Vsih da sem vsošil početek na razgleda, zato sem vsošila da bi se zelo, o kaj sem zelo vsošil, zato sem početek je disdravil.  So this again, it's the same complex, I mean the same exercise show now, this is dual unitary. Of course it's by far not complete. No dual unitary D dimensional system can be written like this, but it's an interesting family which is inspired by dual interest for qubits. It's like a representation of a high dimensional equation. vsega je zelo, da je vsega štoči v klasike limit. Nastavimo, da se ne vsega vsega vsega. Zato da se ne vsega vsega je zjavil, ta časja, da je delasya, in tkaj je, da se poživimo, kako tega vsega je zelo, tkaj je vsega štoči vsega vsega.  S swapom je zelo vsočen, in je ne zelo in trakčen, je zelo vsočen, je zelo vsočen, pa vse je tudi klasikl, ne, ne, klasikl, je semiklasikl, če vsočen model s transferstvim. In zelo vsočen je, da je to zelo vsočen na klasiklu limit. Zelo vsočen je vsočen na klasiklu limit, a zelo vsočen kaotic klasiklu dynamics klasiklu spins. Modelj, da klasiklu mapi poklačaban pojstroňje, klasiklu spins pojstroňje, kaj je zelo Vietnamese, je symplektik, vsočen je sample structure, sample bracketi, Zelo vsočen je nek Reno Diamond, zelo vsočen mas vsočen transferstvim dynamic, vsočen je klasiklu automat. Evo je l Nahov塊 parameter takčen za klasiklu buddies noted sequč snStuden in vsočen na klasiklu limit. klasikl markovčenje. M plus in M minus now becomes infinity dimensional, klasikl limit become infinity dimensional classical stochastic matrices and their spectra determine the care of correlations. So that program has been actually done. I mean this was a work done together with students in sergi. Alexios Christopoulos and Andrei Adaluka and Dimakov Rizhin. I think it's a nice curiosity. I don't know if it will turn out to be how much development will be stimulating but it's a curiosity that you can also do duolinitries for classical classical klasikl klasikl map lattices. Ok, now let's go back to our discussion of spectral correlations. So, now once we define the spectral form factor, let's discuss its kind of essential scales. So yeah, now you see the reason why I decided to put this strange normalization factor here so that we get no normalization here. So this is, sometimes people define it differently but ok for us this will be the, I mean you want, well, yeah, eigenvalues in the minus here, put minus here and plus there, but it doesn't matter, it's the same. So it's a model square of trace of u to the t. So now there are two timescales, there are timescales which are related, I mean, well, there is basically a single timescale which is completely universal and that's related to the density of states, right? The density of states is basically number of levels. So there is the spacing between adjacent levels which goes like 1 over n, right? It goes like 2 pi over n. So now this defines a timescale, meaning that there is a time such that this will become of order 2 pi and this timescale is called Heisenberg time. So now, right, because what happens with the dynamics, I mean, you see, I mean, maybe there is another, maybe it's instructive to write another and multiply these two terms. Then it is n, n prime e to the i phi n minus phi n prime times t. So it's like, you see, it's like sum of quasi random terms, right, which become really quasi random after time t which is larger than mean level spacing, right? Larger than inverse mean level spacing. There is a minimal spacing which is of the order of 1 over n. If time becomes larger than n, then this becomes multiple of 2 pi. I mean, then even the smaller spacing generates kind of the coherence or the phasing relations. I mean, all these terms are now completely kind of defaced and they can be considered as quasi random. So what I want to say is that there is an absolute time, Heisenberg time, after which spectral form factor becomes completely structuralism. We cannot have any structure anymore. So for any kind of ensemble of random matrices or any class of dynamical systems for times longer than Heisenberg time there is nothing really interesting anymore. There is just quantum recurrences and nothing else. OK, now let's see how does, let's how does spectral form factor look like for typical classes of universal classes of random matrices. So spectral form factor in random matrix theory. So there is the Heisenberg time and Heisenberg time is of the order n, as you see. And then there is a scale n also associated to spectral form factor. And so what can happen is so there is a special value n and it turns out that spectral form factor basically cannot be substantially larger than n, but it can approach n. So, and then there are different types of random matrices. The so called Dyson's threefold way. There are three fundamental classes of random matrices which are unitary. This is related to standard Gaussian random matrix ensembles but I am using unitary rather than Hermitian matrices. So these are called Dyson's circular ensembles but they are completely analogous to standard Gaussian ensembles. So there is a unitary ensemble which is called CUE which is just a unitary group. It's equivalent to unitary group with a hard measure. So the idea is if you don't know anything about your evolution operator you replace it with a unitary group. This is the kind of variant of random matrix ansatz for unitary matrices but usually what people do is they replace a Hamiltonian by a random Hermitian matrix. Now we replace a unitary by a random unitary matrix and see what happens, right? And then we can compute people have computed spectral form factor for unitary matrices so basically you average over unitary group there is a well defined integral over the unitary group with a hard measure which you can evaluate trace u and model of square trace u to the t model of square and this can be computed I mean there are tricks in random matrix theory which allow you to compute this actually there are some very nice tricks but I have no time to talk about them so it's a very nice function it is a linear function of n and then it plateaus when so basically it's a stepwise linear function it goes like linearly to n and then it's so these are and usually what you have to do is you have to use this I mean there is this standard wisdom when you use each of the random matrix ensembles you use unitary ensemble for systems where there is no time reversal symmetry so called anti unitary symmetry so when there is no time reversal in your chaotic model then the common wisdom is to use unitary ensemble either CUE or in the Hamiltonian case GUE and by the way I mean the four-spectre form factor is the same for circular and Gaussian matrices because we have to do thermodynamic limit I mean this one actually is the same even for finite and well I have to be careful for Gaussian ensembles time is continuous so there are some corrections but in thermodynamic limit is the same now when you have time reversal or other unitary anti unitary symmetries you use orthogonal orthogonal circle or orthogonal ensemble which is formed of matrices V which can be written as U times U transpose where U is sweeping over unitary group with respect to the hard measure so this ensemble is not a group anymore I mean these are kind of I mean the first ensemble was really a group this one is not so these are complex symmetric matrices you see the way that's written this means that V is selfish symmetric but it's complex so it's not like in Gaussian Hermitian ensembles in GOE where this is a real Hamiltonian now we cannot write it as a real sometimes people make stupid assumption that this is just orthogonal matrices these are not orthogonal matrices these are complex matrices which are symmetric so we don't want to to see this without time reversal and then for that people can compute spectral form factor which is well now we have again you can just do integral of a unitary group but you have to compute U transpose to power T model square and then you get again analytic result 1 plus 2T over N I mean it's a funny object for T less than N N to N minus T log 2T plus N divided by 2T minus N or T larger or equal N now we don't have to remember that but what is important is that this starts with a slope 2 so for small time it starts with a slope 2 and then it goes with twice the slope of the unitary and then it goes like this smoothly to the plateau so this is GOE and then there is another ensemble which is the symplectic matrices which I will skip for my discussion but complex circular symplectic ensemble which has slope 1.5 and then it has a spike but I will probably I should not even discuss it because it's not be important for the rest of our discussion just to let you know that there is a third ensemble which corresponds to spin 1.5 systems with odd total spin so with half integer total spin and time reversal which has kramar degeneracy so time reversal which squares to minus 1 but as I say I will not say anything else and then the third ensemble which I have to discuss is the so called Poisson ensemble which are not really random matrices or if you want they are random matrices but they are random matrices which have Poisson that is a random IID which is 0 and 2 pi for that I give you an exercise which is instructive so this is really easy exercise but it's still instructive to compute spectral foam factor it can be done you can imagine these are IID complex numbers so you can average out everything and what you get is spectral foam factor for this ensemble is just flat so for Poisson ensemble we have this and this is usually related to integrable systems so there is a conjecture there are two conjectures two main conjectures one is called Bohigas conjecture or I prefer to call it quantum chaos conjecture there are other people before Bohigas who understood it quite well so Bohigas conjecture says that when you have a chaotic system chaotic dynamical system you have to have random matrix spectral correlations spectrum now it goes one way so I think it goes both ways but it's identified I mean when you have chaotic dynamical systems but you have to have a proper definition of chaos which is here meant where a system has a classical limit and classical dynamics is chaotic then you expect random matrix spectral correlations this conjecture is not proven there are some heuristic ideas which I will briefly discuss in the following so for a physicist's mechanism is known but for a mathematician's there is still proof so it's a very deep conjecture and it asociate chaos with random matrix spectral correlations and this is what I am going to take also as a definition of quantum chaos for interacting spin chains or many body systems alike and then there is another conjecture which is it is well known but it is less well known as a classic conjecture it's called Derrit-Abor conjecture which says that when you have integrability integrable dynamics you have Poisson spectral correlations so this conjecture was formulated the way Bohigas particle was 1984 and this other conjecture was formulated even before in 1977 by famous Barry and Tower and they had very nice geometric picture behind this for systems which have few degrees of freedom and where you can write eigenvalues in terms of quantum numbers because when you have integrability then you can write at least in a semi-classical limit you can write eigenvalues in terms of quantum numbers in terms of the so-called TORUS quantization so you can write Ljubel-Arnold-Toraj you can find Ljubel-Arnold-Toraj and you quantize them you find that each eigenvalue is associated to particular TORUS where the actions are quantized like even old Niels-Wort or TOTAS I mean that one has to look at the actions around certain loops and the actions have to be multiples of plant constants so there is a very nice picture of Barry and Tower which showed us in generic case how this connects to Poisson statistics so these are two classic conjectures which we will use as a working definition of chaos and regularity but as I say my motivating question for the rest of my lecture is to show you some idea how one can some