Let's get the shoulder up here. So, yes, we have an exam coming up. And we will have a short review for about my office hours as well. So, again, the exam covers the materials through lecture notes number 7 that we completed yesterday or last lecture, sorry, Tuesday. And through the problems that start to have those solutions out, we're going to get this in as possible, all right? OK. So, after a month plus of establishing the foundations of quantum mechanics, what we're going to do now is try to put the mechanics back to quantum mechanics. We haven't really talked about mechanics, physics. We have this information theoretic foundation that we've established, but the most factor of the physical world, that's what we're going to do. That's what we're going to do for their main bear apart semester. So, I'm fond of this quote from Archon Paris, who's one of the great thinkers about the foundation of quantum mechanics. He was fond of saying, I think, roughly, quantum physics happens in the lab. It doesn't happen in the Hilbert space. So, we want to have a hook back to our space, our physical world. The Hilbert space is abstract, so there's a hook that connects these two together. And I think the best way to think about it is based on Noether's theorem. So, Emma Noether survived this theorem from a Bronte mechanics, but it follows, generally, all of physics. That if we want to think about space and time, we want to think about the symmetries of space and time. And associated to every one of those symmetries, the symmetries that are so-called continuous symmetries, that is to say, that you're described by the lead group, so we'll roughly explain what that means. Then, every one of those symmetries is associated with conserved physical quantities. We have conserved quantities in the world because there are symmetries. So, the reason that energy is conserved is to the degree to which the laws of physics are time-translationally inherent. So, time translation is associated with constant research of energy. And what Noether's theorem tells us is that those conserved quantities are the generators. So, that's what we want to define as well. Other symmetries are, we might have translational symmetry, stage translation, or the isotropy, the rotational symmetry of space that's associated with conservation of angular momentum. And that tells us that angular momentum is the generator of the group of variations. So, the hook between these space-time symmetries of the world and these physical quantities is through Wittler's theorem, which will derive next semester. Basically, what Wittler says is that all symmetries in quantum mechanics are unitary maps. So, there's our connection between the Hilbert space and the lab. It's through symmetries which have a space-time physical space interpretation and unitary maps which have a Hilbert space. There's our hook. And so, the mathematics, just the very basics of it, is that we're talking about symmetries. The set of symmetries form a group. And groups are sets that have a composition law. They have a composition law that's associative and it has identity elements and inverse elements. And we can represent the elements of the group as through unitary operators. So, for every element of the group, there's an associated unitary operator. And this is a representation of the group in that the composition law is just the matrix multiplication or the operator multiplication. Take two operators, multiply them together. That's the same thing as the operator that you would get if you did the group composition law. Yeah. It's an amazing, like, excuse me, question. But if you say you have time-translation symmetry, could that system not have space-translation symmetry? Yeah. I mean, we could have a circum-circum stance and, you know, we have walls here. And if we combine ourselves with these walls, this is not completely spatially symmetric. If I go over here, it's different than over here. Of course, what that means is the momentum is being taken up by the wall. So one symmetry can preclude any other symmetry? It cannot preclude, but they're independent symmetries. They don't have to have all of them. But the degree to which the overall universe is spatially the same as the laws of physics are the same in all parts of the universe. And there's no special direction of the universe, and the laws of physics are the same that all instant time is the degree to which these are concerned. OK. But as I was saying, those symmetries are the set of symmetries, the set of things that perform and say a time translation are a group. And we can, through Wittner's theorem, say that that group is represented by a set of unitary operators. And the fact that this is a representation says this. And that the identity element of the group is the identity operator. And the unitary associated with the inverse element of the group is the inverse of the operator. Which, of course, is unitary is the dagger. OK. And so what we're talking about now is time translation of that particular symmetry which is dynamics. OK. And so we have the group here, let's say, so I have time translation operation. And they are just a set of all times. OK. So this is every thing that translates by some amount of time is defined by the time by which I'm translating it. OK. So this set, of course, is a continuous set. It's the real line. This is what makes it a lead group. Is that the set of elements of the group forms a smooth surface. In this case, that surface is the one-dimensional one. OK. That's what makes it a lead group. It's a manifold, more precise. And the composition law here is just if I have two time translations, well, that's just I translate this addition to the composition law's addition. And the inverse, if I want to go backwards in time, I just have a minus sign. OK. And the identity element, 0, that's either. That means if I add no time to it, I haven't changed the translations at all. OK. So we're going to translate relative to some fixed time. So we're going to say if I want to translate in time, bless you, some time t0 to time t. So really, I have to say what my initial time is. OK. So my element of the group is represented by a unitary operator, which takes me from t0 to t2. So this is the time translation operator that translates me from that time t0 to the time t. All right. So this is my element of the group. And we also have this composition law, which I can write in the following way. Suppose I go from t0, if I want to say here. So here's a composition law, which says I translate from t0 to t and then from t to t1. That's the same thing as translating from t0 if t1, if t is between t1. All right. So now what's special about lead groups is that they're continuous. And because they're continuous, there is a sense of differential calculus. That's important here. Which means we can talk about infinitesimal translations for infinitesimal elements of the group. That's to say there's a notion of a near identity element. So what I mean by that is the following. So the identity element was if I have this, this is the identity element. I don't do anything, right? Translate it like nothing. But if I go to t0 plus some dt, some very small differential. Well, this is something which is equal to some anti-unitary operator that's a function that's proportional to dt. Why does that have to be anti-unitary? Well, the composition law would work if that's a linear operator. So that's for sure. It's got to be linear or otherwise the composition law won't work. But it's got to be a unitary operator. So that terms cancel out? So it's got to be the case that you dagger u is the identity, right? And what is that?  Because this is anti... Excuse me. Anti-permission. So if this is anti-permission, and I take the dagger of it, I get minus a, right? And this is then 1 plus dt, okay? And that's equal to a cross-terms dash. And then I get a dt squared. But order dt squared is zero if this is a differential. So in order for this to be a near-identity unitary operator, it's 1 plus something anti-unitary. And this thing is the generator of the group. Because it allows me to move away from doing nothing. It generates the transformation. Now, if it's anti-unitary, we can always write it as i or minus i under permission operator. And in this case, since this is time, it has units. That thing I'm going to call omega. So the anti-permission operator here is minus i times a permission operator. It has to be. And as we discussed, then, last time, notice theorem is the generator of time transformation. So that means that the generator must be proportional, that her mission generator must be proportional to energy. So in some proportionality, constant times the energy operator. In the energy operator, we always call the Hamiltonian. And we argued last time that this is some constant that has to have the units of energy 1 over the constant has to have the units of 1 over energy times time. Because you, for this differential map, this constant alpha has the unit of 1 over energy times time. Because this is dimensions. So what we have thus is that the generator of time transformation is the Hamiltonian and we want that to show a small distance from c0. That's the identity minus i times the Hamiltonian dg. So we want to solve for this time translation operator. Right now we have it as a differential. Let me write down a differential equation. So let's say I seek this map. The map that takes me from c0 to some finite time t. That's what I want. I have this. I can now have a differential equation for that. The way