 To je zelo pravda, da imamo tudi tudi, in tudi za to, kaj je vse online zelo, zelo, da vseh vseh vseh vseh vseh vseh vseh vseh vseh vseh vseh vseh vseh vseh vseh. Vse nekaj sem počusti, da Adizh Dabulkar, ko je izvršenj iz ICTP, za druge začne. Dobro, srečo, srečo. Vse je veliko, da me nekaj pravi inograti toj spremskaj skolj, nekaj, nekaj fizika, ker je to je izvršenja iz ICTP, in fakt are remaining really in person after two years of Covid. And as I understand this is the tenth edition of this very nice school on an important topic. And as I understand this year will have about 30 participants who will participate in person in patročno tudi o 150 in in tudi, kot in vzeliš. Vseh, imam veliko prav, da se všel jih. Zelo biš ukazati, da imamo mnogo djih sprihlušt. Tudi vseh sprihlušt. Ja zelo boš sem da boš potrebojat, ki da so prej tako odstavili, ki se odpočila, da je to možemo vsega vsega vsega vsega vsega vsega vsega. Je to neko tegnične detebi, ki se prišli, da se vsega vsega vsega vsega vsega. Vsega, da je to počut, da sem vsega vsega vsega vsega vsega vsega. Čakaj. Protočno, tudi je zelo, da je počkaj počkaj, kako je nekaj počkaj, in tukaj smo počkaj v Politechniku in Torino, in v Universitetu Franco-Italienske, Ne zelo. Ne zelo. Ok. Ok. Ok. To je program. As you see we have 5 speakers, 5 courses. And the course of Tania Sharpey which will be in the afternoons is actually she could not come to Trieste so she will give her lectures online and but I will be in presence so I will do the teaching assistant for her course so and then also we have Gulce. Gulce is here, so no, not yet. So we have a teaching assistant for the course of David Wolpert will also give some lectures on introductory lectures and also Stefano Ruffo will say this and some of the last 3 lectures of this course will be given by Nicolo Defennu, right? Ok, so then this is general outline of the course as you see, lectures are 1 hour 45 minutes but we leave it to the speakers and you to split this lecture this lot of 1 hour 45 minutes eventually in 2 or to start earlier or to finish before but the important thing is that at 10.45 there is a coffee break for you which will be upstairs and with some calories for your brain and so essentially from 10.45 to 11 we have a coffee break and ok, so some rules ok, so it will take some time so your attendance is compulsory so you are supposed to attend each lecture and please be on time lecture start at 9 am start when the program at the time of the program I know it's very heavy schedule for 4 weeks it will be very intense but this is also for the also you should consider that the lectures also put a lot of effort in preparing the lectures and being on time and ok, so still not my screen sharing is post ok, I don't know why ok, so then there are final exams which are compulsory for all of you in presence and and these are essentially marked in bold here ok so at the end of the first of the second week you will have the first two exams then the exam of professor Sharpey will be at the beginning of the fourth week and the last two courses will have the exam at the end of the spring college ok, so we have a lot of online participants and and and we set up a slack space for them so that they can interact with speakers, especially those that cannot attend live the lectures because of time zone difference sorry so essentially you the virtual participants received a link to connect to this slack workspace in order so that they can ask questions offline to the lectures and these questions will be dealt by the lecturers either online or at the next lecture either offline or at the next lecture online ok, so then well this is really very important information so I should share again I don't know why this is ok, so this is working now so lunch ok, so lunch and dinner are offered in the main building of ICTP which is called Leonardo building which is up hill diploma students know very well where it is master students maybe you remember and so there are two ways to go to to the main building one is through the park and so you should go down to the to the harbor and then there are stairs that enter into the park this is a very nice walk and then there are stairs that lead you to this Leonardo building I mean we can do this walk today together if you want the other possibility is to take a shuttle that brings you from no, it's not working so maybe I'll just do like this so there will be shuttles ready at quarter to one at the reception out of the reception that can bring you up to the Leonardo building ok, so also in this building which is called Fermi building is the administration and the medical service especially if you I mean we are unfortunately still living in covid times so we should pay attention to keep this place a covid free place ok, this is a responsibility of each of us really to be extremely careful about this because this could hamper the whole spring college and unfortunately I don't see our head of administration here who could give us some more precise instructions on this but maybe we will tell you more about this for the moment just let's keep the usual I mean the measure that you learn so well in these two years ok, having said this I think we can start and enjoy the college and any problem just let us know, ok thank you very much and well, the floor is yours, one thing I don't understand maybe you know whether speakers can take their mask off you know, atish? ah, ok so I will keep it for a while if ok ok, so you can hear me welcome to the first series of lectures of this spring college and I didn't really realize that for Italy it's the day after the anniversary of the start of the epidemic it was exactly yesterday two years ago that we got the news from Codonio of the first serious case of many infected people and I really