possible mechanism in random matrix vector correlations in interacting many body systems like dual-unitary circuits so now let me tell you now since I went a little bit to an old story of semi-classical quantum chaos I will just continue for another 5-10 minutes there to tell you a little bit more on this history so that could be that goes in the subsection under title semi-classical semi-classical chaos periodic orbit theory so this was like the main buzzword in the conferences and workshops which I attended as a PG student and young faculty in the end of 90s mid 90s so this was all about periodic orbit theory then somehow we got close down and now probably most of people don't know what it is but I think it's still worth reminding ourselves from time to time because it's been really a nice program but the whole idea of this program was actually inspired by Berry 85 I will just now give you a two-line two-line calculation of spectral form factor for chaotic systems from Berry I mean which will kind of explain at least the main features of this random chaos conjecture namely the linear ramp of spectral form factor so as you will see there is I mean this as I already tried to explain before I mean there are different time scales and spectral form factor covers different regimes looking at short times means long quasi energy and this is something like what people call spectral rigidity if you look at spectra across large distances you see that the fact that you have this ramp of spectral form factor meaning that spectral form factor is much smaller than for integrable dynamics for independent levels I mean this comes from assuming that levels are independent random numbers but in reality spectral form factor is many body systems exponentially smaller because this gap between these two values is exponentially large is 2 to dl so that's something which is really remarkable and that says to do with what people call spectral compressibility or long range spectral correlations in random matrix spectra but then you go to the very end close to the Heisenberg time you still have what is called correlation hole so there is still a gap between what you would get for random levels and this is related to level repulsion you have probably seen what people like to draw in numerical investigations is the distribution of level spacings when you take two adjacent quasi energies and you look at distribution of level spacings and for Poisson independent spectrum you have Poisson statistics that is level spacing is exponential but for chaotic spectra which which is associated to random matrix ensembles you have the so-called Dignar Dyson or a distribution which has a gap I mean which has probability that vanishes for small spacings that's referred to as level repulsion so the level repulsion can be mapped can be identified with spectral form factor behavioral spectral form factor at times which are close to Heisenberg time still I mean there is a gap because the spectral form factor is smaller than Poisson which is manifestation of a level repulsion and now the very offered already many many years ago that he offered a very clever and a cute argument why you should have a ramp of spectra why should you have a linear ramp of spectral form factor and this is something that I think it needs to be reminded because it's so cute so now elaborate on this argument a version of this argument for floke system so usually it's given for sorry for of course you have also a linear ramp there is just different slope but these slopes can be explained as well in terms of simple argument due to barrier but let's ignore the simple simplicity so I will now write the version of the barrier's argument for floke systems so the idea is to write trace of u to the t so now the main the main question in this game is to be able to write in one way or another some analytical analytical formula for the trace of u to the t trace of u to these as I already maybe well I'm not sure if I have already explained sufficiently well but it's like it's even simpler than correlation function correlation function was like having two observables this is very clean I mean no observable so this is like really a partition sum of a classical vertex model but with complex weights with very simple boundary conditions it's just a trace it's periodic boundary conditions you have which means you have u to the t but then you take a trace which means you identify these qubits this is one, two, three, four but when you take a trace you have to do the periodic boundary conditions now if you take periodic conditions in space then basically this is like a partition sum on a two-dimensional discrete torus periodic in time, periodic in space so now the question is can you do something like this I mean now I'm sorry I'm now jumping back and forth between semi-classical and quantum anybody now let's go to semi-classical forget about spin change for the moment just for the moment and see what Betty taught us and then we'll try to find some parallel to that so now what you can do I mean just following textbook of Feynman and Hipps for example if you read a beautiful textbook of Feynman on path integrals you know that this is just a propagator trace of propagator to power t so this can be written in terms of a path integral which is sum of all classical trajectories which are closed which are periodic which are periodic time t t iterations of a floke dynamics and here it is a classical action divided by hbar so that's that's a nice formula but now you can do saddle point approximation or stationary phase approximation to this formula now when hbar is small you can do saddle point of stationary phase which means you look for all trajectories in which this phase the action is stationary and these are just classical trajectories this is a classical variational principle which give us classical dynamics but now the condition is periodicity so these are periodic trajectories so basically you can write this in terms of periodic trajectories of length periodic trajectories of length so sum of all periodic trajectories of length t sometimes there are countable sums then the question is what does this sum mean and it turns out that for some nice chaotic systems this sum is countable so that you can actually organize these trajectories into a meaningful sum and then whatever is left here from this path integral is just a sum which has individual terms and each term has an amplitude and a phase which means just the classical action evaluated at the value of the saddle point or stationary point and the prefactor is some Jacobian something related to Leaponov exponent of the periodic trajectory so it's the inverse basically it's the inverse Leaponov exponent so it's like inverse Jacobian which means that the more chaotic trajectory the less it contributes in a way that it makes it convergent or at least somehow not really convergent but conditionally convergent for a nice chaotic dynamics and then whatever we have to do now remember what we have to do now is we have to compute trace of u to the t model square which means you have to just come up with product of two sums and then what Barry suggested is that this double sum is a horrible double sum but it basically you can use a random a kind of assumption of how we call this random phase approximation that all the terms for which these two because these are large numbers h bar is small so these are large numbers and these large numbers will give you many multiples of 2 pi so it will give us a kind of pseudo random contributions which we cancel out unless these two actions are exactly the same so that is the so-called diagonal approximation in the diagonal approximation so what we want is sp is equal to sp prime not p is equal to p prime but we want the actions of in these terms that action of the trajectories are the same and now you see why time reversal becomes important because when you have trajectories then the systems which have time reversal symmetry the priority trajectory which is kind of closed in phase space has another trajectory which is just its time reversed partner so it can be paired with itself or it's time reversed partner simple sum of ap square plus a factor of 2 which happens in case of time reversal in case of time reversal invariance so that's a clean argument why you should I mean how you could explain just from dynamics that the ramp has a slope 2 for orthogonal for systems with time reversal compared to systems for generic systems it's just a factor of 2 there is this sum of jacobian squared inverse jacobian model squared and that is actually another kind of interesting observation which is can be proven it's a rigorous mathematical theorem that this is just equal to t the kind of sum rule and it is known as hanae osorio del meida sum rule it's a well-known thing in classical kometon and chaos theory and then once you have this then this is just t or 2t systems which don't have time reversal so that was a various argument and people have then struggled to do more I will now skip the rest for this semi-classical game then there was a tour de force of effort of many groups which culminated in 2004 with the kind of derivation of not proof but derivation of random matrix factor form factor from periodic theory was Fritz Hake in the company he was the leader of a group in Essen in many collaborators they were able to figure out the whole combinatorics of this it turns out that you have to then pair not only these orbits but orbits which are now related more remotely to obtain higher order terms this was just a reading order term which was good for short times but then to get all the terms of random matrix you had to do much more but it turns out it's possible this is now understood now let's go to many body physics this was just a warm up but now let's say what we can say for a many body system it's a it's a sum rule I cannot I think you have to assume that your model is hyperbolic or uniformly hyperbolic so all projectors have to be unstable so it has to be chaotic so I don't think I can give you intuitive explanation for harmonic oscillator I don't know because for harmonic oscillator ok so let's say for harmonic oscillator what do you mean first of all I mean first of all I assume that we have floky dynamics otherwise I would have to slightly different but for floky dynamics ok you can think of what harmonic oscillator I mean you know harmonic oscillator has very strange periodic trajectories first of all it has just one periodic trajectory I mean it's in other words all periodic trajectories have the same period I mean it's a monochromatic system it's strange I mean harmonic oscillator is always bad when you do chaos they are always strange I didn't get you can you speak up? yeah even if it's oh sorry as harmonic we can consider some one dimensional motion I mean it resolves this problem monochromatic city but then we can just semi-clatically quantize all trajectories understand more or less and probably this calculation will lead to I don't know as far as I remember it's crucial to assume that the trajectories are unstable so lead chaos and then one dimension would not work yeah yeah ok but you know it's ok ok it's a really side track for us so it's just I can give you the reference if you want to check maybe I can just write it down so these are two postdocs students of Michael Berry ok now ok let's go back to spin chains but before going to chaotic spin chains I don't know how am I doing with time ok so probably have to speed up a bit but still I wanted to give you at least I will give you another exercise there are a couple of things which can compute very easily instead are useful to build intuition so spectral form factor in spin chains so now I will just take an example we start with an example, non-interacting independent quantum spins I mean I will assume also for most of the rest of my lectures that d is equal to 2 so what you can call this spin on half chain if you want a qubit chain and I will first consider an example of non-interacting independent quantum spins on half ok if you want localization