I do that is the the way in which the differential equation which says how this changes in time just from calculus is I think a small delta t. I translated by a small amount what it was before I would get that and divide by delta t. That's the definition of the derivative. What is this? Well, for so this time when I translated by a small amount delta t according to the composition law is first I go from c0 to t and then I step a little delta t. And this is a different, this is a near unitary map. I'm sorry. Near identity map. Very close to identity. Stepping by a little delta t. So this is one minus i over h bar that Hamiltonian delta t. So let's plug that in over here. I plug that in. This is during this out. I plug this in and I factored it out. I get back and this plug in. And when we plug that in and we put those together, what we get is this is equal to minus i over h bar Hamiltonian times u. And this is what we call the time one form of the time dependent equation. The first time we've mentioned the the Hamiltonian is the generator through this differential equation. Often this is written with a partial with respect to time. It doesn't really matter here because there's no other variable. But when we get to wave mechanics and we introduce position and as well as for momentum there's always time and it's often we have to emphasize that with other partitions. So I'll just write back that. So what is the solution to this equation? Whether or not it depends on time. So right now let's say this is just an operative that doesn't depend explicitly on time. I have to come back with that. That means anyway. Because this is the generator of time translation so why not we have h dependent time? So h given h assumed independent time. What is the solution to that differential equation? Exponential. So the solution u is the exponential of y. Yeah? But what about g? We got t0 here though. So we have to have it and we have a differential equation. We always have to think about the initial condition. It would be t minus t0. It would be because at time t equals t0 this has to be h. So that's the solution. How do we know that's a solution? Well we could check how can we check that. One way to check that is to think about this as a way we discuss. Hold on a second. The way we discuss in the homework where we looked at the solution of an operator, we can look at this as a power series. And then just take the derivative of this. And when you take that derivative it works. Yeah, Stephen, you had a question? You answered my question. Yeah, okay. All right. I want to make one point here that every unitary operator is exponential of some unitary operator. I can write it equivalently as minus i times some k where this is Are you trying to give spoilers to your next lecture? What's that? You keep saying anti-unitary. It's because symmetries can be either unitary or anti-unitary. And that's just stuck in my head. We can show it one way. If I have an operator of this form and I take its adjoint what do I get? Either plus i k because k dagger is k. And that is v dagger. So these are my unitary operators and the things in the exponent are the generators. All right. So now it was alluded to the question what if h itself is time dependent? What would that mean anyway? Yeah, so let's first of all let's, I want to just say something about the physics part. Suppose the Hamiltonian is an explicit function of time. A little bit of a weird thing anyway, what does that mean? How could that possibly be? Yeah? Maybe the magnetic field changes in time? Right. It's a good example. When we have a Hamiltonian as a function of time, what that means say for example as he suggested the Hamiltonian is a functional of something like for example a magnetic field and that magnetic field itself is a function of time. Now this is a little bit weird and I want to explain why it says this is weird because what this is saying is that the Hamiltonian is a function of some variables which we're taking as classical variables. We're taking this as a classical field. We are not quantizing the magnetic field here. We're treating the magnetic field as a classical parameter which is explicitly a function of time. Now when you can do that and when that's fair is a very subtle and deep question. We're not going to get into it for a little while maybe not ever this year but we'll try. But for the moment we have when we control quantum systems we shine laser beams on them we shine microwaves we put beads on semiconductors and put currents and we treat those variables as classical fields and that's how we drive the system so in some sense it's an open quantum system but it's not open in the sense that we talked about last time where we treated the environment as quantum degrees of freedom. This is classical degrees of freedom so this evolution is still unitary especially if this is deterministic I mean if the magnetic feels a little bit noisy well then we lose some information but to the degree to which we know what this field is and we control it very well this is still a unitary evolution even though we are interacting with it from the outside there's a way in which we can very subtle points but we know about dates and time alright so given that with that said we just have to be some mathematics now we say my differential equation is that u dt is equal to minus i h bar the Hamiltonian which is now itself some time dependent operator the operator itself times u so now how are you going to solve this one and we can do that same power series again and try to put it in but I can't just make that concept let's do a little something suppose I have a classical function which is what's the solution to that differential equation can you solve it yeah exactly so I can I can say this is the f dt over f of t times g of t dt right I then integrate this from say t0 to t make this a t prime because I it's a dummy variable now and then this the left hand side here is the log of this integral and so then if I just then exponentiate that I get that f of t is f of t0 times the exponential so I could just say well let's just try that as the solution to this in this case that would say u at t and t0 is u with well that at time t0 that's the identity and then I have e to the minus i over h bar t0 to t dt prime the integral of the Hamiltonian that would seem to be the generalization of what we wrote over here as the simple case where h were time independent so let's check that in the same way let's write it in terms of the power series okay so as a power series this is equal to the sum over all the powers that's just expanding that in a power series but there is a real problem here because when I write let's look at for example let's write out the first few terms so this is equal to 1 minus i over h bar and then I have plus a half over h bar squared integral v0 dt okay so far but if I try to take this derivative I'm not just going to get the same thing one power down because there's a question of what order is this in the question is does this operator commute with this operator if they commute I can take the derivative it'll be perfectly fine but if they don't commute check for yourself I won't get back this I only get this if they commute with one another so this is only the solution the Hamiltonian commutes with itself at different times and this is why actually solving for the time evolution of quantum systems is hard and why we need Feynman diagrams to solve for you know functional theory whatever this is a very hard problem so we'll come back to that next semester when we talk about time-dependent perturbation theory this is only the solution if they commute with each other very good so that's the general solution but often instead of just solving for the whole time evolution operator at how the state itself evolves as a function of time Hamiltonian of the state how are we going to do that? well the state let's just consider a pure state or almost always for the rest of the semester talk about just pure states we have some state at some time t we can think about that as the propagation from time t0 to t that's what the time evolution operator does it takes you from time t0 to time t so now I want to look at how does this thing evolve as a function of time so to do that I'm going to solve for differential equation and that is equal to the time derivative that's the only thing that depends on t and this we think that the state is generated but I don't want to for the moment let us again just take the we'll consider time independent Hamiltonians pretty much for now so this is equal to over here minus i over h r the Hamiltonian the time evolution operator is plugging in what we have and this is so we have another form of the time independent equation it says that the way in which the state is changing as a function of time is given by the Hamiltonian not the time independent if we wanted to write the time evolution for an arbitrary state we'd be mixed according to Hamiltonian dynamics to do that there's lots of ways to do it anybody have any suggestions yep can you maybe try to take the adjoint of this equation? sure we could do that so let's just say for example this guy is a statistical mixture of states this is one way to do it for sure and there's the adjoint let's take the partial derivative of this so that's the partial derivative of that times that plus this times the partial derivative of that using the product and this is that and this is the adjoint and the adjoint is plus i now in terms of the termination operators it is equal to so