Thank you very much for the invitation. So we just heard the title and we'll talk about the action of the diffeomorphism group of a manifold in the space of metrics of positive scalar curvature. So let me begin by fixing some notation. So we talk about compact manifolds with boundary often. If we have on the boundary a fixed metric of positive scalar curvature called a curly R plus Mg, this is space of Riemannian of PSC metrics, which near the boundary have like a color form, the form g plus dt squared. And if M is closed, I just omit the subscript g. So that's my notation for the space of metrics of positive scalar curvature. And then we have the diffeomorphism group of M, the group of all diffeomorphisms denoted dif M and denoted dif delta N. By that, I mean those diffeomorphisms, which are the identity at the boundary and a little bit over the boundary. So you have an action that's very obvious that if your morphism group acts on the space of positive scalar curvature, fixed by pullback. And from this action, you get two things. You could say, okay, look at the space of, so each diffeomorphism F gives you a pullback map F star. And let me denote by H odd of R plus Mg. Johanna, we don't see your slides. You don't see the slides? Yeah. I see the slide. Oh, you see the slide. Okay, so then it's my problem. That's it. Maybe, is it a problem? Okay, sorry. I see it. Maybe you need to pin it. So this, can you see that? Yes. Some of these are not for me, but well, let me figure out. Yeah. Okay, so H odd of a space X, that's the space of homotopy equivalence from X to X. That's not a topological group. It's something a little weaker. It's a topological monoid. So you have this map sigma coming from diffeomorphisms going to the homotopy automorphisms. And also you could look at a metric H in R plus M and look at the orbit map from the diffeomorphism move to the space of metrics. So that's a matter of notation. And so that's of course, we have heard it in Bernard's talk. One idea, so people asked, does this space R plus M have non-trivial topology? And one idea of course could be you take an element in the homotopy group of dif M and let it act. So look at the action map and you get a different and get an element in the homotopy groups of the space of PSE metrics.  So there we know we have, if M is spin, we have all these tools from index theory, this index difference map. And you could ask, do you get a non-trivial element here? So that was an idea by Nigel Hitchin, the long go and he proved some results for spheres and then later other people proved results with that. But that has been difficult. So you learned in Bernard's talk, together with Schick and Stimler, that's exactly, they did exactly that. They constructed for certain manifolds, constructed such elements in the homotopy of dif M and prove that by index theoretic means that the resulting homotopy class in R plus M is non-trivial. And I want to talk about the phenomenon that's slightly strange. The phenomenon is that this action map is often fairly close to a trivial map. So this explains why it was so, why it was so difficult to implement this strategy. It's because very often, and sometimes it's even a theorem, but that sometimes this action map is actually the trivial map. So that's an insight that we had.  And I want to start with some examples of this rigidity phenomenon. And they all come from the surgery theorem. And the first example is, was also already mentioned by Bernard. So you are, okay, let's try to implement the strategy. What's the first manifold you can think about? You think about the disk. And not dimensional disk, there we have a classical theorem that calculates the homotopic groups of the diffeomorphism group of a disk in low degrees. And the answer is slightly surprising. You get in every fourth degree, you get a copy of Q, if you're tensile with Q. And for an even dimensional disk, you get actually zero. So that's a very classical result where Farrell Schoen, so it's almost 50 years old. And then Bernard together with Boris and Thomas Schick and Mark Walsh, they asked, do you get non-trivial elements in the homotopy of the space of PSC metrics on the disk? We're here, I mean, I mean those PSC metrics which near the boundary are just the wrong metric. And what they proved is, well, this map is rationally zero. That's bad news in a sense, yeah? So you don't get for a disk, for a disk you can't see that the space R plus is not contracted by. So that was the, maybe that's the first instance of this phenomenon. So that's the second thing. So let me talk about spin manifolds and it turns out, it turns out that the theorems are not about the group, the action of the diffeomorphism group, but about the action of what is known as a spin diffeomorphism group. So the spin diffeomorphism group, it's not only those diffeomorphisms which preserve the spin structure, there will be a finite index subgroup of the