you can also call this L bits so suppose the system is non-ergodic suppose it would be it would be many body localized then you can reduce it to independent spins and the question is can you then compute spectral form factor for such a model so I mean I just tried to argue that it could be more general than just right away having independent spins but as such then I will assume that my my gate can be written as a my time evolution now can be written as a product as a product of L single qubit gates where each single qubit gate is just let's say for simplicity let's say transverse field so it has a transverse field h so it just rotates qubit just rotates around the z axis with coupling to a magnetic field of strength h and now let's just assume that these are random fields so let's assume that we have no interaction but what we can have is still a general kind of rotation but it should be different for every side so this corresponds basically to Hamiltonian this corresponds to Hamiltonian dynamics where Hamiltonian is because these are independent so we can just add it up because they are commuting so we can write it in terms of the minus h when this h is sum over j from 1 to L hj sigma and now a question can we compute spectral form factor for that and now we have a very nice handle on averaging I explained to you already that we don't expect the form factor to be self averaging now what can we do here we can average over random or whatever random fields so we can define spectral form factor as an average over this ensemble of independent spins where I take expectation value with respect to vector of h and now there is a calculation I wanted to do on board but I invite you to do it yourself because I want to move a bit faster yeah it's still I'm a bit unhappy I'm not doing it but as you see I mean it's just an exercise of manipulating tensor products and traces of tensor products so one thing you can do immediately you can write this as expectation value of trace of u to the t tensor product u to the minus t and then you separate expectation value on each independent spin separately and then what you get at the end of the day is expectation value of independent spins and then you take a trace of each independent spins which is minus 2 i ht and the rest of the details I invite you to do it yourself so I'm just writing now this is the last matrix which corresponds to the last tensor product of 2 by 2 matrices and then everything is to power l of course but now you do expectation value now these are random spins sorry these are random fields and as soon as these fields are flat in 0 to pi so this cancels and then result is 2 to the l result is flat so it's the same as for Poisson so it's just to show that independent random spins correspond to what you expect for regular integral systems now let's go to something much more interesting local interacting now I will for the sake of concreteness and in the view of the lack of time I mean I wanted maybe to show you also the general statement for general dual unitary but this I have to skip so I will close my lectures by just outlining a calculation for a specific class of dual unitary models which are like more intuitive than the most general dual unitary circuits so I will now discuss SFF locally interacting kigtizink model so this is also how we came up with this I mean this was like the first result which we had for spectrophone factor but I think still for the pedagogical purposes probably the easiest to explain so or at least it has maybe the most physical kind of interpretation in terms of something which is discussed a lot throughout the literature so this is like related to transfers field easing model which is a popular model on its own so now what we will do is we will take like a transfers field easing model but we will or two field easing model transfers and longitudinal fields but we will take a kigt, we will kick it with transfers field so what I mean now is take a time dependent Hamiltonian a vector of longitudinal fields and now I will assume I will use the same notation I will take a vector of longitudinal fields and this is a time dependent Hamiltonian it has an easing part which depends on longitudinal fields vector plus a kick and this kick means that this piece of Hamiltonian is switched on and off in a past way with delta, train of delta let's say, I assumed at the time the period of the drive is equal to 1 and then the easing part is just classical easing model with external field if you want so there is a coupling j so coupling easing coupling j and then longitudinal field hj which is potentially different for any site periodic boundary condition and then I have a kick which depends on a single parameter which is called B the transfers field strength so now of course I will immediately phrase it as a floke system and I will write a floke circuit for that I just wanted to start with the Hamiltonian so could also think of how to realize it maybe with some past so now the floke operator corresponding to kick easing model would label now kick easing which explicitly depends on external fields so this is also something that now changes through the spectrum previous lectures previously I on purpose started only non-disorder system so I said, ok, we have a fixed gate let's make it translation, invariant in space also in time now I will have to mess up with this order a little bit because of non-self non-self averageness of the spectrum form factor but I will switch off the disorder at the end of calculation but it's important to have it and it's important to average over it and the crucial step of this calculation is to be able to compute averages over this order and there will be a trick which crucially depends on the fact that I have dual unitary circuit so dual unitary buys me a lot because I can do this order averaging explicitly and sometimes analytically so this is like in a nutshell the rest of my lecture I will try to explain to you in a brief in a simple example how to do this order averaging how to formulate doing this order averaging as a clean mathematical problem and then you have to still solve this problem and it's not so simple so I will skip most of the steps but at least I will connect it to a very intuitive to a very simple problem let's say for which you can easily see intuitively what should be the solution but as I say, the previous lectures were kind of very fundamental the other steps were kind of super simple and nothing was mysterious I mean this last part still will be hiding a lot of pages of proofs so I will warn you I mean I will not be able to do all the details here ok, so now what is the what is the floke operator you can write it in terms of two pieces it's kicked and this is easing this one depends on the field you make time of the product you have time dependent Hamiltonian it's a standard textbook quantum dynamics you write time of the product but now just two terms, non commuting terms of course these two terms don't commute so you have to write these two pieces like this ok, and then what we will want to do is to compute spectrofoam factor as expectation value with respect to field trace of easing to power t ok so now it turns out that this easing model now there is this standard analogy between quantum dynamics in 1D and statistical physics in 2D which we can now make completely explicit here so what we can do now is we can write this trace I mean the key thing is to write this trace of the propagator as a partition sum mentioned a couple of times but now here we will be able to do it explicitly in terms of basically 2D easing model this is a 1D kicked easing model and if you try to write out this partition sum you see that it really looks like a 2D easing 2D easing model so basically what we will do now we will take kind of path integral again this is like following basically the idea here you write this as a path integral but now it's a discrete time path integral so you have to slice t times the complete set in between this propagator and then what you get is basically sum over tau t-spin configurations which I will call as tau so each tau correspond to tau goes from 1 to t and then you sum over and this underline means that these are this is a s tau 1 s tau 2 and so on to s tau l so each vector s tau is a vector configuration of spins in 1D but it depends on the index tau which is also going across the other direction which has tau values I mean I will have to speed up a bit so I will not write all the details of this derivation but again it's something that is forward so the missing details I invite you to to try to do it yourself as an exercise so so once you do this you see that you get sum over all spin configurations let's call s s tau j so it's like a partition sum over configurations of 2D classical spin spin lattice and then we have a product over tau over j goes from 1 to l so we see this a product over j because this is diagonal in the computational basis so you can write it immediately as a product over pairwise terms and then there is a kicked term but kicked term again is a product because it's a sum of independent terms but this is not diagonal so let me just write it so the matrix elements of this guy let's call them v tau j s tau plus 1 j so this couples between s tau plus 1 and s tau so s tau plus 1 and s tau but the same j because it's a tens of product so these are just matrix elements of each of these terms s s prime is just s e to the minus i b sigma x s prime that's just a definition and then there's this other part which I said is also a product j s tau j s tau j plus 1 plus h j s tau j and now putting everything together basically we can write it really as a partition sum of an easing model so skipping a little bit of details here which are just straight forward I can write this really as a simple partition sum which is again a complex weight is l times t over 2 sum over all classical configurations s tau j e to the minus i and then here it's an energy functional of this spin configuration vector of magnetic fields and this energy functional is sum over two directions tau 1 to 1 to t it's periodic boundary conditions in both ways and this is j s tau j s tau j plus 1 plus j bar s tau j s tau plus 1 j, see this is anisotropic to the easing model it has two different interaction constants horizontal direction one in vertical direction time is vertical and then there is also a field which only depends on position but not on time so only on one direction so it's like a classical to easing model in striped fields so fields are random but they are modulated only in one of the directions they are flat in one and random on the other but it's all classical the only caveat is that it's classical but the weights are not positive otherwise it'll be just classical stuff and now what is this and what is this j tilde you can figure out this j tilde from this representation it is minus pi over 4 minus i over 2 logarithm of tangent of b so it's just parameter b now hidden somehow in the exponential okay now we have to stare at this expression now we think okay we are doomed because this is not integrable people in geniuses like Baxter, they taught us how to solve easing model or even onsager before and they claim that this type of easing models are surely not integrable so we forget about it how what can we do if there was no external field this would be integrable so we could use onsager solution or one of the beautiful Baxter solutions this is not integrable so we have to do something else but it's not hopeless what should we do so now I will use some diagrams which are like a version of tens on networks again which will explain what we can do so one thing we have to recognize stare at this formula is that we can easily switch between space and time I mean the structure of this formula is such that it is like an easing model in both directions so if we switch between space and time we just have to replace j by j tilde and j tilde by j and this is the same structure so basically what we have let's just write this partition sum what we have is now really a nice cartesian grid this