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Quantum KacMoody algebras and categorifications
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Title  Quantum KacMoody algebras and categorifications 
Title of Series  Aprèsmidi en l'honneur de Victor KAC 
Number of Parts  6 
Author 
Hernandez, David

License 
CC Attribution 3.0 Unported: 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  10.5446/16433 
Publisher  Institut des Hautes Études Scientifiques (IHÉS) 
Release Date  2013 
Language  English 
Content Metadata
Subject Area  Mathematics 
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00:02
mn you know reasons did you know the current I I'm in and I'm only at the time to image condition the brew that gives the stock was the confluence of the look of the clock at the close of voting good it's OK OK so the subject of stock would be so 1 of the many directions the final continue developed in the fears of Catholic Bishop breasts which we be regions not proceeded to call them because was until some examples of critical institutions so 1st I would like to remind some desiccated objects so that we know we have already discussed today I 1st fighters would get advance so that the start with stable sympathetic emotional complexity of West switching of G which is a symbol of unity Morton and equal so for example that use survived bouts of the talks said to exceed those then we have to look at Jim house which is an infrared emotionally measure Brussels which can be defined by extending and expanding this and to use the carrying of 209 in form and liability and then we have some kind extension nonconventional on extension of energy that we really do not and she had in the stock and services this is the fungus magician blast went off with no deviations that we would use news In this OK so of course it is a Newfoundland and emotionally as blast and it's a suitcase as we so susceptible the very bottom infinite emotion and measure blood and 1 of the reason is for
02:14
doing the weekend CEO hammer which said that the such positive another presentation so it can be defined as the sentences of practitioner from opening about but it does or the presentation which is an area to the south presentation of defending which manages object we a couple matrix with which is computed on sense of Division of which is replaced by a unified country metrics for example have been discussed with the pressure stocks this was to make this friend and emotional measure was important because there are now seen as much of an infinite dimensional and that'll go on June and they have impacted enough same structure and we have and reserves such as which face the "quotation mark wants Pyongyang to completion and so so this is known from most of you were against it so for example for tool we have is catalyst which is just discovered metrics to which is just replaced by a new matrix where we had the equivalent underlined which is this matrix and the Frankart metrics which is used to construct the tankers would issue because was teaching tool OK so this a measured by the Nielsen applications Mathematica and mathematical physics as well we have seen on which the today so I will not give complete distortion of
03:56
them because in fact they would like today to focus on the formation of offenders leadership and can close
04:09
it does mean discovered in the 18 by making Fenton jingles that's uh so this not millions of years requests can be found the charred formations which could condemn so sometimes could also contemplates would assure us multiphase so this after a 1 corpses publisher and switch on the formation of the universe Edinburgh pinkish upon your object of circuits would usually so it is usually not you show Virginia we depends of course on she wishes because would achieve up by the bond Q which is a complex number which is which candidate he has a population parameters which is not the whole complex number and this was a classical situation is when H is equal to to the whole show is equal to 1 and it scares me because you object which is an investment group engaged pop off 2 so just take the garbage cans was this still could be assumes that killed this context and that is not instead so we have this this much fun in the office of How Pleasure because and there is no more
05:38
than member from among case and I will give to data some examples of the kinds of this case Wednesday because we did price of afraid bank Khadija discussed as the beginning of the talk so in this case when get home ,comma financial work so for example you tool finally sold 1 definition it is just to give the presentation of the department by genitals and relations so it can be defined of the family of 6 genitals and 2 of them against in the response to the capital to the July and thereafter relations which after an hour of contaminants observe relations we should play in the definition of consolidation but was off to the formation of violence and relations so for example this are examples of contemplate relations this continent finally apartheid to and this is an example of quantum separation in contempt as we did you part of type when any language 2 is equal to 1 really go over the same period a University of Georgia on My associated with it but through what they would like to emphasize here is that this this and this and he was the other particular property which is an analog to the property of the final budget motives which as block that is that is