diffeomorphism group. Instead, you have an extension of this by Z mod two. It's because a spin structure has an automorphism of order two, so-called spin flip. So it's not quite a subgroup, but it's very close to it. And this is a group we will be talking about. So what we discovered some years ago is a following phenomenon. If you take a spin manifold of dimension at least six, which is simply connected and spin mild-bordant, and then you have the following result. You take two spin diffeomorphism manifolds, you look at the pullback maps on R plus M, and we found out that these pullback maps commute to homotopy. So why is this remarkable? It's remarkable. By slight reformulation, we see why it's remarkable. So this action map, it starts from pi zero of the spin diffeomorphism group, that's so-called spin mapping class group, and goes to pi zero of the space of homotopy automorphism of R plus M. And the result says it's a group homomorphism, it's homotopy automorphism, that's the pi zero of it is a group. And it factors through the abelianization of the mapping class group. If you take a commutator of two diffeomorphisms, then it acts trivially. And this is remarkable because this group, this is a highly non-abelian group. We know a lot about it. We know that it's an arithmetic group by a theorem of Dennis Sullivan, but it's complicated, it's big. And this one is completely mysterious. So we don't know the homotopy type of R plus M. And even if we knew the homotopy type, we don't know what the group of homotopy classes of homotopy self-equipment should be. It's a completely mysterious object. But this homomorphism, it factors through an abelian group. And this abelian group is often small. So one example that played a role in our work was you take S3 cross S3. And then you take the connected sum of many copies of it. And if you take enough connected, enough copies, then it turns out that this abelianization of the spin mapping class group is actually the trivially group. So it tells you for this manifold M, whatever diffeomorphism you take, whatever spin diffeomorphism you take, the pullback map on R plus M is a homotopic to the identity. So that's the phenomenon, that's something we discovered. It was on the way of the proof of the theorem that this index difference map is subjective. This index difference map to KO theory is subjective. So now if you know it's an abelian group, it factors through an abelian group, you ask what abelian group could it be? And they have the following construction you take. If you have a diffeomorphism of a closed manifold, you look at a cylinder and you can glue the two ends of the cylinder using this diffeomorphism F. And then you get a manifold of one dimension higher, the mapping tools. And if you take a spin diffeomorphism, this mapping tools has a spin structure. And you can look at the spin cobaltism class of this mapping tools. So we get a map from the spin mapping class group to the spin boredism group in one dimension higher. And it turns out to be a group of morphism. And of course the spin cobaltism group, that's an abelian group. So that's a candidate, that's a candidate. And it indeed it turned out to be two. It was a PhD thesis by Georg Frenk. The main result is so in this under these hypothesis, you have a spin manifold simply connected and often of dimension at least six, then there's action map factors through the spin cobaltism group, the other mapping tools. So this says you take a simply connected spin manifold, you take a spin diffeomorphism. And if the mapping tools of the spin diffeomorphism is null boredom, then the pullback map on R plus M is homotopic to the identity. So that was Georg Frenk. And he has more general versions which work for arbitrary manifolds, but then you have to closely look at tangential structures. And I don't want to talk about it right now. Yeah, so that's just a special case. So you have a more general theorem which works for all closed manifolds. So let me say in a couple of words how he did it. So you have seen in Bernard's talk that if you have a spin cobaltism between two simply connected spin manifolds, then you have to make that spin cobaltism simply connected and then you pick this suitable hand and body decomposition. And this tells you how to obtain the M1 from M0 by a sequence of surgery in high co-dimension. And then each step you get homotopic equivalence from one manifold to the R plus and one manifold to R plus on the next one and the next one and the next one. And what Georg did was to look very closely at this and to find out that the homotopic class of this map does not really depend on the choice of the antibody decomposition. That was previously done by Mark Walsh. But then he also went one step further and it was that this map really depends on the cobaltism class on the cobaltism. It really only depends on the cobaltism class of the cobaltism. And if you know that, then it's not so far to