is x and this is t this is magnetic fields h1, h2 up to hl then there are periodic boundary conditions so now what we have done is let's call this as a partition sum of a two-dimensional classical-like easing model but we started from basically transform matrix I mean this was like in the beginning this was just a 2 to the l by 2 to the l matrix powered t times and doing the trace so this is in terminology of start mech this is called transform matrix so basically we evaluated this partition sum in terms of a transform matrix now I probably should use some colors so I completed a picture but let's say this was a transform matrix which I called uki and I iterated it iterated it t times and then I did the trace now what I can do I can take instead this matrix and this matrix I will call u tilde ki and this pans explicitly on hj and I will fill it at this particular wire but otherwise it has exactly the same algebraic structure because the problem is symmetric under exchange of space and time you just have to change parameters this is the same but just I have to change parameters j for j tilde and vice versa so basically what we have to do we have to take parameter j tilde which is a function of j and b and b tilde of j and b so this guy is a function of j and b and this guy is a function of j tilde and d tilde so there is a simple transformation which I can spell it out for you I have not written it down explicitly but there is a simple transformation which is explicit which allows us to form column transform matrix out of the row transform matrix so the other difference is a matrix which acts on spin ring of t-sides so this is a 2 to the t by 2 to the t matrix this was 2 to the l by 2 to the l and this is 2 to the t by 2 to the t so sometimes it is better to contract the other sometimes one, sometimes the other depending if t is short and l is long it is much better maybe to contract along columns right it is easier to power a smaller matrix because you can diagonalize it you can figure out its spectral composition and then things become easy where is u tilde? u tilde is this column yes and u is the row dependence on j and b j tilde and b tilde b tilde appears because you have to where was the no I mean b tilde appears because you have to now write j as you have to write now j in terms of b tilde so basically you have to write j ok maybe this should be right in the transformation right these two equations should give you this transformation right this is implicitly given this transformation right so this is called spacetime duality I mean our spacetime flip this equivalence between the two the propagator in these two directions this was the first time observed in the article by Boris Gutkin Thomas Gurren company spacetime duality now but why is this useful I mean then the question is it really sounds like a super cool property but in fact this was what preceded dual unitarity dual unitarity is basically generalizing this feature not completely because I have not yet unitarity but now what I will insist now I will insist that this guy is unitary it has the same algebraic form but now I will ask him to be unitary right so I will when is it unitary it's unitary when this matrix when this parameter j tilde and b tilde are real so u is unitary if and only if j tilde and b tilde are real otherwise it's not unfortunately unitary for that I have to sketch another thing so for that I have to sketch the key trick I mean I think this will be the main part of this explanation to show you how to do the averaging how to do the averaging of this object but you see this object is a two replica object it has two traces so I have to now unfortunately erase a little bit because I want to make another picture slightly below I will take a complete identical copy of this picture which represents now this represents trace of u to the t and this other picture represents trace of u to the minus t so it's just complex conjugate again this is x this is 1, 2 to l 1, 2 to l this is again time and now the product of these two pictures again these are two independent tensor diagrams tensor network diagrams so if since the things decoupled into product there is no coupling seemingly no coupling but there will be coupling because there will be averaging we have to do the disorder averaging and this disorder averaging will produce coupling but let's see how first of all how we would do disorder averaging if we would contract along the rows as we wanted at first this would be impossible because disorder is hidden in the spatial modulation of the field but now what we do rather is to contract along columns where for each column field is different and in the subsequent column is completely independent so what we can do we can average over the field independently because field is IIT so if you contract this diagram column wise we can basically average locally so then it becomes like a quantum channel like a noisy quantum map where the field can be averaged over in each instance of the map because space becomes the new time then you can average over disorder because disorder is IID in space so that's the key the trick in the nutshell so what we will do now we basically take all these things together and we baptize it as a transform matrix so that's how it goes basically to replica calculation disorder averaging is done by spacetime flip then you can use the fact that disorder is IID then we are in business ok ok in the rest is technicality so I will have to I think I will wrap up in 15 minutes for sure but let me now just ok so how does it go now let me do now this calculation now this is a three line calculation which I will do for you just to make sure we all follow this argument now this is I will just put a star here this is the conjugate of the matrix of the many body matrix this is still a vector of the fields right now I will do the duality so then there is this duality formula says that I can write trace of u kicked easing to power t as a product as a trace of a product of j going from 1 to l u tilde to hj I mean instead of doing this sweep where I take the same propagate doing this sweep where this is the same at all times but it has modulated field I do this sweep where I have product of matrices with different local fields but constant in the new space which is the old time so this is a constant field easing models but they have different value ok great so now we are doing that and then I use again the fundamental feature that trace can be factored so basically I can write now think as a trace of this guy tensor this guy has to be a complex conjugate right and now I can now I can plug this averaging inside because now I can do averaging independently on each factor so basically this is trace of the product to l and then I have expectation value of hj now this becomes I mean I can forget about j here because it is the local field which is constant it is homogeneous in the new space and it is I do it independent averaging so I can forget about j so basically I can also forget about the product here put here to power l and now I baptize this as I say as a transfer matrix ok so now I have basically reduced my problem of computing spectral form factor as a trace as a again as a kind of partition sum of two replica model but I mean it is like a transfer matrix to some power some transfer matrix now sometimes this transfer matrix acts on tens of product of two spin chains so this guy in the morphism of c2 to the t cross c2 to the t so it is I mean it basically it acts on two spin rings of t sides one, two to t and another one as well why do I need two spin rings well these are the two spin rings one and the other but they are coupled because of the averaging but this coupling is very nice I mean now I I will try to do these steps two steps to really show explicitly how this matrix this transfer matrix looks like but I feel tempted to go to the computer and then I will probably lost you also so better not to go into all the detail so right so now so let's see I mean what we want to do now let's assume that the field is Gaussian assume hj Gaussian with field with mean h bar variance sigma square so I will assume that this expectation value is evaluated as a Gaussian integral any function of h I will compute as an integral minus infinity to infinity Gaussian kernel h bar divided by sigma square over square root of 2 pi so now I want to compute what do I want to compute and then I also do I define you kick teasing of h which now depends on the local field kick teasing so that's the dual kick teasing I mean that spatial kick teasing but you see I mean I assumed that probably I went too fast there but I will assume and I have assumed that my utility is unitary and unitaryity of utility means that I mean I require that j j tilde and b tilde are real but the fact that requiring j tilde and b tilde real implies that they have to be equal that j equal to b that all these parameters have to be equal in modulus and this is equal to pi over 4 so they are all either plus or minus pi over 4 now there are many cases four different cases I will not discuss all them separately but if you just stare at these if you see that the only solution which makes j and b j tilde and b tilde simultaneously really is the one where you start from pi over 4 pi over 4 plus minus and then also j tilde and b tilde pi over 4 so that's the value and this is the so called self dual point of the kick teasing model which corresponds to dual unitary circuit so in this case this is a special instance of a dual unitary circuit I decided to be just more specific but I could formulate these things also very generally if I wanted ok so now one useful identity is to isolate the z field let's call mz let's call m with m I designate the components of monetization so total z so now this is in time so that summation index is tau or 1 to t so I can always write like this I remember how kick teasing was formulated he was here so this was h-easing was diagonal and it has only commuting terms so you could separate one body term from two body terms and one body term is just this diagonal ok and then let's simplify the calculation of the transfer matrix now it's a Gaussian integral plus and what is nice now this is just algebra of manipulating tensor products so what I can do now I can write this as this tensor product this times this tensor product this but then the first factor is independent of h I can put it out of the average so it's a unitary matrix which is just a transverse field easing model there is no longitudinal fields here so this is unitary matrix which is by the way also free-forminizable because it's just transverse field easing and the rest is just a Gaussian integral of single body terms a Gaussian average of think but then computing this you get it's a Gaussian integral it's an exercise so I will just spit out the result it's again a Gaussian now I have to speed up a bit so I will try to flash just the main things so what I get now is some super operator you have seen super operators during this week already so you can think of this as a vectorization of a super operator this is like a taking commutator with respect to mz so it's just this super operator squared and back so it's like a linear quadratic form commutator with mz so I can basically pull up so what I will do at the end I will put it I mean these two terms commute so I can just put this guy back inside here so at the end of the day I have a kind of general expression for the transverse matrix which is you kick easing and now I go back and then times something which I called contractive map which depends on the variance only and this is like a Gaussian of a commutator and remember to just remind you what we are doing now let me if we have already evaluated the spectral form factor as a trace of this transform matrix to power L now for this specific dual unitary case of kick easing model this piece is unitary and this is kind of contractive or better to say non-expansive so it has spectrum this is just exponential of a commutator commutator is a kind of Hermitian super operator so it has a spectrum which