07:18
contaminated from this that I mentioned has been intervening beginning of the talk so which is it for doing so
07:27
it's a Sulaiman confirmed and back with wages was a student of history so that is in fact a and there's not presentation of the quantum of hunters with Japan can also be defined as a simple extension of the continent which is completely and added to the political picture and so the way to to explain this is forecasting is was the following a picture of course committed today ,comma so we have a Fuji is a finite emotional Najibullah said to find them but then we have to answer by a physician and in some critics installation of superG the offenders with measure because most of them markets would issue bonds was the other corresponding consumed what which is the formation of the enveloping opinion Jamal unwanted children saying say that in fact is this the financial West can also be defined by accusations of support quantum will Futurity in fact we have to process is some sense that improve commute which proceeds and Inc precise stems in this surge of us presentations which act as a market so so that it is 1 of Subaru residents which makes this which make it possible to study properties of presentation of this as abroad so that they would like to discuss today so
09:10
quantum of tankers would should the many applications so I would just missed the fields and and then after which choose and 1 example that would like to today so fast journalist who To provide solution of the continent Baxter equation which is the closest relations which is known by many of Quran so for example the ages and it gives a solution explicit solution in the case of a city to which is called a debate on probation Stewart of quantum of advantage of associated to work with the solution of the company in Western aggression so this case created too With there's like the season their asking the text with and it's so that it's possible to use presentations Rifkind ,comma tankers with measure was to construct solution of contemplation equations so I just give some some examples of the rich applications also application to a desiccant suing bassist crystal business relation to 2 German premium than consumer's screen alliances also went when there's a connection with the links with this description and in ecosystems is that it's possible to provide solution of this stance by using of conditions for contempt as we get a bus and just like an example of such a system in which His era what people called obtained relations which relations which depends so there is a lot of independence we depend on agency which are some of survivors and this user relations which is administered in a batch of people and winger Chris 200 restaurants and still presentation Suria from them because we judge was give solutions such as system it's about infected is associated to take aim at within and it's it is an example of some of which motion on class of situations which are good too that's what so we could discuss this much longer but they have just 24 minutes for relief for cues from the and those a example of application to protest good mystery that getting litigation so this is what they would like to to explain also by they said so presentations 3 of this measure boys period which ends factory folks use on a particular category of documentation that so of failing mention presentations this as it was so it was a simple objects this is getting we are actively finds his press station which is you could confirmed shoddy Preston but in Geneva and the structure of the of simple presentation is unknown it's been infected student premature representation to for example is a dimension is that slammed into hands of cannot Kasuri character from 1 of genocide of the simpler presentation but how about the half simultaneity Ireland understanding of this category of circuit degree of some subcategory this category of so this is but received
12:55
so too do it we will consider a "quotation mark comes a category permitted we mind what's what's means so I mentioned that this year pure you finding that the Netanya Jalabert the Hopfer about so there is not much of an offensive the categories is the 10th Circuit Italy Sweden and that it's was to make not only the Exxon evaluation but also turns up products of fish it's something that we get because we have multiple challenges the manager thanks as a consequence we can define the Getty a supported creak so let's what is this so fast as gold is just the people with the basis even basic item intensities of simple objective category we have the obvious among them cases with a 3 which is the good and the good and then we can define the ring structure on the book by using the kinds products which we take the view by placebo objective to confidence because