hope that nightmare will finish soon and getting together is a good sign that something is moving on so so so you can see my name Stefano Rufo I'm teaching statistical mechanics at CISA and begin in this year I will also teach a course of dynamical systems at the University of Trieste in couple of weeks so my I think one can see also the blackboard you know so my email is rufo cisa.it and you can reach me for any question but I'm also registered on Slack so those of you who are connected to Slack can ask questions also on Slack so this will be a sort of crash course in long range interactions and you will see the topic it is in a while but not for advertising I would like to show you a book which was published few years ago in Oxford University Press I'm one of the author and it collects series of results that were obtained beginning in the 90s in this field of research so the lecture I will give six lectures six lectures and the first one will be a sort of introductory lectures on generic features of long range interacting systems and and the three lectures on quantum will be given next week by Nikola Defeno so Nikola should have been here but he was called for an interview in Houston and today he's in Houston and then since he managed to go to the US and stayed next week also in Boston for another interview he is currently a postdoc in ATH Zurich and so his topic will be specifically quantum long range interactions I think he is also available especially when here it's night for discussions and questions you might have I will provide to you his email also for connection to him so let's start I hope it can go I see I have the same problem as Mattel stop sharing no, the arrows don't work so you can see in this form but if I go full screen there are problems ok, but until it is visible it's ok so I will begin by sort of general introduction some in which sense I will talk will talk about long range interactions but there are several definitions in the literature so I want to be precise to what definitions I will make reference when I speak of long range interactions and then I will I think I will spend the first half an hour to the first discussing about the first topics some of the some of the information will be on the slides and some other I will give on the blackboard so I have prepared some notes and also at the end of this lecture I will leave you with a few exercises to do and I hope that you will be able to do them easily and and of course if you have questions and I'm available even during the day to reply to the questions ok, so wow, what's happening on the screen there is ok I accept any contribution from you even this one it's ok ok, so so how to start so it's I like to start with stories and historians on my involvement in the study of this topic begins here in Trieste so I was attending a very general conference on STATMEK and at the time I was performing numerical experiments on a model that I will tell you about maybe in the third lecture and I was obtaining from my data computer simulation a negative specific key so for me was a sort of of mystery and I was very worried that my program was not working and was giving numbers from God so so there was really no no and I was lucky enough to sit near a guy in astrophysics and this shows that interdisciplinarity is very important and so he asked me what are you working on and I wanted to be provocative and I say I'm working on negative specific key so and then he looked at me and he said whoa that's standard for us so this opened to me the door long range interactions and in fact the statistical mechanics of self gravitating systems is a very interesting topic but very difficult one for several features that gravity has, Newtonian gravity has in particular the fact that the Newtonian gravity is a singular at zero distance so particles tend to collapse in a core because they attract each other and the attraction sees more and more as you get close and another feature which is difficult in I see another sign for the museum beautiful colors so so I another feature of gravitational systems is self gravitational systems is the fact that we live in three dimensions Newtonian gravity is in three dimensions and if you run a code with a self gravitating particles so the interaction is v1 over r in 3d orbits are not closed and orbits are not bounded so it happens that if you start a simulation with say thousand particles thousand Newtonian particles which is a small simulation at the end of the game you will get maybe two third of the particle in the cluster but some of them will have evaporated outside and this is a very bad feature for statistical mechanics because you would like to keep the particle confined in a box concerned boxes you learn it from kinetic theory so what people are bounded to do is to put is to put the self gravitating gas in a box and and let the particle either be absorbed rebound on the boundary of the box so and this is a field in itself is a very complicated area of research another person I could have met and I didn't meet at that meeting was a person in plasma physics plasma physics is another field of research where long range interactions in the sense that I will define are at stake plasma is matter ionize matter and charges are free to fly and you get positive and negative charges so it's really I'm starting with physics 1 you have positive and negative charges and what tend to happen if you have a system of positive and negative charges there is a tendency to screen so for instance if these are ions which are heavier there will be a cloud of minus charges around the ions and this is called the device sphere and the interaction outside this device sphere there are several pluses and several minuses and globally this is neutral so what will happen if you put