathematical problems that can solve our engineering is defined what is the mathematical problems in right now but I agree with you that the basic of the networks would be the relay and the need to France then you can have Cal well when when Maxwell was the creation of things what would have said so a piece of a single to formally ban Maxwell's equations think things don't work that way so we are just too many would say things the special events and crime and I think also that he's nonchalant died of equality it is natural that the quotas for more than 3 variables I mean it's something very important because it said it is not easy to understand where they're coming from and there when the number of robberies increase so when you need working the system that down many more many more and yeah so another point the question was another question that of the panel's but are we asking too much to mathematics weight this question and bring the documents but but I haven't I went through the the document of age 20 20 vision which it which is basically the vision of the EU for for for the 2020 and that and you just try and then the 1 term which is progressing in the trenches innovation and and if you look at the progress of the society look at the number of the work progress which is puts in that document is is very few if you look at the number of times innovation is stated in its growth which means that we're looking were pushing much more and more people to have results in a very quick manner in the sense of advancing the pact on economic and energy aspects of studies at a given was done by Citicorp who about the impact of mathematics ,comma the GDP he trains out that certainly if it's true future competitive confirmed afterward that it 15 per cent mathematics have an impact on the French economy of the order of on the GDP on the GDP growth of the order of 15 per cent which is quite beautiful what I saw and 50 per cent in 1 discipline having such an impact is with huge and the question and if you see also in industry G-20 outward-looking not morning to doing the progress of the society but having really innovation behind inning thanks to you think an NAC also but the pressure were having to get more and more results rapidly for mathematician that can be translated into something you think that we are overdoing it the words what we think of a can of what mathematician can bring us or do you feel comfortable with that see you as an academic difficult to believe the situation you changed in the fact that I'm John 1 were connected to industry now than before in your work or not only were losing millions from up here is not the best guys should ask a guy from yesterday said that to answer the front for my own work and that there were 2 months because In you wouldn't know more and more people in the industry that you get some requests now that mathematics should have more and more impact not on doing good the progress of science but having an impact on innovation because from the documents they see this is exactly what requesting 1 more from from from from mathematics community it's an issue for findings from the from institute like teachers the final moments so far from my point of view I have to defend the idea that the screw fruitcake but maintained that a very high level of security To be able to develop a very high level the conclusions from so it's not something completely new to me this is the end of the year after Of the applicant contact without the same view when the splitting of the term differently on a especially young people should be encouraged to take risks and to those things which will be used to 15 20 years after the U.S. and issue put the ball in terms of popularity the metric and and assurances that the political ability to industries school external matters just keep system I to we have just 1 millions more stories it's not exactly but industry that it is the relation between the said Hi theoretical mathematics and applications and some years ago maybe 6 innings will remember very well when I was still there ,comma Times and the was contacted by the I wanted to and you to renew an interim exactly what it was was a European project on the Net you know going with the re-enactment and each so it's something very theoretical and then they ask that they asked her you probably don't want to we're responsible for this minutes of the financing this analogy to the inclusion occasionally the last year in fact to find some publications of so Indonesian surrendering defied the trend has been if I wanted to be part of this but finally said yes but of course Was it wasn't something that I didn't understand very well and certain doing things about at that time there was no I mean I think that the these you these are highly theoretical project had the 2 to demonstrate that there could be some applications choose to before its advisers I think you can also get some very interesting problems he has all from the applications were involved with yes that yes definitely yeah and so I think it would clearly was said before the Easter Rising sold when something is wrong and that people would come and try to 2 expected this 1 way or the other way and it is talking to industry and point-to-point were in London with difficult questions and walking and the talking and that prints accused in your the thing is vanishing because of in 2020 nonsense scoring but they also were you essentially only push people to To meet an act jointly and even if there is no substance to as it so that I can and our as a doesn't go this way Goldstein individual grants to individuals while taking a stand the way using your was going the wrong way and a wrong way and we should say to me all we should state clearly and I'm ready to state anywhere any time but I don't think you Commission is doing the right thing in terms of funding the research that it's not the way it should be done and that no other continents countries do differently we should look at how awareness of works which was properly and sold pretty much what prefers we go by point-to-point interaction with industry asking questions interacting with industry as many of us do and learning about problems thinking and and and slowly developing new ways of thinking that in the end we will give answers to adjust the wasn't going to things which are not content for its engineered by nature and prevents you young people to take risks sold on point-to-point interaction with industry out of the right-wing discouraging things said to me do it's just not what should be done and it's not like that at some of the things work in the U.S. and the work I must say was better and he was that your In terms of the interaction between industry and I think the goal of that is the way it's 20 20 but this is also the name of the we're not unveiling putting the emphasis on what should not be the emphasis so I don't it's it's easy to do 1 of the so-called tool to create this point-to-point induction by direct funding from industry to work at Indian and that's how it should work right on the Internet I think it's much more developed this is vanishing you they used to be that the violence on the the architecture history architecture with that of the year 2000 and then that was the European police said Well why don't we make the project in 2004 was lower than competitors in this thing collapsed sold the I think point-to-point is disappearing from the fault way of asking fundamental questions to the right back Anthony Kiedis appearing at the end this projects not work correctly so young people or rights of disappointed all the glassware so that's as simple as that and so we should say thanks and I had a couple of questions but I think the time is running out and are just as the people around if if there are some questions to ask to the panel no question OK so like me in a while we were trying to do it .period 2 . pdf This information and that's the skin this year that the scheme were doing with all we're trying to identify the prestigious researchers from around the globe that his forces in Europe and in France and tried to create a point-to-point link by inviting people and trying to produce a document of research together only on our on our problems it is a very happy I like to think through the traders went went away and Alcoa also from your 1st point of who will have the opportunity to continue working together newly we identified somebody there and that there will be no welcome to talk to us and give a talk basic candidacy pumpkin plunged his results have been used in producing and help have also that successful next year and workshop uh the bus hitting the outside and thank thank you all for coming and staying until 4 30 and get back to work

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Dualitätstheorie

Diophantische Gleichung

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Polynom

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Hyperbolischer Differentialoperator

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Vorzeichen <Mathematik>

Fahne <Mathematik>

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Güte der Anpassung

Dichte <Stochastik>

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Optimierung

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Entscheidungstheorie

Polynom

Forcing

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Physikalische Theorie

Heegaard-Zerlegung

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Gruppenkeim

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Optimierung

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Relativitätstheorie

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Energiedichte

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Mereologie

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### Metadaten

#### Formale Metadaten

Titel | Where are we 100 years after Shannon? |

Serientitel | 2nd Huawei-IHES Workshop on Mathematical Theories for Information and Communication Technologies |

Teil | 06 |

Anzahl der Teile | 06 |

Autor |
Debbah, Mérouane Ullmo, Emmanuel Belfiore, Jean-Claude Otto, Felix Baccelli, François |

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 | 10.5446/20259 |

Herausgeber | Institut des Hautes Études Scientifiques (IHÉS) |

Erscheinungsjahr | 2016 |

Sprache | Englisch |

#### Inhaltliche Metadaten

Fachgebiet | Mathematik |

Abstract | Panel: Mathematical Theories for Information and Communication Technologies: Where are we 100 years after Shannon? |