of the prime and when we look at complicity of under the simple objective is to support that could defines having structure so that is just a technical point we have to be careful because they're getting away that's important so we have to use more interested in the job and went on to say delays caused such a gift so we get a nice ring which saw its associates doesn't not actually basis which is the basis of a simple objects and spent in fact it's normal it's president of Lincoln's thinking that this court and agreeing in fact is committed to and it's likely that in this context because a categories that greeted the news depends of replied that there is a logic to the private consultants you but when we look at the what crank it becomes committed to the peace dividend job enough of the results of the state the proposal so so this is
15:00
what the complex which come from cuts with history no relocation soldier that we really Category 5 markets occurred objective in issuing were just look at the end of next month in a potent symbol of the gene which which is a friend and emotional OK so for example a salute reconsider its called issuing serve and so for example ingenious efforts we have seen from the Canadian national we have that end the survival of the popular mattresses this 1 of the banana and we have much will coordinate his exwife and the answer is the answering it is just a sea of exwife said brilliantly that will get and this trend as values basis and that is the important basis which was defined by mistake which is again because I can't think of a hiss of the ring which is defined by using some geometry condemnation of Austin and uh and so this object as soon as I stood very much to be done with that name bases for example example of this is free of any kind made his name but in this case because it can be written explicitly that engine habit in case was that so we have decided after 18 months which he explains it sets an example and so Solberg it's important question to try to push the of consensus jobs on this this stranger with a his bit many people have tried to understand this and so the pointer would like to give develop that it was very true to have some information by using it as a Category I explained so this is what we mean by getting litigation of and abide by the presentation of the content is with so when visiting the was so for COM so
17:14
that there is a subcategory supplier of state which category Pfizer ring which is this not the phasing it means that it's possible to write an isomorphism between this region as a complexity Feingold quoted the creak of just getting with the prime which preserves natural basis because here we have the basis of simple objects explained and here we have to do with chicken conveyed to accept an earring isomorphism cheese that it was probable that it's bringing some of them which possesses the debate and of course we have we have to use a complex fighting with the Ukraine because this is just as the engine of the of the season decision was just what we stand necessity revealed never to interior spilled ownership became so I Photos sources to the point that we like to mention that sales and to the finite emotional legal but the prime here is related to the intelligible to workers will get you blocked Geagea to this item of the dates and I would be more precise and .period but just to get at is that this is forgotten and so 1 way to say it and that's the end there is a dramatically cut of this ring with a statue be going out but now we can Alaska what why are we doing this it's interesting to produce such categories stations so that is an application of this that I would like to move to
19:01
extend the fact it's related to the junior high motivation of getting notification which so I gave an example of this sort found many which more than has been the duties to use categories to answer some agequake optimistic just and try to exchange information between the 2 and so it it possible in this case to produce something so we can use properties of the categories since the set so that users referring to not publicly which is not true for amateurism but objections that's so if we consider the support that of an object this category OK so we can do this as well and sometimes to a 2003 that then this is a very different areas to make use of the ousted for this kind of just under which years old the the categories at the Citadel consultations during the investigative leads strong as it was with the situation because the nominees were such that the this appears to know what we can do is to call the police the dentist offices will continue in favor of its theme of this implies that In the end countries ourselves and if we make a family of 4 demands that the quality of the for the installation of and so this is the statement which was the subject of ammunition the incident and switches to the study last year in which translated mentioned it to the next and it's certainly good news will hold on to Caribbean it in fact is that good quality there is no it's religion articles published in his just to find a bunch of people and best assignment