together a system of positive and negative charges they will tend to form a cloud clouds of neutral charge and all the excess charge will be pushed to the boundaries so if there is an excess charge it will be pushed to the boundaries this is what I teach for instance to first year physics students when I say if you have a conductor the charge will be on the boundary ok there is a strong relation here there is dynamics but ok but it's very important in plasma physics are instabilities that arise when when the charge is globally unbalanced this can happen in several regions of the plasma especially near the boundaries so plasma physics has a very strong interest in what they call a one component plasma one component plasma and the one component plasma is a system of electrons which is confined with a strong electric and magnetic field so there is a region of magnetic field be in the vacuum and as you know the electrons wiggles around these magnetic lines these are magnetic lines and then you put you put some sorry some electric field that bounce the electrons in a certain area this is what is called the one component plasma and the dynamics of this one component plasma falls into the realm of long range interactions because the electrons for instance what they do maybe I will show you a movie at some point they look at the charge in this in this plane orthogonal to the magnetic field lines and and they look at concentration of charge and curiously this charge obeys the Euler equation which is used also to understand climate on the earth surface for the motion of the atmosphere so you see very beautiful vortices cyclons and anticyclons of charge in this plane so this is for motivation but then of course as a theoretical physicist I did want let's try again to to share if it works I don't know so I will go on with so I need to define my setting so it's already 20 minutes for motivations so my setting will be very general and I will define long range interactions by the potential sorry, I will put again ok, so let's take matter in a certain volume and particles interact each other with binary interactions we have one particle here particle i particle j there will be a certain distance r between the two particles and the potential is between the particles is v of r one over r to the alpha at large distance so I concentrate on matter which interacts with power law so alpha equal one for both Newton gravity and coulomb and there are not many examples in nature but one interesting one is alpha equal 3 which is dipolar interaction there, in the room you don't see so we can put it down it's better now? ok, I'm sorry but I'm used to use all the blackboard in three dimensions, yes in three dimensions, yes you will see also what happens in other dimensions for the moment I fix the dimension and ok, so for instance in these dimensions in this slide you see a region of values of alpha for which you can do a very simple calculation which is keep drafted here so I would like to compute the energy per part of matter that is homogeneously distributed between an inner radius small delta and an outer radius r ok, so what I do I do an integral I do an inter, you see it here between delta and r of in these dimensions d dr which is dx dy d times times rho ok, I take matter homogeneously distributed times 1 over r to the alpha this will be the so in matter here I didn't put interaction let's say it's coupled with interaction j or g or any interaction j ok so so it's very easy to see what happens if there is a spherical symmetry this integral will give you I didn't put the expression but you can derive it can look ah, this could be an exercise what is this quantity here, so it's the angular volume of in the dimensions times rho and then you count ok, this is d minus alpha and you have to estimate d minus alpha between r and d so you get as an estimate of this integral rho j the coupling ok, divided by d minus alpha is a constant is important and then you have r to the d minus alpha minus delta to the d minus alpha ok, now you understand why I have put this delta here because it serves as a regularization of the interaction at short distances because there could be divergencies of this interaction at small delta so for the moment I keep this delta fixed and this is something which is really done in practice in the two examples that I've shown for instance in Newtonian gravity the potential is regularized at short distance in several different ways or the particles when they arrive at very short distance they interact in a different way so they could be for instance hard particles that when they get close they collide or they could be soft particles when they get close they interact with a different potential or matter could be quantum and then at very short distance you will have the effects either of the Pauli principle for instance if you if you take fermions or of the Heisenberg principle because you cannot follow the trajectories and the velocities of the particles when they get too close so I exclude this part it's a phenomenological parameter but what is important is this part here and it is clear that when alpha is larger than d when alpha is larger than d then epsilon goes to a constant when r goes to infinity k when r goes to infinity and alpha is larger than d this exponent is negative and so as r goes to infinity this term drops down and you get a finite epsilon ok this property was realized by Gibbs himself the founder of statistical mechanics it's not easy to find the quote but if you are patient enough and you go to the very first rigorous book in statistical mechanics which is the book of Gibbs you find this remark interaktion should decrease faster than 3 in 3 dimensions and this was known to the physicists to 50 years ago physicists and mathematicians