this is equal to I can factor out the Hamiltonian this is the Hamiltonian i over h bar with a minus sign the Hamiltonian acting on the density of the derivative that's this first term just to take it out and then I can take the Hamiltonian out the other way and so what we have is that the partial derivative with respect to time of rho is equal to minus i over h bar the commutator of the Hamiltonian this is another form of the time dependent this is Hamiltonian evolution of the state but it could be initially mixed this preserves the purity preserves the adjoint right no this is not the Heisenberg equation of motion we are going to maybe you have seen that before in the Heisenberg equation we are going to talk about that next lecture if you have seen it this is the state the state evolves so now of course once we are wanting to solve the sugar equation very special states that play a very special role and those are the eigenstates of the Hamiltonian they we care about them because they are the thing that tell us all about dynamics so in dynamics special role of the eigenstates or eigenvectors so the Hamiltonian the Hermitian operator Hermitian operators have energy values or energy Hermitian operators have eigenvectors let's call them U this is the energy eigenvalue you know they are real numbers because this is a Hermitian operator and the eigenvalues of any Hermitian operator are real we don't know whether they are positive or negative this is not actually a positive operator and the set of possible eigenvalues can be anything of any rule number at this point unless we know something more about the future of the Hamiltonian and these states or this equation is known as the time independent now for many physicists and quantum chemists this is all about quantum mechanics the rest of it that we've been doing I never think about it is it going to solve the Schrodinger equation for some big molecule or some solid state material of course this is a piece of the story in quantum mechanics but it's not the whole story but it's an important part because once we have the energy eigenstates then in some sense we can derive everything about dynamics first of all let's say one thing about what's one thing that's special about the energy eigenstates suppose at time t equals 0 the state of the system is one of the energy eigenstates that's suppose that's true what is the state of the system at a later time well that's given by the time of new from now on I'm just going to take let me take t0 so here t0 is time t0 so according to the rule we translate the state in time according to our unitary translation and this is equal to e to the minus i over h bar and have a tonian times time so what is that the Hamiltonian these states are defined as eigenvectors of the Hamiltonian so when I act this on this what do I get h acting on u is the energy you have a power series how does it get initial to the energy you're exactly right this is the power series so this is equal to e to the minus i over h bar so here's a little aside over here if I have a function of an operator acting on that that is equal to that right? so you just have to replace the operator by a tiny value that's a rule keep in mind okay we said that the overall phase of the state is irrelevant right? because probability depends on it so this is irrelevant the overall phase the overall phase doesn't change any probability for any measurement outcome which means that the probability of any measurement we do is independent of time that's why these things are called stationary states you've heard that term before in other words if you are an energy eigenstake you are a stationary state nothing would ever change you would measure the same thing every time no matter what time I call it okay these were the Bohr Organs now suppose on the other hand I am in a superposition of energy eigenstates so suppose I had somehow managed to prepare that state at some time then I'm going to call t equals 0 then what is the state I'm related to time so what is that like this on this guy and what do I get and I get the phase right minus I in 1 t plus c2 is in line with I h2t over h bar is this a stationary state no if you are not degenerate if this energy is different from that energy then there is a relative phase I can factor out if I like this one phase I can do that if I choose to what we see here is that there is a relative phase and that can make all the difference in the world you can turn this state into a state that's at a later time but they are falling to this state if this became a minus sign okay so what this says is that dynamics depends the overall energy of the system doesn't it can be set wherever I like what the ground state energy actually is doesn't affect the dynamics what affects the dynamics is how different energies are relative to some initial fixed energy one other thing once I have the energy I get states there is an easy way for me to express the time evolution operator so I have my time evolution operator again let's set t0 to 0 and let's suppose we have this time independent Hamiltonian I can express this in the basis of energy eigenstates let's take those energies just for the moment to be discrete energies okay we'll get it back in a little bit so the set this form of basis for Hilbert space that is to say they form a resolution of the identity again I'll just for the moment take these to be a discrete set but this might be interval so now I want to express this in this basis what is a representation of you in this basis remember these are eigenstates of the Hamiltonian there are also ways you can get at this you can put the energy on both sides oops excuse me but because the Hamiltonian is diagonal in this basis right that's to say the Hamiltonian is diagonal in this basis with those eigenvalues any function of the Hamiltonian is also diagonal in that basis with the eigenvalues just given by those functions is that clear so this is a representation this thing is sometimes called the propagator because it propagates the system in time so people would like spontaneous measure this not this but it's a good question which is if I'm in an excited state of an atom which I think about as a energy eigenstate it's not a stationary state it decays to the ground state well what that's telling us the dynamics of the electron say the proton is not just described by that binding force of the electron to the proton in the hydrogen atom for example because if it were it would be a stationary state and the reason is that it's also coupled to other quantum degrees of freedom and those other quantum degrees of freedom are in a electromagnetic fashion and so if I had a stationary state of the vacuum and the atom it wouldn't do anything but it's not a stationary it's not an eigenstate of the coupling to the vacuum and it's because of that that it evolves and the fact that it does so irreversibly in that unitary is related to what we talked about last time when you had a large number of degrees of freedom and all that stuff of complication and sophistication very good so I want to finish with an example let's go back to the good work I've ever talked about this semester a stick we'll talk about something else so let's talk about a spin what has particle in a magnetic field and we'll take this to be a constant magnet so we've discussed this before the energy of the spin in the field is related to the interaction between the magnetic moment dipole moment and the magnetic field and that energy is minus magnetic moment not the magnetic field now in this case the magnetic moment is an operator we take the magnetic field to be classical there's my Hamiltonian and the magnetic dipole moment is proportional to the spin and that proportionality concept we typically call gamma this is what's called the gyro magnetic ratio no that's the g fact it's got this has got the word magnet on another stock so this is equal to the following so let's write this as minus so this is minus gamma b dot s and s is equal to s is equal to this is an energy if this is an energy and this is h bar what does this have to have to have the units of h bar something is energy h bar omega right h bar omega is energy so this is a frequency energy divided by h bar is frequency better than that and so we'll call it capital omega so my Hamiltonian here I can write as minus h bar omega over 2 dot s and let's take the magnetic field to be in the z direction we'll call the direction of the magnetic field the z direction that is tradition and so that tells me that the Hamiltonian is minus h bar omega over 2 sigma z so now I ask you what are the eigenvectors and eigenvalues of the Hamiltonian what are the stationary states and the energy levels of this Hamiltonian that's the eigenvalues and what are the eigenvectors yeah they're up and down the z axis so the eigenvectors the eigenvectors of the Hamiltonian are plus and minus along the z axis and the eigenvalues are minus plus so if I were to draw an energy level diagram of this system it says that spin up along the z is the ground state and spin down along the z is the excited state and the splitting between them is that this one goes down by h bar omega over 2 and this one goes up h bar omega over 2 this corresponds to the case where the spin or mu v are aligned and this corresponds to the case where mu and v are anti-aligned that's the excitement the system wants to align the spin for the magnetic moment now I made an explicit assumption just a little aside this is will at some point that gamma was positive a positive number