was reportedly told us to use the thinking was that the restaurant and as usual so I think it's another indication of the importance of going through the motions of velocity also to policy statements which involves all classic purely musical instrument the soldiers who be you never knew what that feels that it is simply a disinterested in uh who will use them at some point some statements which actually increased it will be the future we will have good news for on the work of local year is the primary lever so it's category which is defined by using some fundamental presentation so we pick up some fundamental presentation is the category and we looked at the severing of support and between the generates the cosmos was evident when the delicately acceptance of the stable by so I was surprised at what they did not expand its own when leaders it's not stable by the majority in fact this discipline is very small compared to the 4 categories its we just pick up a finite number of fundamental whatever politician but it's going to go with his infinitely many so that they have much more information is a continuation on the bulletin between overseas and the of the leader of the world the future of the creation of a city that is exactly as it was when the size of so if you want to that there is a control of the war with characterize down there we we consider we define it as a category of objects with a conch condition of simple terms of job unheard of then we poverty that is stable but patents and at the other questions it you thank my
00:00
Complex (psychology)
Greatest element
Standard deviation
Multiplication sign
Closed set
Direction (geometry)
1 (number)
Infinity
Measurement
Bilinear form
Food energy
Derivation (linguistics)
Carry (arithmetic)
Field extension
Field extension
Lie group
Quantum
Loop (music)
Condition number
Stability theory
02:14
Spacetime
Conformal map
Presentation of a group
Algebraic structure
Analogy
Mathematical model
Complete metric space
Icosahedron
Affine space
Matrix (mathematics)
Presentation of a group
Triangle
Area
Theory
Algebraic structure
Mathematical physics
Division (mathematics)
Weight
Cartesian coordinate system
Measurement
Metric tensor
Mathematics
Field (mathematics)
Helmholtz decomposition
Natural number
Physics
Object (grammar)
Pressure
Matrix (mathematics)
04:06
Presentation of a group
Parameter (computer programming)
Mereology
Affine space
Frequency
Arithmetic mean
Analogy
Quantum
Geometric quantization
Fundamental theorem of algebra
Theory of relativity
Block (periodic table)
Parameter (computer programming)
Group theory
Complex number
1 (number)
Local Group
Category of being
Algebra
Universe (mathematics)
Universelle Einhüllende
Relation <Mathematik>
Quantum
Dependent and independent variables
Object (grammar)
Family
Separation axiom
07:17
Process (computing)
Observational study
Presentation of a group
Student's ttest
Measurement
Affine space
Category of being
Field extension
Field extension
Commutator
Quantum
Quantum
Diagram
Loop (music)
Geometric quantization
09:07
Commutative property
State of matter
Ring (mathematics)
Mathematical model
Basis (linear algebra)
Multiplizität <Mathematik>
Ordinary differential equation
Summation
Group representation
Tensor
Object (grammar)
Hausdorff dimension
Vertex (graph theory)
Descriptive statistics
Physical system
Social class
Theory of relativity
Product (category theory)
Process (computing)
Basis (linear algebra)
Measurement
Connected space
10 (number)
Category of being
Hausdorff dimension
Natural number
Equation
Relation <Mathematik>
Quantum
Normal (geometry)
Abelian category
Resultant
Relief
Point (geometry)
Octahedron
Product (category theory)
Presentation of a group
Link (knot theory)
Algebraic structure
Student's ttest
Infinity
Local Group
Frequency
Canonical ensemble
Isomorphism
Nichtkommutative JordanAlgebra
Directed set
Equation
Quantum
Free group
Associative property
Condition number
Dynamical system
Variety (linguistics)
Theory
Independence (probability theory)
Algebraic structure
Ring (mathematics)
Cartesian coordinate system
Field extension
Computer animation
Logic
Factory (trading post)
Social class
Object (grammar)
Group representation
Series (mathematics)
14:58
Geometry
Point (geometry)
Complex (psychology)
Presentation of a group
State of matter
Ring (mathematics)
Decision theory
Modal logic
Algebraic structure
Survival analysis
Basis (linear algebra)
Infinity
Subgroup
Local Group
Canonical ensemble
Object (grammar)
Isomorphism
Category of being
Process (computing)
Military base
Basis (linear algebra)
Content (media)
Ring (mathematics)
Cartesian coordinate system
Category of being
Isomorphism
Lie group
Koordinatenring
Theorem
Object (grammar)
Film editing
Directed graph
Group representation
19:00
Point (geometry)
Presentation of a group
Observational study
Algebraic structure
Basis (linear algebra)
Subset
Manysorted logic
Term (mathematics)
Velocity
Object (grammar)
Quantum
Analytic continuation
Category of being
Condition number
Area
Process (computing)
Theory
Incidence algebra
Price index
Group theory
Category of being
Lie group
Object (grammar)
Abelian category
Family
Local ring