is real and it is between 0 and 1 and it has eigenvalue 1 as well it has eigenvalue 1 corresponding to all vectorized operators which commute with mz so if you apply this to a vectorized operator which commutes with mz then eigenvalue is 1 because this is 0 and then e to the 0 is 1 so it has a non-zero kernel I mean non-trivial kernel or if you want non-trivial eigenvalue 1 eigenspace that is of course very important so the point is now because you see I mean we want to do the thermodynamic limit now so what we want is basically to show that there is a kernel or eigenspace of eigenvalue 1 that becomes the dimension of eigenspace a number of eigenvectors of eigenvalue 1 the second thing to show is that there is so basically what we will show what we will not show but what we can show I will just describe in 5, in 2, 3 minutes what we can do with a lot of hard work but nothing really I mean the main kind of progress is to be able to write just really brutal mathematics so what one can do is one can show that first of all eigenvalue 1 is degenerate and it has multiplicity which is e or 2t now in our case it's 2t for dual unitary circuits which wouldn't have time reversal symmetry to be t so it is exactly well in this case as I say it's 2t but then the second thing to show is that there is a positive gap with respect to the rest of the spectrum so that there is no other eigenvalue on unit circle other than 1 so we have this situation which is well it's not mixing because the eigenvalue 1 is is multiblet degenerate that's why we have result which is not 1 but this is related to t and this is related of course this t now what we are doing basically we are looking for the eigenvector and these eigenvectors the fact that these eigenvectors are t-fold degenerate is related to time translation in variance symmetry so basically now time is the new space so we have basically a problem which is translation variant in space which was the time the number of sides is t so we have translation variance in this space and now we have basically eigenvector in each symmetry sector we have the translation variant the composition of this problem in symmetry sector we can show we find a unique eigenvector and that corresponds to spectrum from factor being t I think I will stop here I will not go into any formulas I wanted to flash through a couple of lemas but I think it doesn't make any sense I mean the key is in this kind of words that basically it's all about translation variance in time of course this is the hard part of the proof is to show that in each symmetry sector the eigenvalue is unique there is no other eigenvector and this is the hard part so this basically is algebra is to basically show that the presentations of the some algebra of some operators some operator is irreducible ok so I think I've said more or less everything I wanted to say I'm hoping to questions so I'm still here for a couple of hours so let's discuss more thank you so much for the beautiful lectures questions can you classify the dual unitary so the canonical representation when you are writing so the jx, jy part you take to be pi by 4 so when you when you start classifying the dual unitary in the previous lecture and you write u equals to there is a jx, jy sitting and you get it to be pi by 4 and here the self dual limit is also pi by 4 so is there any yeah it's related of course I mean this pi over 4 is kind of really halfway between two trivial cases I mean these models are very similar to these models that people discussed in the business of time crystals where they have this pi I don't know how they call it pi time crystal phase where one of these parameters will be pi over 2 it's the most yeah maybe since you ask I think it would be instructive to write a phase diagram of this kichtising model there is two parameters j and b which are crucial and from 0 to and basically you can limit this parameter space to square between 0 and pi over 2 and when two parameters are equal this is like a critical line why critical let's assume first that there is no longitudinal field so then this becomes a free fermion model you can write a dispersion relation for quasi particles and in this line it is gapless I mean it's critical so this model is critical in this line but then it turns out that if it's pi over 4 I mean there is another line where you can also argue that the same and the intersection of these two lines is this pi over 4, pi over 4 which is the coolest point of this parameter space which is both critical and chaotic so as I also like to call it critical chaos and since you asked I mean there are many things I forgot to say but one thing which is absolutely important I mean after this calculation we've shown the spectrum form factor is 2T now we did thermodynamic limit so we pushed Heisenberg time to infinity so we can only access the linear ramp of course nothing else but it's extremely cool in times which are very short because for genetic models we would find the so-called tawless time effects effects which are non-universal for short times and only appear to satisfy random matrix statistics after a time which is called tawless time I mean related to some transport phenomena or whatever something non-universal in this dual geometry models in general there is no such thing spectrum form factor start to follow random matrix from time one onwards which means there is no timescale which means this is a critical chaos this thanks for asking thanks for being around the whole week and yeah thanks to Tomas again for the nice lecture


Thank you very much for being with us here today for this our third in the LGBTQ Iran series. We have the multi talented someone as to whose visual we've just lost momentarily. He works in Iranian theater and brings together trans art therapy and activism. I'm really delighted to say that his film Hamantor Hamatun Manu Mishnasin you all know me has been shortlisted for two very important international awards. Now, whilst we wait to get someone back I'll just go through the order of the day if I may. Someone's going to share elements of this upbringing. And look at some film expert excerpts from his theater work, followed by his own commentary about the work he does in trans theater in Iran. We then have Dr. Bahar Azadi as discussed as a specialism for PhD studies were trans studies in Iran. Before sharing your questions with someone. And now please bear in mind the chat section we're going to keep closed for this section. And then we will please for the Q&A any questions you have address them in the Q&A section. And someone's going to speak in Farsi and I will be translated. So thank you very much so much. Thank you so much for being with us today. He'd like to say hello to all thank you for being here and also to thank Bahar, Aki and myself for part of this event. So I am someone all of us are born at a certain place in time. I was born as the last child of a very large family busy family. I was born in 1967 the photographs you see before you are with a very very old friend and also with my parents to the right. Sadly they are passed from this world. I tried very hard to be a well behaved child but unfortunately I was rather naughty. I was in love with my mother and my father and my father-in-law. I loved my mother and argued constantly with my father over my mother. The majority of arguments I had with everybody was about the love of my mother. I loved her so much that I wanted to even be by her side. I was in love with her and I was very happy with her. I was very happy with her. I was very happy with her. I was very happy with her. The majority of arguments I had with everybody was about the love of my mother. I loved her so much that I wanted to even be by her side. And this picture you see is me age 13, a picture he requested that we take together. The picture on the right is me age 23 years old when I was performing in the performance of Mahdakeh Mahdakeh in Iran. The multi-talented artist photographer who took this photo with us took this photo. It was a very difficult time for me. The picture shows how sad I was. I didn't know what to do, what to be. And Hushang wanted through the medium of photography to help me get a better grasp of myself. Hushang also took a photograph of the productions of Mahdakeh in America. It was a part I played as the main female role I had in this. This was played in Shahood for 90 days taken around various parts of Iran and I was recipient of many awards for my part in this play. After winning the awards I remained in Tehran and did not return to Shahood. And I attended multiple classes. And I worked with wonderful artists including Dawood Rashidi and this is a photograph from the Richard III performance in 1999. Although I was young I played the role of the queen's mother. This play was really important. It was a master class for me. Learning about humanity, how to deal with others with humanity. It showed me so many ways that I can progress within the world of theater. I entered the medium of TV and cinema. These are two pictures from them. In the picture on the left I played a part of a woman who lived in the basically in wasteland in open land. And in another you see me play the part of a magician who is in the streets in the open air. I don't know quite how to explain this idea of basically people in the open air living on the streets and on the roads in between cities. Thank you very much. So I then went on to work with the grandies of Iranian cinema including Kimiai. In one of the pictures you will see me play the part of a bodyguard. In an earlier film I played a part of a female in a village though Mr. Kimiai realized that the issues I had with my own identity. Only female to ever play this kind of a bodyguard role in film. You will also see some films he's worked with Tahmin Amidlani. But this film was for four years it was not given permission for showing to the public. And at the time that it did come out it just so happened that I was also performing. By then I had had my gender reassignment and I was working in another film. So for people it was very interesting to see both these characters as female and later as a male that I played being shown at the same time. So you will see the 2006 film that he worked with Reza Amini and you will see a picture of a TV series that he took part in called Sunny Nights. And before that I worked with Asghar Farhadi in a series. I played one of the main roles in a house in darkness 2003. After I had done my operations the actual director wanted me specifically to play a male part in the film. So having played female roles it's not a director but actually she would. So Mr. Kamal Tabrizi who I had worked with before when I had been in my female sexual self and also invited me when I'd had my gender reassignment only after two operations to specifically play a male role. He found this very interesting to see me in both female and male role. Mr. Bahar Janak Sabadi, I had worked with Reza Amini for all these years and I had worked with Reza Amini for all these years. I had worked with Shama Akhar and I had worked with Bazi Khan and Bazi Gari for all these years. All these years whilst also acting in films I directed and acted in the theatre as well. The majority of my work in the theatre related to women and gender. The last supper and Bazi Khan were actually shown at festivals. However both were disallowed from public display so therefore we were not able to share these plays with the public even though they won awards. But I'm sure that I'm too passionate about it. So even though they won awards at the theatre festivals we were unable to share it with a wider audience. They said your work smells. In Iran when we use this term your work smells in other words there is permeations that go beyond what is the obvious. So it's basically a worry into politics, society, economy and what have you. Mr. Bahar Janak Sabadi. All these years I fought to get my work done. All these years I fought to take my work to the stage even till today I have problems with getting my work out. You have heard about my two performances and you have