like Michael Fisher and David Ruel in the beginning of the 60s were setting the base for the study of matter using what is called the thermodynamic limit and they realized that they could get thermodynamic potentials in like here we get the energy only if it exists of decreasing fast with distance of the interaction potential was made of course if the decay I've chosen the power law instead of an exponential because of course the exponential would fall for instance Yukawa potential would call faster than the exponential this is a sort of critical situation in which I'm testing the stability of my thermodynamic description ok so most of what has been done in the 60s and the 70s on the on the short range but in case which is alpha larger than d is very interesting but will not be the subject of my lecture course because the subject of my lecture course will be the case in which alpha is less than d or maybe ok I will introduce a quantity which is called sigma which is alpha minus d so and if sigma is positive I'm a little bit invading the region of of the founder of statistical mechanics because you see I'm going in a region where the energy per particle is well defined but I will reach only a value that I call sigma star and if sigma is less than sigma star and the sigma star will be defined depending on the problem and you will hear a lot about sigma star in the lectures by Nicolò Defeno you can get collective phenomena that are due to long range interactions although the system is extensive so although the system of energy per particle is well defined for instance an exercise that I will do pretty soon very interesting one maybe not well known the fact that there can be phase transition in one dimension in this region between sigma star and zero sigma star and zero so phase transitions in one dimension who has heard about phase transition in one dimension is there in the audience someone who knows no so what what would you argue first of all you know what is phase transition I think so okay and there is an argument which is due to Landau to Landau and Leafsheets which tells that if the interaction is short range and I will repeat the argument I will leave the argument at the end of the lecture as an exercise so first exercise check exercise check an expression for omega d and study this expression and see that in three dimensions it is angular volume of the sphere and so on in Italija we say solid angle I don't know if it's spread out in the world this this term okay so what happens if alpha is less than d now let's take over again so what happens is alpha is less than d alpha is less than d that's all equal d and 0 then it's easy to check that the energy per particle it's here is the volume to the 1 minus alpha over d this is a simple calculation the volume if you want is r to the d so you can express the energy per particle both using the volume and using the radius of the region where matter is contained so if alpha is less than d this is less than 1 so 1 minus alpha over d is a number less than 1 I'm not considering alpha negative I'm considering alpha positive and of course I could include alpha 0 alpha 0 is a very interesting case in which each particle interact with all other particles and there is no decay of the interaction so alpha equal 0 is what usually called the mean field or all to all okay the mean field or all to all interaction so, okay what can you do if this happens so if energy is super extensive in the volume so grows with the volume and the solution to this problem was given long ago okay let's first of all try to talk about the physics and then give the solution which is interesting mathematical solution but it's a mathematical solution and I would like to understand the physics okay, usually in nature we have systems that are described by Hamiltonians by energy functions and the energy function is made of kinetic energy plus potential energy kinetic energy in standard conditions is the sum of is the sum of single particle contributions the velocity squares of each particles okay so this part of the energy is goes like n because you are summing contributions of of each part if I'm going to slow, please don't tell me you're going to slow I know all these so I will go faster because there's slides, I have 20 slides and I am now at 9.39 and I have covered two slides so I'm filling up the notions what is not on the slides but it is in the book and I will give you the PDF of the book for free by the way just to relax for a while you see this beautiful picture this is an artist that I met, his name is Neil Sudo from Finland and I like very much his land art this is oranges and he rotated the camera in order to make a sort of cluster of particles and this reminded me the clustering phenomena in self-gravitating system so I asked him can you give me the the rights to put it on the cover and he said, okay, yes and then I said, okay let's get Oxford and tell them you want to be paid for that and then he contacted and lost contact with him and so finally got to be paid by Oxford and then I asked him how much he said $100 I said, oh these Oxford guys these are really bad guys I mean you should have asked at least $500 no, I was so excited that my cover finishes on on a book, okay, but it's I like it very much you can look at the arts of this guy okay this is what my friend Jan Levina from Brazil calls core halo distribution so there are sometimes in self-gravitating systems situations in which they form a core, very dense core and then there is a halo around and you will see that they can arise in much simpler situations okay, let's go back to my Hamiltonian and of course since this is pair potentials because I can square okay, so already there is a problem at this level because if you let and grow and there is no way that you