right um if gamma is a negative number then it splits it's always the case that the magnetic moment when it's aligned with the magnetic field is the lower energy and when the magnetic moment is the higher energy but it's not always the case that the spin in the magnetic moment are in the same direction because if it's an electron they're in the opposite direction because of the charge because of the band-band fragment but you want to change the actual edge of the electron what would happen is spin down would be the lower energy because spin down would correspond to see in this case the spin and the magnetic moment are in the same direction if it's a bit of a collapse then gamma becomes important to know if it's a bit of a collapse then you need to know what gamma is if you have higher spins it depends that's a much more complicated question that's what the LFR higher spins I just wanted to get across the point that when we have to be careful about what this gyromagnetic ratio is when we look at real physical problems ok but with that aside this is correct ok so so I'm just going to hear say gamma is greater than 0 so now the question is let's look at the dynamics ok let's suppose at time t equals 0 the state of the system is spin up along x what is the state of the later time yeah well so how do you solve the initial value problem there's lots of ways to do it but the simplest way is to follow you decompose the initial state in terms of the eigenstates of the Hamiltonian that's the first thing you do so the first thing to do, step one decompose the initial state as a superposition of energy eigenstates so generally that involves putting in a complete set and doing all that but you can just read that off because we know that it's better than this what is this so this is a superposition of spin up along z and spin down along z ok and so initially the probability of spin up along z is equal to the probability of spin down along z is a half ok what is the state now at the later time we just did that so we just apply the propagator to the state so what is that well this guy picks up the energy of the plus eigenstate and this guy picks up the phase factor associated with the spin down state each one picks up that phase is here I mean given by those energy levels so we plug that in what is the probability to be plus z at some later time the same and because these are stationary states the probability to be in the eigenstates doesn't change the time the spectrum of the state relative to its the eigenvalues of the Hamiltonian are not changing the time but that doesn't mean nothing is changing the time what about relative to the x basis which doesn't commute with z sigma x and sigma z don't commute so at a later time something won't happen well there's lots of ways to do that what we want to know is let's express the state of the later time in basis up and down along x we could do that so I'm just going to I can put in a complete set of states or I can just remember that up along z is a superposition of up along x and down along x and spin down along z is a superposition but the other sign I just substituted it that's one way of doing it not too late to do it so this then is equal to e to the i plus e to the minus i over 2 spin up along x plus e to the i over 2 minus e to the minus i over 2 down along z I mean x which is sine and cosine what we have here thus is that with respect to the x basis we have the cosine over 2 spin up along x plus i and down along x so what is the probability to be spin up along x at some later time cosine squared excellent, good job and similarly for down it's sine squared or 1 minus cos omega over 2 plus and this is the minus for using some trigonometric ideas so if I were to plot this what I see is that as a function of time the probability as a function of time starts out with the probability to be up along x and it's the probability to be down along x it started out with x and then it becomes spin up I mean it comes from down along x where this should be all of the same amplitude and this is i over 2 it's in a linear superposition of the 2 it's not the parable lecture of both it is, it's exactly what's happening so what it says is let's just complete this discussion saying the following thing what is the expected value of say the spin along the x direction as a function of time 0? well let's know at any fixed time on that average over time this is equal to by definition the sum over the energy the spin eigenvalues times this is equal to hr over 2 times the probability to be spin up along x at time t minus hr over 2 is the probability to be spin down along x there's lots of ways to do this problem I mean this is this I could write it out more explicitly to this operator this matrix that's the expectation value this is 1 plus cos this is 1 minus cos so this is equal to cos maybe t the mean value of the spin is cos if you did the y we times hr over 2 and the y component if you did the same thing you would find sin so what's happening in this problem is exactly what z suggested here's the z this is the magnetic field in the z direction we started the spin along the x axis right so here this is the x axis this is the y axis we started the spin here at time t equal to 0 the expected value was here at later times it's here and it's possessive so far more perception that is exactly what you would see classically if you put a magnetic moment in a magnetic field you put it in a direction other than it it will possess around that if I put it like this it would possess like that like a gyroscope and the quantum evolution is exactly the same as far as the mean value goes it's not a classical spin that's in a certain direction because if I measure it I'd still have this I mean if I measure this bit I have to find it here and I have to finally find it there but the point of the matter is the mean value the expected value rotates now of course at all times there's a 50-50 chance of finding it here and here because all the states in this equator present that alright if you give up your homework I have you left here you can use the tail


Okay, we are live this morning. Just for a moment, we just want to say a happy St. Patrick's Day. You'll notice I got a green hat and I think that Senator Chittendon has a green hat. Others have green on so Senator Kitchell, you have green on this morning. I'm not going to have anything on. I just want to tell everyone this morning, I sent this to the governor governor this morning and he texts back right away and he said, just when I thought everything was it was as worse. Okay, welcome everyone. It's Wednesday morning and we are going to get started and we have an issue from a transportation equity and inclusion. Michelle boom hour will lead us off and with that Michelle I think we'll turn it over to you. Thank you very much Senator for the record I'm Michelle boom hour I'm the director of policy planning and intermodal development for the Vermont agency of transportation. I'm here with many partners this morning from AOT and across state government joining me are Susanna Davis who is the director of racial equity and the chair of the governor's task force on racial equity racial equality excuse me. We also have Lori Valburn our chief of civil rights and labor compliance Christine Hetzel, our organizational development director, Colleen Montague who is with our VP trans training center and soon to be joining our civil rights group. Mike Smith our operations director from DMV. And Gamal our division director for finance and administration and and Gamal our highway division director and chief engineer. And we are going to be walking you through our efforts of historic proportions which are significant that we have engaged with over the years on equity and inclusion. We're talking about some of the efforts that we will have going forward to expand our base and to broaden our footprint in terms of how we assure that the agency of transportation is delivering services in an equitable and inclusive manner, and also accommodating service in such a manner as well. But I'd like to start by turning it over to Susanna who is just going to talk about the framework at the statewide level and how all agencies of state government are pulling in this direction. Thank you. Thank you. Okay. All right ahead. All right. Thank you. When I started this. No, I wouldn't see it. So, at the state, we are taking a very overarching view of racial equity. It's something that has to be accomplished and pursued across the enterprise because racial inequities exist in almost all of the work that we do and almost every sector that there is whether it's housing, education, criminal justice, business, et cetera. So racial equity is something that's being built into policy, not just the AOT, not just in AOA, but across the enterprise. And that's really important because what it requires of us is a certain level of uniformity of policy, right, that a person who's a resident or a visitor to Vermont can go to any agency for any reason and receive roughly the same level, kind, and an equality of treatment and services, and that their outcomes are not going to be determined or influenced by race or ethnicity because that's what racial equity is, right? It's not saying we've got to treat everybody exactly the same in all circumstances. Rather, it's saying whether people's outcomes are good or bad, race shouldn't be a factor in that. And that's a really important distinction. So for the state, some of the things that we're doing are some of the things that we