never been to the stage before. In our film and your theatre. My theatre. Here you see two of my most recent theatrical offerings. You all know me 2016 and photos below show be who you are not 2017. Both these plays were shown in non-governmental small sort of basically fringe theatres with much public support and admiration however they were never able to make it onto the major theatres within Iran. However I am delighted about this independence. These are more photographs of how can you still be who you are not, be who you are not, which was a play without dialogue. After these performances, us the mayor of the Berlin Festival and also from France we had invitations to perform this play in France and Berlin. Mr. Bahar Janak Sabadi. The play you see here 2018. The Idle Out is actually an amalgamation of the two earlier plays you saw. However within this we had 12 minutes where we were invited trans people onto the stage to join the audience and engage in conversation. The workshops that we did allowed the trans people to face the public, engage with the public, ask the public questions and likewise to be prepared to take the questions from the public. The most recent performance is autopsy, it's six episodes and in this we bring up all the issues around LGBTQ. So these are some more images from autopsy 2019 where in each scenario we look at different experiences of the various sectors of the LGBT community. So you'd have one section within the trans, certain issues there, one between the lesbians or gays or what have you, now he's broadening it but actually bringing in the wider community. So the scenes you see here are from the various rehearsal techniques, the top pictures are from workshops in Berlin which I was asked to hold for the students. Thank you. Thank you very much. Someone has now explained to us in brief some elements of his work and now we're going to ask Aki to kindly show the video that he's prepared with basically a montage of his various theatrical offering. So Aki, over to you for the... The people of the community are going to work with a different way of working. And in the midst of the bloodshed, they are going to have a hard time with the girls. I would like to thank all the women and the people who are there for me. Good evening. Good evening. I'm working. You're going to have a hard time. Dad! The community has to be self-employed, self-employed and without any work. There's no way to make a living out of it. Do you remember this place? No, I don't. I don't want to go there. I don't want to go there. I don't want to go there.  Yes, I'm going back home. It's that this theater is armed. That is to say, a weapon to fight against domination, both from the point of view of the job, but also from the point of view of the change... Something that we have to do until it's done. Until it's done. It's done in two ways. First of all, you have to change the agency. I'm saying this personally, you're a good person. Thank you very much. One thing I've said before is that I think it's very difficult to understand the language. It's very sensitive, it's very hard to understand. I'm just saying that just watching that brief moment of someone's work, there's something very corpore, engaged, involved, and emotional. I have tears in my eyes personally. I love you too. Thank you so much. Do you have any words to say to Mr. Sadeh Bahar? Yes, I just want to say that the theater shows its work. The work of theater is to show the wise, why do things happen? We live in an aggressive world. My style of work brings in the violence and the aggression, and it involves the audience in that process of aggression and what have you. We don't have the authority. What does that mean? It means that we have the authority. Minority. The fact that we are a minority needs to be addressed. In this way, everyone is a minority to everybody else. We were born trans. We decided a certain point to operate our physical self to what we believe. We used to practice for up to seven, eight months without a single budget, and everyone would turn up with their hearts and minds fully engaged. To remove shame amongst the audience. When I would ask a trans actor to take a lipstick and ask the audience to put the lipstick on them, this would allow the audience to actually face their own prejudices. Many have had their heads cut off, like Ali Reza. The theater of similarity, to show what is. The actual project of showing what is allows and teaches people to face themselves and the issues in front of them. Thank you very much. Now we are going to hand over to Bahar who is going to give us some more academic overview of someone's work. Thank you. Hello everyone. I'm so happy to be with you here and I would like to thank Roya and SM and so as university for inviting me again this time as a discussant. I will not take much time because we have this opportunity to hear someone and I met someone in 2017 when I was in Iran, and I did my research on my, my PhD, and I had the chance to participate in his workshop and some of his performances and later in Paris for two nights of performances of Be Who You're Not and I have two points to make regarding someone's works and performances. The first remark is that one way is the way different audience members in Tehran, Paris and Berlin reacted to the omnipresent violence that is in his work. I think that everybody felt this violence that is omnipresent in his work. So one response or react to the violence they observe in these performances. Do they reproduce it and contribute to the cycle of violence or do they avoid or control the violence. The second point is about what someone have already mentioned is about the work and how he used the theatre as a trap and he tried to facilitate the experiencing of shame. And this experiencing of shame it's not only for queer actors and audience members, it's really for everyone who participate in his theatre as audience or actor. So he encourages us to face or encounter a feeling of shame on an individual and collective level. This is made possible through the participatory nature of his work, which is inspired by his drama theory of stage. For example in Autospe as he said also it was really interesting for me that one of the trans actor, trans woman actor of this piece, asked the man, especially the man in the public in the audience to put lipsticks on her. So men usually react differently to this form of participation of course because this challenge, their perception of masculinity, femininity and gender norms by putting lipstick on one participate in the disruption of gender norms, at least in this little participation. So not only his theatre is participatory but also doesn't have a fourth valve. It means that there isn't any valve between audience and actors. And most of his piece doesn't follow a pre-written script. Someone is inspired of Antoine Arthur, Augusto Boel, Brecht and so many other directors and authors, but more generally as what I feel is that he's really interested and inspired by the theatre of the oppressed. So, according to Julian Boel, who is the son of the Augusto Boel, Brazilian director who invented this form of theatre name, the theatre of the oppressed in the 17th in Brazil. The theatre of the oppressed exists in more than 80 countries. I don't know if Julian Boel is aware that it exists in Iran by the only someone. Someone inspired of Antoine Arthur, I think I will let him to explain more because of the violence that you felt in his work. And Julian Boel, so regarding the theatre of the oppressed, said that it took a long time for his father, the founder of the theatre of the oppressed, to understand that the theatre of the oppressed works but not for all subjects and for all times. Let me just very briefly give you some elements of this theatre because it can help us to better understand the work of someone else too. In this form of theatre, there isn't any, as I said, there isn't any forceful, so it's up to the oppressed to take charge of their own representation. There is the centre of gravity of a forum theatre, which is not the stage but the audience. So the form of classical theatre are themselves form of operation. Because we have in one side those who are actor and on the other side we have the audience who are sitting all the time in dark and have just the right to upload it at the end of the theatre. And according to Julian Boel, this form of theatre, the theatre of the oppressed is a practice for the revolution but emancipation is a larger process than this. This theatre of the oppressed is just one step or one level. So to wrap up, I want to say that someone is not just an actor in cinema or theatre, but also a social actor. A social actor is an individual who exercises agency, opposed to fix social structures that determine individual or corrective actions. From the viewpoints of action theories that you may know these theories but I don't want to talk about theories because we don't need it. An individual construct and shape their identity, their beings, they work through the choice and variety of ways rather than fixing to prefixed structures. Like for example gender is perceived as a prefixed structure that is assigned to us as birds. So someone as a social actor, not only in his lived experience as a trans man, but also in his theatre disrupts or challenge the power relations and structures. I let someone to develop more these comments, mostly about the violence. I think it's very interesting that he shared with us what are the different reactions of the audience in Tehran, Berlin and Paris to this only present violence in his work. I think after the audience questions. So thank you so much for your attention. I will translate in Farsi for someone and then we will return to your questions in the audience. Saman, I am very pleased that you have included me in this program. I tell you very briefly what I said. I pointed out the two points that you said in the beginning.  And this challenge is only a shame and it is more than a shame for the players, for all the audience that watch this program and feel ashamed. And this shame is not only about the norms or the consequences of gender and gender, but it is even a shame that when I see someone who is not happy, I am allowed to interfere, I have to interfere more. The other point that I said was the joy of the matter. One of the methods is to fight with joy or to make a living with the joy of joy. And for me it is very interesting that this film, which has become very popular, which you have used a lot in the past works that have been done in Brazil, is a reaction of the audience in this film. And I think it is very interesting to talk about it. And with this joy, how did you get involved? Did you make it popular? Did you make me popular? And with that joy, what did I do?  