get an energy per particle this part of the energy will keep growing keep growing and keep growing and dominate over the kinetic energy one could say okay, no bad because as potential energy grows matter will get colder and colder and finally it will reach zero temperature because kinetic energy will be extremely small with respect to to potential energy so do you see around that we are all at zero temperature? no, I would say no okay so in fact what happens is that as you increase system size because of short range interaction the system is chopped into parts and equilibrium will be an equilibrium with zero temperature because of that because kinetic energy can compete with potential energy but if you don't have additivity which is the first hypothesis that you find in any book of statistical mechanics which is a consequence of the interaction to decay faster than d you won't get the equilibrium that we see around us because the energy will dominate and kinetic energy will be dropped off and also you could not see boiling water you put fire under a pot and you would like to see water to boil and then to become vapor so to go through a phase transition and this you cannot appear because the system will be dominated by energy and entropy will not play any role in the matter so it won't be able to compete with energy because again entropy which is combinatorial grows with n and another consequence of this effect is that since free energy is u minus ts u goes like n squared s goes like n and the system will be dominated by energy ok so you won't see phase transitions so what was the idea and the idea is due to fantastic mathematicians that I encourage to read the biography of this guy which is really impressive so he was born and lived part of his life in a country which is nowadays in big trouble he was known to the mathematicians in Leopold in Lviv or Lviv in now in Ukraine at that time was part of Poland and then emigrated to the US and he was I mean he is responsible for so many contributions to random process Feynman-Katz integrals and so on this is really a minor contribution he got a very strange and funny idea so ok, if the energy is so there is energy per particle go like this so the energy is N time this and you can rewrite N in terms of volume so you see in this slide that if alpha is larger than D as I was telling the energy goes like volume if alpha is smaller than D the energy goes like volume to the 2 minus alpha over D energy now I am playing with extensive variables but I will follow the rule that A is an extensive variable and A is an intensive variable so I will try to keep the 2 definitions during all my talk so the free energy goes like the volume because the entropy goes like the volume the energy goes like the volume everything is ok if alpha is larger than D but what can I do if alpha is smaller than D and what cuts propose is to rescale to rescale the coupling to rescale the coupling in such a way that you get a free energy that increases with the volume and that's a very simple exercise just rescale the coupling I don't write it it's called the cuts trick it is a mathematical trick you rescale the coupling by V to the alpha over D minus 1 and if you do this you get a free energy that goes like the volume alternative what could you do you could rescale the temperature ok by 1 minus alpha over D in such a way that the free energy now grows like 2 minus alpha over D it grows like the energy so it's an unusual scaling for the free energy but it allows the temperature which now depends on the sides to reach the scale of the energy of the potential energy so I believe that you are not used to neither of both so where is in nature an interaction that depends on the sides that's why it's a trick and on the other hand if you measure temperature with a thermometer you believe and we have a thermometer at the entrance of the building you believe that this does not depend on the sides of the body to which the temperature is measured ok so both are tricks and why you do these tricks you do these tricks because you want to go to the thermodynamic limit without encountering the problem of competition between kinetic energy and potential energy and without encountering the problem of lack of competition of entropy with energy ok but then you know that also the thermodynamic limit we are made of moles of matter so none of us I invite you to compute how many moles you are instead of kilos but none of us is an infinite number of moles so you can play the cast trick at the reverse once you get a very very large system you fix the size of the system and you read back what are the intensive variables in terms of extensive variables given the volume given the finite size of the system so that's the idea you do the trick in order for the limits to converge it's a typical mathematical trick and once you reach the limit with intensive variable you fix the size and you read back the extensive variable of the system this is the idea this is the conceptual idea it has been done very successfully even more sophisticated ways for instance for the theory of liquids there is a very important series of papers mathematical papers where which is by the way the only way of getting phase transition rigorously in liquids ok, so but I don't want to enter in these so I've put here the slide to be more specific on another feature I mostly spoken about about extensivity so the fact that I want to increase the number of particles the volumes in order to get the density and so on but I didn't speak about another feature of which is in fact even more important now that we are able by the cut streak to perform the thermodynamic limit I think I will stop at 10 and then I will do 5 minutes break ok, so be prepared for stopping 5 minutes you should resist and accept