have done are to include racial and social equity into our strategic planning. One of the ways that we do that is by conducting EIAs, that's equity impact assessment. It's a tool that we rolled out last year, we're using it now very actively during the legislative session. And what it does is it's basically a questionnaire that accompanies any budget or policy proposal that comes out of the executive agencies. And the reason that we use EIAs and they're used across the nation in many jurisdictions, very sound, well tested, well received and extremely informative. And the reason we do them is because it ensures that we're asking ourselves the right questions before we roll out a policy that could have unintended consequences for different demographic groups. Now, we put it out under the guise of racial equity, but in reality it actually serves a lot of historically marginalized populations. The LGBTQIA plus population, people living with disabilities, people experiencing poverty, people experiencing homelessness, et cetera. So it's a very well rounded overarching tool that helps us to evaluate the equitable distribution of benefits and burdens of our policies. So that's something that we're doing at a broad level. Other things include expanding and improving our data collection. We're a little bit inconsistent when it comes to race data collection. Some folks are using the Census Bureau categories of race, which many of us people of color don't like, by the way. And others are just using kind of a different list and it creates a little bit of inconsistency, which makes it hard for us to compare data across the enterprise if it's being collected differently. So our data collection strategy is going to be improved. And one of the ways that we can help that is by supporting some of the other proposals on the table, which includes staffing for the racial equity office, which would allow for more data and policy analysis. Some of the other things that we are working on include having equity liaisons in every agency or department, which I think is going to be featured in today's presentation. So just having a person who can be the point person or a point person in a given agency's department for equity is important. I think a lot of people assume that this work sits with and lives with one person or one agency. But again, if we know that there's disparities in every sector, we got to have eyes on it in every sector. And so that's another thing that we rolled out so far as well. And then there are some things that are a little bit more specific to AOT or agencies like AOT, because AOT, unlike many of our other agencies have a lot of federal requirements they've got to meet. And many of those federal requirements do hinge on equity provisions. And so you're going to see in today's presentation and of course you members of the committee already know AOT is one of the agencies at the state level that tends to be further ahead on equity work, largely because of the need for compliance with these federal regulations. And so because of that, I think that AOT is well situated not only to serve as a model for some of our other agencies and departments around the state, but also has a good eye toward how state infrastructure and I mean physical infrastructure, spatial infrastructure and service infrastructure, all three of those. How those various levels of infrastructure can must be used, not just to accomplish the technical goal of getting, you know, people in cars from A to B, but also the overarching and ongoing goal of ensuring that we're doing so in a way that doesn't create disparities in the benefits and burdens that we create. In transit, what that means generally is things like, are we putting health deleterious infrastructure items in neighborhoods that tend to be prominent with people of color? Are we putting health promoting items in neighborhoods that tend to be absolute or largely white? Are we building, are we raising parks so that we can build superhighways through communities where a lot of seniors or youth tend to live? Or are we looking at where people need to go in terms of getting to work and how people commute shape up what that means for them? For example, if you're a person of color, statistically speaking, it's likely that you live in or near Chittenden County in Vermont, but that's not the case everywhere. You've got a lot of pockets of people of color who may live in areas that are underserved by transit systems. So how do we ensure that where you live, which is still often tied to your economic prospects, your job prospects, whether you were able to get a job or were passed over for it because you have a name that starts with an X, right? Whether where you live is impacting how you live or how far you have to go to earn your living. All of these things are interconnected and are all related to different levels of racial equity. So I'm going to stop there, but that's a little bit of an overview of what we're working on at the state level and some of the considerations that go into this work, especially as it relates to transit and transportation. Thank you very much. All right, at this time I'm going to share my screen. And we will head into the presentation. And I believe that Lori will be kicking us off. Well, thanks so much Michelle and good morning everyone. Thank you senators for inviting us in today to discuss this. It's a topic near and dear to my heart. And thank you as well to Susanna for the kind words but also for the amazing leadership that she is showing and leading the charge. This is such an exciting time. This isn't just a moment. This is a movement. So I wanted to share a little bit about what we have been doing at the agency of transportation in some cases for decades. In some cases, some of our newer initiatives. And we will head into the presentation. And I believe that Lori will be kicking us off. Well, thanks so much Michelle and good morning everyone. Thank you senators for inviting us in today to discuss this. It's a topic near and dear to my heart. And thank you as well to Susanna for the kind words but also for the amazing leadership that she is showing and leading the charge. This is such an exciting time. This isn't just a moment. This is a movement. So I wanted to share a little bit about what we have been doing at the agency of transportation in some cases for decades. In some cases, some of our newer initiatives as a background for what we are planning to do and already starting to implement in order to meet some of the goals and expectations that Susanna was talking about. So as she indicated, our agency has a head start on this. We have had for decades now a great incentive to build our programs, hopefully through an equity lens, and with the idea of ensuring non discrimination because that is the expectation. So our title six program is one of the prime examples of this and the title six program is intended to assure non discrimination and all of the benefits and services that we are providing to the public. This is something that has been baked into our culture for many years. We have the title six program takes its roots from the Civil Rights Act of 1964 and all the legislation and court decisions and executive orders that have come down since then. And it sort of serves as an umbrella for all of our other programming around equity inclusion, affirmative action, etc. So we have had and continue to have a pretty robust title six program. Every single year, Secretary Flynn issues new policy statements in this regard that get disseminated to our organization to all of our sub recipients posted on our website. We have made assurances to all of our federal funding partners that we are in fact going to administer all of our programs in a way that guarantees equity and inclusion. That being said, we obviously want to make sure that we're not just checking off boxes and so over the years we've tried to breathe some life into this program. And part of that means that we look at how we're where the challenges are and where the barriers are. So for example, limited English proficiency is something that we have certainly tried to tackle and provide an array of translation services and work with various organizations to make sure that everyone who's accessing our services, whether it's at a public participation meeting at the counter at a DMV or anywhere else is going to be able to participate and receive the same level of services as somebody who is native English speaking. That's easier said than done in some cases, and it requires a fair amount of research and mapping and all of those things. So we have a limited English proficiency plan, four step analysis and the like. The other thing that we've tried to make sure of is that this isn't something that's seen as just a program that the Civil Rights Office at the Agency of Transportation administers. So as Suzanna was referring to, when she described the equity liaisons that are now being established across the enterprise and state government. We also took that approach with our Title Six program when we have Title Six liaisons. This past year we reappointed or came up with new appointments for 29 different people who are sprinkled throughout our organization in all of the different departments and bureaus. And there are eyes in our ears. They help us to collect data. If there are any complaints that gets brought to our attention as well. So these are all sort of first steps and things that we feel are building a strong foundation for all the additional things that we want to