This social screenwriter means that your own action is not only about your daily life, but about your own work, your own action. And you shape yourself in the forms of the previous ones. You don't know yourself. And from the beginning this was your challenge, and the challenge that you invite others to. Thank you very much. Thank you very much. Salman, do you want to answer the questions of Bahar to me? Salman is going to answer Bahar's question before we address your questions. The very interesting question you asked about the differences in the reactions between the Iranian audiences versus the French and German audiences. Wow, that's really interesting. So in Iran, the reaction would be for the audiences to get engaged and actually beat up and try to stop the person who was being aggressive. However, in France and Germany, whilst they would block the fight, they wouldn't actually themselves engage in violence. For example, in Berlin, the women were trying to stop the person who was being aggressive. And they were trying to stop the person who was being aggressive. And a hundred women were trying to stop the person who was being aggressive. In this very same performance of Be What You Are Not, I actually put a scarf on the men's heads. Oh, this is a very sort of a gendered social reaction. So in Berlin, the man who had a scarf placed on his head stayed with Iran. However, he actively removed the scarf from a female's head. Because of the symbolism. The symbolism is attached to the scarf. Because I don't see it as a symbol of Russia. Someone is not looking in any way, in a symbolic way towards Russia. But it's clear his German male audience felt a bit protective and didn't want to sub-sume or sub-juice the woman. However, it's clear that the man who was being aggressive felt a bit protective and didn't want to sub-sume or sub-juice the woman. However, it's clear that the man who was being aggressive felt a bit protective and didn't want to sub-juice the woman. Basically, that's why he removed the scarf from the female's head. One night, I told the boys that I would like to reduce the fun. I was trying to figure out what is fun and what is action. Do you want to see who wants to do action? Yes, I was surprised that there was a lot of fun. I said that I would like to reduce the fun. Do you understand that there is no fun without action? Yes, of course. Because there was a lot of fun in the night with my brother and sister-in-law. Where was this? In Iran. Yes, that was easy because he did have an incident where once one of his actors was really choked to death in an Iranian theatre. So he realized from then to gauge the audience before actually saying how violent the scenes should be. Yes, that's right. I hope you answered the question. Thank you. So now, if I may, I will move on to the questions that we are receiving from the audience. I guess it's a bit in the question. The first question is from Masih Zekar. The first question from Masih is, is the operation something that allows you freedom or does it actually bring more to bear upon your shoulders? Yes, I will answer. Operation is a choice. Sadly in Iran, the young youth are actually encouraged to have the operations. And that choice is taken from them? Yes, they are forced to do so. Yes, because they don't say no to the children. Usually the issues around birth, your certificates, like your Noggozhan or not passport, but your basically certain certification in the nation of Iran, there is problems about gender. Therefore, so many are encouraged to do this. It is not always clear that it is an actual choice because for your correct paperwork, you must be one or two. You cannot be in the middle. In our society, you have to be either female or male and no other and this is wrong. Why have we been born trans? And the trans youth have to reach enlightenment and understanding themselves. They must believe themselves and love themselves whatever their physical status. Even in my female body form, I always knew myself as a trans man. My physical designation does not establish how I feel about myself. There comes a point where one reaches the conclusion that I want to alter this physical body that I do not appreciate. Before I actually had the operation, I reached a sense of peace. The operation merely was a process. I had already gone through making peace with my situation. Let me see if it was freedom or not. No, I do not look at it that way. I was always free. I did not allow anyone to take our freedom. This is a personal opinion. The more you accept yourself, the more you are able to understand yourself, the more you are able to understand yourself.  This is a very important part of your life. Because a person is important for his own life. This is when he becomes free. The operations do bring a sense of freedom or they actually create more issues. He is saying for me, it was never the issue. I knew who I was before the jadrahi. The main question is about knowledge of oneself, acceptance of oneself, to feel a sense of self-importance, to find confidence within society. I think for someone it seems the question of before and after the operation are not so much the issue. Because the operation was simply a step. He had already taken the main step which was self-love and self-acceptance. My name is Rick Shassan. The trans actor differs in your film. Do you feel that your experience is different from an artist's experience in films? So, have you found that your experience as a trans artist differs in your film from your theatre work? I am not sure about his question.  Do you feel that your experience is different from your film and your theatre work? So, the theatre I direct is very much based on gender issues. So, the theatre I direct is very much based on gender issues, not just trans or LGBTQ issues. However, the acting I do in the films, I am bordered with the parts I play. So, if I enjoy the part, that is what matters. The actual, it's in the theatre that I get to express my ideas about gender issues. Let me put it this way, does the Iranian cinema community respond or treat trans artists differently than does the Iranian theatre community? So, does the Iranian cinema community respond or treat trans artists differently than the Iranian theatre community? So, the Iranian cinema community respond or treat trans artists differently than the Iranian theatre community? So, the Iranian cinema community respond or treat trans artists differently than the Iranian theatre community? So, the Iranian cinema community respond or treat trans artists differently than the Iranian theatre community? So, he's saying that unfortunately in both fields he's finding some bad behaviour. Because he's experienced life as a female artist before his operation, even at that point he drew a certain line of respect that people weren't meant to go beyond. He has continued with that and now he does very few jobs. However, it's always understood that people have to toe the line of respect. But generally he finds that the trans community are not really treated with enough respect and not really given enough opportunities in the theatre and film world. One more question, I'm deeply moved by your story and your works. Thank you for sharing. My question is, what are some of your physical body practices that help you feel more at home in yourself, in your skin? Thank you very much, I'm really proud of you. What are the physical and physical practices that help you feel more at home in your skin? I don't feel a sense of ownership towards anything, not even my physical body. I have much more of a sense of ownership over my spirit and soul. To not allow any senses or borders for my spirit. This physical self shall go to the dust.  That was the answer to that. Based on what I heard, can I conclude that your theatre is both influenced by the theatre of cruelty and the theatre of the oppressed? Could you please speak more about that in dramaturgy and in the way you guide animals? Let's talk about your theatre, the theatre of pleasure and the effects it has on other people as well as the effects of oppression. I have something to say to Bahar, what is the name of the director of the theatre? He is the Brazilian director of the theatre of the oppressed. The theatre of pleasure and the effects it has on other people as well as the effects it has on other people as well as the effects of oppression. We have no written script ever. We have no written script ever. So we have no script, everything comes through the rehearsal and the workshop and often what you hear in the script is verbatim what has already been said in real life. She is a zendige, ask her name here and salakon. So often what the script when it does come to be is made up of conversations that were had in real life and we bring them to the theatre. There is never a time when it's all rehearsed, scripted and they just say it out loud. It comes from a real place, real emotions, it comes out during the workshops and rehearsals then it becomes part of the play. He believes that this kind of theatre where you watch something unrealistic taking place on stage without any connections with it and just simply the viewer without relating directly with it he finds to be a useless form of theatre. And now the way it has to be is that theatre has to throw a light and shine a light on things that are not seen and literally force people to face these realities. Okay, and that's so by the way, ladies and gentlemen, I must say that we are getting so many questions and because we're rather limited with time we have to finish in about 24 minutes forgive me if I don't get all your questions in. Akhi will be providing emails for the panelists, the discussion, everybody so you can get in touch with us if you have any questions that we weren't able to address. Okay, a question for me here from Azadi. This is Paula Rivetti says thank you for your wonderful work. Dr. Arastu did it, so I'm going to ask this question directly from Paula Rivetti from Dr. Azadi. How do feminist movements in Iran integrate trans people, their experiences of oppression and demands? This is a very, very, very important question that unfortunately in Iran we are. I didn't really did research on this topic but for my PhD I search a lot to see how feminism in Iran have integrated the question of trans people and unfortunately there isn't any integration or mixture of the of this topic into the feminism and we can sell different reasons for that but I think one of the reasons in that maybe the feminist, the real active feminist in Iran, there isn't a lot of people from the community of LGBT or queer people and that they don't pay really attention and the most important question for feminists in Iran are the questions of inequality between men and women and the question of gender which is the very important question isn't really integrated with an approach to trans people. So this is my answer. Thank you very much. Let's go to another question. Please feel free to help me out with the visual of the visa back. I think I'm completely okay. I'm completely unfamiliar with your work. Forgive me if my questions are inappropriate. It seems that the violence weaves together themes of state violence, family violence and violence against queer and transgender people. It also seems that there's an interrogation of sader masochism chosen freely among them between participants. Do you see what's going on? You see, I think I work with the knowledge of this type of work. That happiness comes from the time that I want. There's a place where I want happiness.  And for me, it has become a sin. It has become a sin for me. That's right. So I believe that violence happens when I want it, when I want happiness. That's right. It's a time when violence can be anything. At the point, anyone can be the victim or the perpetrator. The perpetrator comes and takes Ghorbani. You know, when you basically take victim. Ghorbani means more than victim. It's almost like a symbol of victimhood. When they say cut your child's head, sacrifice. It means sacrifice. They choose a sacrificial lamb. That's right. It's a person who comes and takes sacrifice. What happens after that, Saman? Women, women, men, and all LGBT people, must be put in a place where they can be themselves. And they have the right to sacrifice themselves. Nobody has the right to do it. So trans females, trans males, and the LGBT must reach more self-understanding and understand that no one is going to give them their rights. It is up to them to actually fight for their rights. And as Dr Azadi just mentioned, even feminist studies do not include them. It's about finding trans voices and actively making sure we have. The people I reach are the ordinary people, people who seek knowledge, but whose hands are tied and can't find it in multiple places. Okay, so the work that you see is really a social study. It's an ethnographic social study of what's going on. It looks at the aggression within the political system, within the family system. But most importantly, it first and foremost looks at the harm and the issues that one brings onto oneself. So it's me and myself first, and then the state and family and society at large. We must one by one seek to understand more and learn more. And it is then that we will find the independence that humans need to have. I hope that answers some of your questions, Colette. I'm just trying to