the cut streak for a while and then you will destroy it ok, in 5 minutes ok, so and this this property has been in some sense it has been confused with extensivity so if you open a book in Statmeck the two concepts are sort of superposed so ok, if it is extensive it's also additive I would like to make an example very simple example can be more complicated examples the simplest you can think where you see that they are not the same ok and the simplest example is the Curivice Hamiltonian I leave it on there so the Curivice Hamiltonian is the simplest model of magnetism that you can think of spins can think of them as plus and minus variables classical variables interact all to all and I have put the cut streak in this Hamiltonian can one see where is the cut streak in this Hamiltonian there is cut hidden somewhere in the J over N because I have just said that the cut streak is to scale with minus alpha over D and this is a mean field all to all model so alpha is zero in the interaction so I think all of you have been presented to the Curivice model reading books of Statmeck but no one was aware that there is a cut streak in this Hamiltonian and no one was aware that this is an example that contradicts chapter one of the book because chapter one begins by saying we will treat in this book systems that are both extensive and additive and this is extensive for sure because the Hamiltonian grows like N the number of pairs grows like N squared divide by N Hamiltonian grows like N but it's very simple to construct states you can play with that I have constructed the simplest one I construct a state with zero magnetization zero magnetization so the sum of the spins is zero this Hamiltonian can be also written as magnetization squared so if the magnetization is zero also the Hamiltonian is zero so the two parameters magnetization and energy are tightly related into this model and I divide the system in two parts and it's very simple to see that the energy of the total which is zero magnetization is zero while the energy of the parts is minus j over a10 you can do the exercise of computing the energy in case of the two parts and hence the sum of the energies is not the total energy of the system even if you go to very large N you will not solve the problem that's because as you grow with the size of the system there will be cross links between the two parts there is no surface in this model there is no surface in this model because there are old cross links so that this is not true so yes yes yes sorry I was too fast it's not in the denominator anyway you can check it might be a mistake so please check I'm sure that it's not going to zero minus j minus because in the Hamiltonian which proves that ok then you say oh that's a disaster because no one did this remark to the teacher look this example contradicts chapter one of the book but there is no disaster fortunately and Katz was right and that's a very very interesting the model has been studied also mathematically and gives a phase transition of second order of the Q revise type, mean field type which is a good description of what happens in magnetism in this limit of the mean field now you will learn at the end of the of the series of talk maybe already on lecture two that we have been very very lucky to use spins that can take only two values because if we would have used spins that can take three values would have come in big troubles and in particular you will see that this is already an example it's called the POTS model where which describes some mixtures, some other different systems and magnetics also some magnetic systems that the entropy I mean thermodynamic entropy entropy as a function of energy is non-concave so for this case is in extreme situation where the entropy although there is a second order phase transition the entropy remains concave and I will compute the entropy for the Q revise model you will see it in many different ways and the entropy remains concave so all thermodynamics works although the system is non-additive so it's not necessary that thermodynamic works if the system is non-additive so it can happen that if the system is non-additive you get standard thermodynamics there's no problem with thermodynamics but there are cases and I will show several where if you violate additivity non-concave entropy and this is the case of this is the right time to finish self-graditating system one component plasmas oiler equations and many others so in the second part of the talk I will go on with the slides and now I leave 5 minutes of break you just sit or questions first of all questions, yes I would like Angelo, are you there? Yes, yes Can we have Can you hear me? Can you hear me? Yes, I can hear Angelo From Angelo Can we have the audio only from your computer, right? But we here we can hear Hello, Angelo But if you open the audio Hello? No Maybe Hello, Angelo In the hall, can you hear in the hall? Not quite Maybe this one Hello? Just a moment Angelo Hello, try now Yes Very good, great Ok, thank you very much So, my name is Angelo Rose I am organizing with with this spring college So today I couldn't be there with you because I am recovering unfortunately from a small accident but so what I want to tell you that I am working in CIS and so we are organizing a visit to the CISA labs of Neuroscience that will be for the third or fourth week of the spring college so that will be in March so I will let you know and maybe I will coordinate for sure I will coordinate with Matteo to arrange the visits in safety so probably I think it will be two groups of people so to not get I mean to avoid big gatherings and to know about that and enjoy the school and the speakers I think it's a really fantastic opportunity for all of you, thank you Ok, thank you Angelo Ok, so we take 5 minutes break