tackle. Next slide please. Some of the programs that we already have in place I had when I had the pleasure of coming and joining you for presentation back in January. I had described a few of the programs that we have been administering using some of our funds from Federal Highway and our employment diversity and highway construction is one of them. It's one that we're particularly proud of because it really has made a difference in terms of making the highway construction industry accessible to people who would otherwise not have had an opportunity to enter and advance their careers. So this slide does describe some of the achievements that we made in the last fiscal year. It's a very robust program because we do a lot of partnering. We partner with a lot of community based organizations, advocacy groups to ensure that we're putting out the word that we have these opportunities. And the program itself has made a big difference as we take a snapshot each year of the demographics in the highway construction industry. We're looking to see the makeup, not only based upon gender and race but also based upon whether or people are advancing and we're pleased that people who entered the industry through this program maybe five or 10 years ago are now moving up the ladder and in some cases are even project superintendents and and for people. So we do provide an array of supportive services to make sure people get a good start in the industry. And then we provide case management services as well for folks that are working on our projects. Next slide please. Our disadvantaged business enterprise and small business programs we also discussed back in January but just a reminder. These are programs that every single state DOT is required to administer in order to remain eligible for a receipt of federal funding. But it is a program that also provides a lot of opportunities for businesses that are majority owned and controlled by women and by people of color to be able to make sure that they're getting a certain portion of all of the federal funding that's coming into the state. The program itself has been around for decades we continue to find ways to partner with other organizations so that we can actually deliver a lot of business development services to make sure that the firms in the program are getting access to government contracting in general and particularly to participating on our projects. So last year on the women and business minority business owners in the program accounted for almost 14% of all the federal fund funded projects that we awarded. Next slide please. This is an opportunity for us to talk about how we are already kind of developing and delivering the message to our workforce as well as to all our contractors and sub recipients. I think I mentioned when I was here in January that all state DOTs have been required to have a civil rights section by legislation going all the way back to 1975, but I will say that in some states they're not using their civil rights units to full potential, they're completely and exclusively focused on the external workforce, the highway construction industry and monitoring some sub recipients at our agency, our leadership and particularly our current leadership has always recognized that we bring value added and that the message has to start from within our organization. And so we've been really successful at getting a shift in thinking and culture within our organization due to a lot of training and policies that we've been able to implement over the years. And I have a wonderful team of folks that are expert at being able to find ways to encourage all of our agency to be part of this effort. It really does take a village. Next slide please. We also have recognized that we have an opportunity to be using equity and inclusion as part of our brand and part of our marketing and we make sure that this isn't something that we take away. But we have a process even in our hiring process where we attempt to bring on the next generation of our employees who are going to buy into our culture, which includes equity and inclusion concepts and a respectful workplace. So civil rights has been given an opportunity to assist all of our hiring managers with the interview and hiring process as well as the outreach and recruitment process. We also are given an opportunity to serve on a large number of different councils and boards I serve on some with Susanna and with other members of state government are that are working on the efforts that she's been describing. We've also been trying to make sure that we are planting seeds for the next generation, and that includes a very robust youth outreach program. And we continue to find ways that we can encourage a diverse group of students to be considering transportation and state government as their future careers. So with that, I'm going to turn it over to Christine Hetzel, and I'm also happy to field any questions that folks have. Okay, any questions this time. Thank you very much appreciate it. Thank you. Good morning everyone for the record my name is Christine Hetzel and I'm the director of organizational development. I oversee the learning, occupational health and safety and strategic workforce issues for our agency as well as the municipalities through the Vermont local roads program. I'm going to be very brief today in the interest of time, but the VTrans training center really is responsible to create a learning culture across our organization and the municipalities. And I think that we can all agree. As it comes to diversity and inclusion as individuals as an organization as a state and as a culture. We all have a lot to learn, and it's a continuous learning cycle to learn more about the importance of this topic. So the VTTC has a mission to create a culture of workforce respect civility and inclusion throughout that workforce life cycle. And it really does start with our leadership. They are incredibly committed to role modeling civility and respect and it really starts with the tone that they set and then flows through to the AOT managers and supervisors through training through empowerment through the setting of standards and expectations. And I think it's very clear from applicant to employee sunset, the priority that we place on civility and respect. And so when we look at the employee life cycle that workforce life cycle, it starts with the way in which we recruit them. Luria was sharing so importantly, having civil rights, really strategizing and driving the way that we advertise and recruit for employees, how we onboard them, the devotion that we give to new employees, setting that expectation, giving those resources from the beginning, the training and the support, the way that we're onboarding supervisors setting those expectations are incredibly important to create the right environment and the right culture that signals behavior and learning. So employees and supervisors all across our agency have expectations set in their performance evaluations that require civility and respect diversity. And not only the ways in which you should not behave but almost more importantly the ways that you should behave and include people and embrace diversity and differences of all sorts and flavors and colors. And that's where the power of a strong team comes from, is from that diverse mindset and approach, all the way to how we off board people, when people decide to move from the agency, getting their feedback their understanding of how things when what we did well, what we still need to do, and that's incredibly important. Interestingly, we have a high percentage of employees that will leave state government and then return. So the way in which we sunset folks really has a direct correlation to their willingness to come back. Next slide please. So all of our programming is very strategic, all of the learning opportunities are strategic, and are very well aligned with civil rights. And so I think that Lori's team and my team partner continually, and we even trade staff back and forth. Interestingly enough, because we're also committed to this mission so whether it's the way in which we're training pre supervisors to become supervisors and to ensure their understanding of inclusivity, or it's the way that we are growing emerging the way that we're training supervisors how to hire and how to interview, whether it's strengths based coaching, or individual support that we're giving to employees such as their job shadowing rotation programs. All of this is meant to create a culture that that embraces diversity with respect but leverages it to the benefit of the citizens and to create a higher performing work team. And one item I just wanted to call out exclusively is the way that we have piloted decentralized reallocation with HR. We've built job series so that there are career pathways built into the system that are less bureaucratic that help people to move through different job series like a level one level two level three with preset standards that make it much less subjective that make it less about the individual and more about that individuals performance. In addition to that we have many other supporting processes in place the way that we contract and the clarity we have with our trainers about inclusivity and respect the way that we do competency mapping for interview committees, sometimes people can get stuck in ruts in the way that they ask questions, or in whom they think is the best fit, and these competency maps really expand their thinking, and challenge just moving pieces