make sure that I include as many as I can. And how I understand the danger. How about shifting? I don't know how they play out in Iran. Okay, there's a Christina Rostampoul. Someone joined him with the thank you very much for sharing your story with us, etc. You mentioned how in Iran, the only gender identities are allowed on male and female. And other gender identities are not accepted. Could you please speak some about the behaviour of practices you observed in Iran, where non-binary artists or other gender non-conforming people were pushed to choose a gender identity they didn't identify with. Artists who are non-binary and non-gender nonconforming people are pushed to choose a gender identity they didn't identify with. So in Iran, yes, you have to be either male or female, but actually the artistic community is one of the most old fashioned and undeveloped sectors of our community. Because they are afar from the people. They don't see the people. They are unfortunately seeing the wrong things, they are looking for fame, followers and so forth. So he's aware of a large sector of the LGBT community, lesbians, gays, trans who are actually excluded from work. This is not the people who can take the blame. It is actually the uneducated artistic community of Iran who should take some of this responsibility. It has become like the artistic community in Iran has become like a garage where everyone can park up inside. This question is very interesting. She says that in America, this is a choking scene where a woman and a man are talking. She says that this incident had a fresh beginning. And a lot of people are making it so that the police can take the people and tell them not to do this. And the boss says that this is my fault, this is my fault. I think it's really important to let her say that she's actually aware of a scene in her own town in the US where a group of men were prevented police from protecting a woman who was being choked. So basically it's interesting. It's very interesting that there is a total scenario of oppression to Iran, and there is a trans and there is a situation as such happening in America. Collette wants to know how can I learn more and view more of this theater? We have now handed over some of our theater recordings to schools in Australia and Canada for the idea of actually disseminating this theater online. So all the information relating to someone's work and things that may be upcoming and forthcoming, you'll find on his Instagram and on his website. So he said that he's reachable via all these platforms and he can help anybody with issues that they raise with him there. Thank you very much for your interesting talk. In reference to theater of cruelty, the references you made and your inclusion of violence on stage in an ideal theatrical world. This is an end goal to show the violent experience of being transgender in Iran or to invite the audience to dissent and protest the system of oppression, even through violence if necessary. This is an end goal to show the violent experience of being transgender in Iran or to invite the audience to dissent and protest the system of oppression. This is an end goal to show the violent experience of being transgender in Iran or to invite the audience to dissent and protest the system of oppression. So first of all, there is no end goal to his theater. When one ends, the other begins. There have been performances at which the audience haven't left sitting there expecting something more to happen. And he says we practice resistance in our theater practice, which is a really important point. So the very actual creating of this theater work is itself a form of resistance. Do you have anything else to add? I don't have anything else to add, if you don't have anything else to add. Yes, we are from Madadpur. Yes, a question for you dear viewers. Yes, there is a connection and cooperation between the Tajasumi and Tiaat in this work. Is there some relationship between visual arts and theater arts in your work? The visual arts can be really, really productive and useful for the work in theater, and I would love to bring more of it in. But you are saying that you didn't have it? No, because I didn't have it in the past. Till now there has been nothing. Now I have a question for you dear viewers. Let me use it a little bit. Let's see, now we have a discussion on this issue of water. For example, there is a person who is a great Tatek, a great film director in England, named Mr. Russell T. Davis. He came and said that he only wanted to show Hamjenskera on television. On the other hand, we had a series of films. We saw that a man named Eric Anderson, who is the director of Awards Watch, said that he saw a show called James Corden. He saw that when he saw Hamjenskera on television, he didn't want to use the word. He really went to Alaki. This is a really big issue. Especially when it comes to the transgender community. It has a different meaning. It's a story. Because I told Mr. Russell T. Davis that if he only wants to play Hamjenskera, he doesn't want to allow Hamjenskera to be a heterosexual. You know what I mean? They only want to help. So I just wanted to say that you all have a very important role in this key, cure-representable corner on stage and on screen. I'm just bringing to his mind.   So these issues that are coming out around who gets to represent who on the stage and theater and on cinema, because I think it's a bit reductive some of this because if I suppose if Russell Davis says only gay can play gay, then I suppose no gay can play straight. And that wouldn't work for me. I think we should be more open than that. But I just wanted to broaden that and ask someone, what about the trans theater? What does he believe about who has the right to represent trans on stage and screen? So who has the right to represent trans on stage and screen, in your opinion? In my opinion. The time when the girl's film was made, which was not a good one, actually, because the person who played the role of a trans and had the right to represent his life was not trans. So the film Denmark girl, which had a non trans character playing a trans, that's one of the examples he's going to talk about. She played a part. She didn't live apart. So whereas if he had played, if she played a part as a physician, physicist or a mathematician, she was playing the part of that. She could live it as well. This is different. She can pretend to be a physicist, but you can't really pretend to be trans. It doesn't always have to be trans.  They are not representing another representation. So he said, if I dressed you up as your husband and asked you to act as a man, you would only... But baby, is that not all of acting? Because I think this is a really important debate.  Can I have all of these beings? If this is not acting? It is. But we have the language. We have the language of language. We have the language of gender. We have the language of gender. And many families have the language of language. Any of them have the language of language? I wouldn't huff to talk about it. Maybe even when you are being involved in the project, you feel there is being wrong or if it is being wrong. Anyway, that is a different aspect and maybe it is not being wrong like the Ayaz for more people. But it is not being wrong. So this is different. Either it is being right or it is being wrong. And there is no normal life in the most playful and playful way. But when a person chooses a question, his life is very normal. We know very well. Okay.  Exactly. Okay, one more question. Okay, now, I want to play a straight, straight, straight woman. Do you have anything to say to me? I can't do this. Or I'm a trans woman and I want to play a trans woman who has three children. It's very difficult to play. Okay. Because I've just returned the flip ram. Because he's absolutely for the idea that there is a certain reality and authenticity to the LGBT community performing parts within as LGBT characters. But I just asked him the question, what if I was a bisexual woman and asked to play a straight role? Or a gay woman and asked to play a straight role with three children. Does that mean as an actress I can't get that job? I think this is a really important debate that we don't have much more time for. But it's not finished between me and someone because I'm not in agreement with you. It's a really important debate and our time is up. What do you say about the Bahar? Bahar, what do you say? I agree with someone because I think that when we use the real trans person to acting in a film, they are acting their authentic body. That means that they show a form of realistic. They are not in the cliché of trans woman that cinema and media project. They are the real trans person that they are in different forms, different identities, different form of representing their gender. So I think that it is very important. And the other side is that we should give them this opportunity to perform as a trans person because they should be there not only because of showing the reality of being a trans but also to distracting this cliché, this cliché of giving an ideal type of trans. I must say, when it comes to trans, I accept that it is more trans than trans. But when it comes to lesbians and gays, I don't agree with that. Because on the other hand, you are a trans person now. If you want to take a part of the human being, you shouldn't do that.  And the person who is trans can understand the human identity. One of the reasons that I agree with this is that the trans experience is so particular that it's only fair to allow this to be expressed. But I really believe with the rest of the LGBTQ community, this actually closes their arms. Because if saying that as a gay woman, you don't understand what it's like to have a straight life. Because that's what you're saying when you say as a straight person, you don't know what a gay life is.  It's heterosexual. One thing I want to say is that I was born in Baghegara. And I work in Baghegara, in the cinema. Because my films that I make with Baghegara, maybe I look at it from the top, that this difference has been made.  But it's very difficult for someone to understand this. But it's very difficult for a person to understand this.  And I can respect myself for that.   But you didn't come to the world. I didn't come, I didn't come to the world. But no one is allowed to come to the world. Yes, but no one is allowed to come to the world. You have to come. You can be in the film, in the film, in the city, you can come to the film, you can come to the film. I have to think a lot about this. I have to do a lot about this. I do a lot of thinking. When I talk about something, I kill myself. Then I think, I am deaf when I talk about it. I am a person. Okay. We have just had an incident regarding the rights of everybody to be everybody that they can come to work with. everybody that they can be but someone was saying look it actually isn't because I said to him no one should stop you playing a soldier he said they didn't but I had to work really hard to make myself a male hero soldier because I was born a trans man I am still a trans man and on that note I'd like to thank Farsi Baharjan, Mersi Komadi, Akijan, thank you for always looking after us and someone are also very very grateful for your work. She is hoping that the day will come when all the poetry will turn into actual knowledge so basically shawar is all the words people say will in really will actually have a result in an outcome and then ladies and gentlemen just to say any questions you have you can address to someone directly via his Instagram and via his website Bahar Azadi we've given her email at before maybe Aki will be kind enough to quickly provide our emails before we go and the program will be available on Facebook and on YouTube at a later date. So Kodafes, you are in a book on imbacca? Kodafes, Kodafes, Kodafes, Kodafes, Kodafes, thank you so much for doing it, Kodafes, Kodafes, Kodafes and sorry again to all of you who we didn't get to ask the questions of but thank you for joining us. Kodafes, Kodane Gata.