around and really challenge folks to take a step back and really think about the needs of the work group, and to broaden what type of employee could be successful in that role. And finally we have strategic workforce committees that we've chatted about in the past that flow from our strategic workforce plan that really give employees a voice throughout the, throughout the organization at every level to share their experiences with us, what type of programming they feel would support their further performance and promotion, and where we state may still have barriers so we've been doing a lot we're going to continue to do a lot to support this learning environment about civility and respect and inclusion, and we're on the continual life cycle. You'll be hearing more about some of our future plans as we move forward today. That's all I have I know that was quick and brave but I'm happy to take any questions. Any questions for Christine this morning. Great overview. Thank you very much. Okay, go right ahead. Good morning everybody Michael Smith director of operations for the Department of Motor Vehicles. I to will try and be brief but those of you that know me know that I struggle with that. So, from from the DMV's perspective we have with Google translate on our website to help translate pages into various different languages so individuals can gain access. We also translated the form description so that, you know, not only do they, they're able to see the form that they're after as well as understanding that this is the license application non driver registration form so on and so forth. We did this in consultation with the US Committee on refugees and immigrants from Vermont. So we now have our standard license learners permit exam available in 10 different languages. I won't list all the languages they are on the screen. And this does include audio for both those in the in the office taking the exam as well as those using our online testing module. So we began based on some legislation that happened I believe two years ago the new Americans legislation use of interpreters on road tests we piloted that in the Burlington office and had intended to expand that statewide. However, we get slowed down with the whole COVID pandemic. We'll hear more about that in one of the future slides. So we partnered with us CRI the US Committee on refugees to translate the license learner permit non driver and Vermont residency forms into the various languages that we have the tests in. We complete an annual review to assure that we have the most common languages over the last 10 year period. Next slide please. And I wish Commissioner Minowley was here because she loves saying this word that will be duo devices. These are in these are devices which are very simplistic and it has a screen on this side that that our staff are able to use and a screen that the individual on the other side that is deaf or hard of hearing and it allows them to communicate back and forth via typing almost like texting back and forth doesn't save any of the information is just a one one shot back and forth. And then we've got the offices that advertises the availability of interpreter services to provide assistance for transactions and communication with our staff. From roadside perspective. We've created some visitor cards in consultation with the Department of visor card sorry. We've partnered with the Department of disabilities agents and independent living as well as state police. And this is a way for individuals who are hard of hearing to advise officers of that to promote better communication. We use a contracted interpreter services for interactions at roadside. We also use that in the offices. We have a gender neutral option that is available on driver's licenses and ID cards. We also provide our license forms to clarify the applicants for driver privilege cards are not required to answer the questions in regards to citizenship. As that really has no bearing on that type of document. And I do believe that that is the end of my slide so if anybody has any questions I'd be happy to answer them. Any questions for Mike this morning. Thank you Mike appreciate it. You're welcome. Next. My name is Wayne gamma and the division director for finance and administration. I will be able to gain this a little bit of speed here I think a few things that we're working on and I'm going to expand on is we have we because of the liaison group that was on I was talking about earlier. We've created a equity impact leadership committee. And with that we are going to expand that throughout our agency. And then we're going to be looking at policies procedures trainings practices with an equity inclusion and diversity lens. And one of the other things that that we've been doing is we've been working with our federal partners. Some of those partners include the FHWA, as well as AASHTO and NASHTO AASHTO is the American Association of State Highway Transportation Officials and NASHTO is Northeast Association of State Transportation Officials. Last fall, NASHTO and AASHTO were actually working on a resolution addressing race equity diversity inclusion, and Vermont was given the opportunity to look and actually add to it, and Susanna wrote a piece and it was passed by NASHTO. And then it went nationally and voted on by AASHTO and it was also passed. So one of thanks Susanna for helping advance some of Vermont's also likes and wants, as well as the national groups. And also, we work with them to try to gather any and all information from across the country with other states and our peers. We also work with our tri-state groups, which New Hampshire and Maine are best practices for many others. The other thing that we're doing is we, as I said with the liaison piece, we are working, I'm sorry, sorry I lost where I was. So we're working and learning from other agencies, and we're sharing many ideas with them. As you heard earlier, we have done quite a bit over the last few years, but we need to continue to grow and do better. Many of the other agencies have things that we don't do or just starting to get engaged with. So we're learning from them and we're also giving and teaching some of the things that we're doing. And with that, I'm all done on my section and turn it over to Ann. Any questions? Okay, go ahead. Thanks. Thank you very much. Good morning. My name is Ann Gamble. I'm the agency's chief engineer. Every year, our civil rights section does many equity and inclusion trainings, and we're going to continue to incorporate those topics and push them out to our staff and contracted partners. We'll work directly with the VTTC and civil rights staff to develop this training and implement it this year. We will review our AOT engaging the public guidance document and use it as a resource for the training. The VTTC hosts engaging your audience with finesse. And this will be specifically targeted to show staff how to assess the community being presented to to support inclusion. On the DMV side, we've expanded the use of interpreters for road tests. We have the necessary contracts in place for these services and our workforce safety guidance to allow for this activity moving forward in a safe and effective manner. Next slide. Our planning and engineering staff have developed a new project selection and prioritization process in conjunction with local governments and regional planning commissions. We are in the pilot phase and intend to incorporate an equity screening process in this pilot program. For projects that are farther along our staff will use the tools they've learned to use targeted engagement strategies to enforce, inform and enhance best practices. Through the VTTC and Vermont local roads training centers, we will provide the same training and resources to our municipal partners to further support diversity. Our project design staff will also work closely with civil rights in consideration of additional inclusionary language for future contracts. And I just wanted to bring to your attention to that both the DMV and VTTC have both added language interpreters on our websites. So to you, Michelle. Thank you, everyone. I'm very excited about this body of work. We're going to be expanding to include a technical advisory committee of staff and potentially external partners going forward. We're going to be conducting an in depth review of our agency wide programs and practices to assure that the most current tools and applications for equity awareness and inclusionary activities are incorporated into the core of our mission. The agency will basically implement the outcomes of this gap analysis throughout 2021. And we will base hope to have basically an agency equity work plan with a dashboard of activities to entice to complete this mission that we will outline for ourselves as we go forward. And I've been involved, Wayne mentioned AASHTO and NASTO, and I have been involved with their work over the past year in my role on the Transportation Policy Forum of AASHTO. And I can say that Vermont is pretty far ahead in terms of our efforts and we're excited to continue to move forward and share best practices with other states. So I know this has been a topic of concern for the legislature. Obviously for the governor's office for quite some time now. And we are very diligent in trying to find ways to assure that the agency is a leader in this in this realm, and I'm happy to take any questions or questions for the rest of the staff. Yeah, when we started off you said it would be a model for others and it certainly is a real I could good overview. Do you know if other agencies follow the same model, or they're all trying to do the same. Yes, all other agencies are moving forward with this type of framework everyone's got a little different twist on it right now but because of the leadership group that Suzan oversees these best practices are being shared across the enterprise. And I know that the agency of natural resources has a very active leadership team working on this and certainly all other agencies of state government are moving forward as well. Great. Good. Yeah, good presentation questions from any committee members this morning. I do have a comment. Last year, we had a couple of conversations and I guess maybe this is more than transportation but one concern was related to the nature of certain exams and I remember. Senator ash was very concerned, particularly with the state police, the way in which wording and so forth made a difference, and we were very pleased to see in fact I one of the new additions to our state police force I believe is always a Somali from Burlington area. And so part of the concern was how different words or requirements actually are problematic and the other which Mike reference in fact was something was brought up in transportation and that was having the ability to have a translator with you when you're taking your road test. And so my question becomes one of how how we sort of think and I think probably Susanna Davis office is really trying to help with that. It just makes me wonder how many other kinds of situations whether it's language use or the assumptions made about recruitment in the first place before you even get the eligible applicants are influencing the workforce or access to services and so it's a more general because several of the things that are referenced in fact were generated as a result of a legislator sort of picking up and following so that's fine but but it also needs to be done internally so I just want to raise that as something I think we need to all think about as we do our work every day has sort of an eye toward the extent to which we may without thinking about it have obstacles either to getting employment or to getting a particular service not necessarily a license but you know could be any kind service from any of the programs administered. So that was just one observation I wanted to make is that this is a start but I think it's and that's why I was glad when Susanna mentioned really one office isn't going to change state government and it's how to build that that sensitivity on that eye for does this make sense or are we creating an obstacle here it's really got to be developed throughout all of state government and that takes managers it takes staff it really is a collective effort but that's that's my only comment that I would like to offer as it relates to some of the discussion that we've had here in transportation. Anybody want to comment. If I make just to respond to the senator go right ahead. Thank you and thank you for the comment senator I completely agree and I think just expand a little bit. That's one of the reasons that we're sort of tackling racial equity and state government in and you can you can chop it up a million different ways but the way that I have found was useful is to look at three main categories. The first is how we are as an employer. Right so making sure that we're creating healthy work environments that are sincerely inclusive which doesn't just mean getting more brown people in the photo on the brochure. But really means meaningful inclusion appropriate emotional paths that are right so that's how we are as an employer. How we are in terms of our system and I'll get back to that in a moment and then how we are as a provider of services how are we interfacing with the public and what opportunities are people getting or being shut out of. And for the middle piece about systems that part is important because it really makes it both is focused on real transformative change not just technical change so I'll give you an example. You know we might say oh hey we're underrepresented in terms of our staff who are of color so next year let's just hire 19 brown people. And you know you could do that but is that addressing the hiring scheme itself that may be exclusive exclusionary. And so that's what we need to say systems not just pursuing individual work around and technical changes but really a transformative change that's going to help us get at those root causes so I completely agree with what you're saying and so much of it really does have to be a hand in hand effort right so for example if we're talking about language access one of the ways that you can build language access is to make sure that you know we have enough multilingual liaison in the school, which is sort of a pipeline to people being able to stay in Vermont and have longevity here, because they've been supported from early ages. So it is very much a multi tutorial approach I appreciate you saying that. Thank you very much. Appreciate that. Any questions, comments, many one. Great overview this morning is really, really good, good knowledge and we understand exactly what's happening in the agency that's a. I'm glad to hear it's going throughout state government that's great, great news. Anything else anyone don't like that at this time. I'd just like to thank the committee for the opportunity to spend time on this topic and and to for us to have the opportunity to present our information. And as we go forward, we are always available for questions or input or suggestions you may have. So thanks. Thank you. Sounds like it's working well appreciate it. Thank you. Okay, I think that takes care of this portion this morning. We're going to take a break until 10am and our next item is at 10am.


Hi everyone, Sean with jaspyscasebrakes.com here doing 2021 Bowman Sapphire five box break pick your team number eight We're all card ship and we're giving away a 2021 Bowman Sapphire box itself So the way this works how to be entered in the free Bowman Sapphire box giveaway buy two or more teams in the break get entered to win No max entries two teams one entry four teams two entries six teams three entries etc If you only buy one team you'll not be entered, but good luck top name wins the sealed box Here is our list of teams and respective customers cool, so from Jeff and the Diamondbacks Down to Steve Birch and the Nationals So let's print this list out We'll go through the list and see who has two teams and qualifies for the box break the box giveaway at the end of the break But here are the five boxes. We're going to break for this break and the one we're gonna give away at the end We'll set that over here to the side And get into these in the meantime Here is that final list that we have Last spot mojo Jeffrey Nance and the Diamondbacks Thanks to everybody for getting in and good luck See if we can find a pad paracha I mean sapphire just like always Jose Rodriguez Bowman first auto for the White Sox Eric Ainge Xavier Edwards to 99 for the Rays Chris Co and nice Aaron Sabato, so a two-auto box another nice one there for the twins Steven George and Two-color box also hunter Bishop to 125 for the Giants Yens McLeese to auto two-color box Let's keep that going Kevin all-kintara for the Yankees Chris Co and another nice Aaron Sabato this one's to 125 for the twins and Steve George and Austin Martin for the Blue Jays Matthew Shearer Just stuck behind you Simeon Wood Richardson Jefferson Espanyol for the Diamondbacks and Jeffrey Nance with last spot mojo Someone close it out nice Rex. I'll get that on the schedule then Jose Rodriguez again for the White Sox Eric Ainge and another double auto William Holmes for the Angels and Michael Langer So no color in that box But another double auto box No No Rex check the schedule I think it'll be there's two more breaks than that maybe Unless something else sold out before that as well Wander for the Rays Chris Co and Alexander Ramirez to 25 little orange auto for the Angels and Michael Langer and another double auto Antonio Gomez for the Yankees Chris Co So three out of the four autos or four boxes so far have been double auto boxes Not too bad fifth and final box Cody host to 125 for the Dodgers Stephen George William Holmes for the Angels Michael Langer and Riley Greene to 20 nice one for the Tigers and Chris Co There you go guys, that's the break that is 2021 Bowman Sapphire we get the one box give away as well to do so Let's pop back over to our list Customers I remember every two teams gives you one chance at winning the sealed box So we're gonna copy the customer list over to a separate spreadsheet alphabetize So Anthony with two gets one Brandon and Brian. Thank you very much for getting in Chris with six gets three Darren, thanks for getting in Eric gets one. I Coppola, thanks for getting in Jeffrey. Thanks for getting in gents gets one Joshua, thanks for getting in Matthew gets one Michael gets one and Michael B gets one Steve B with one and Steven G There you go So from Anthony down to Steven. We got a 12 entries on the randomizer So Steven back up to Anthony name on top after Five and one six times gets the box. Good luck six and final time. Congratulations to Michael Branson You got yourself a sealed box six times on the randomizer six times on the dice Michael on top and there you go guys. That wraps it up. That was 2021 bowman sapphire five box break Number eight pick your team from jasky's case breaks calm. I'm Sean jasky's case breaks calm. Thanks for hanging out We'll see you next time