get to the theorem. So it has an interesting special case. The interesting special case are manifolds where you have all rational Pontriagin classes zero. For example, you take a stably parallelizable manifold. And then you look in the old literature on cobaltism groups and you find a theorem that for such manifolds, the mapping tools of any spin diffeomorphism has finite order in the spin bothersome group. Not too hard to prove, it has to do with the multiplicativity of the signature. And, but as a conclusion, you get for such manifolds, for a manifold with trivial rational Pontriagin classes, for any spin diffeomorphism, the action map on R plus M does have finite order. Some power is extravially. And so you see, you see for those manifolds, very difficult to get from diffeomorphisms maps on R plus M, which are non-travelable. So then we have, and this is maybe the main new result I want to talk about is, we have a generalization of georg theorem to higher homotopy groups. So this was about pi zero of the spin diffeomorphism group and pi zero of the space of homotopy self-acquivalence as we could ask, what about higher homotopy groups? And then we have the following result. We need some technical adjustments. So we couldn't get it done for simple connected manifolds. We had to require that the manifolds are two connected. So pi two is also zero. We have the same dimension bound, D at least six. And we could not talk about the whole spin diffeomorphism group. We have to talk about those which fix a certain disc.  So you still have a map like this. And what we found out, it factors through a certain abelian group, which I call, or which is pi K plus one of empty spin D. And I want to explain what this is. What is pi K plus one empty spin D. So that's, if you know a little bit about cobaltism theory, you know that Tom identified the cobaltism groups with the homotopy groups of a certain spectrum. And the type of spectrum, which is nowadays known as a Tom spectrum and empty spin D is a certain Tom spectrum. Which was introduced in this specific version of spectra was introduced by Martin Tillmann. And the homotopy groups of a Tom spectrum have always, always have an interpretation in terms of cobaltism groups. And then what the right interpretation is depends on the spectrum and here it's as follows. So it is, you take manifolds of dimension D plus K plus one, which are closed, you take a vector bundle of rank D on the manifold. And you fix an isomorphism of this vector bundle V, or a stable isomorphism of this vector bundle V with the tangent bundle, the N. But it's not an isomorphism of vector bundle. It's only if you stabilize, if you add sufficiently many N and I wrote I infinity to be a bit more weight. Yeah, so that's the type of cobaltism group. And then what is the cobaltism? Yeah, sure, it's a cobaltism of manifolds K plus D plus two manifold. And on this cobaltism, you have a vector bundle also of rank D, which restricts to the given vector bundles on the two ends. And then you have an isomorphism of the same sort of what I said. So that's an abelian group. And we claim, and I didn't write our names, here to the theorem, that's the theorem by Oscar Render Williams myself, proven in 2019. So that's a new theorem I want to talk about. So how do we, let me explain the map A. So you take, we take an element in the homotopy in the homotopy of the diffeomorphism group. And what can we do with that? An element in pi K of the diffeomorphism group that gives me a fiber bundle over a sphere of one dimension higher. Yeah, the dimension of the sphere is one higher than the degree of the homotopy group with fiber M. So what you do is you take two copies of DK plus one times M and you glue it together along these maps from B and X. And this manifold N has a spin structure and it has a vertical tangent bundle. Yeah, you have, that's the kernel of the differential of pi, that's a vector bundle of rank D, dimension of N. And then you'll see, you exactly get an element in this group pi K plus one of MG spin D, exactly in the description here. So this map A generalizes the mapping towards construction to higher homotopy groups of the diffeomorphism group. And that explains the, that explains the theorem. Yeah, that explains the map A. And this map A is not at all an isomorphism. Yeah, it can be often be quite prevalent. So we can, there's one thing. If you look at this homotopy group, you see the manifolds in this co-border in this picture, you have K plus D plus one dimensional spin manifolds. And you just forget that the tangent bundle has a specific form. And by this, you get a map to the spin co-border group. And if K is zero, then the composition, you first apply IA and then this forgetful map, you get the mapping towards construction. So this says that for K equals zero, we get a result which is quite close to Georg's theorem, but not quite. This obvious map is not an isomorphism. If it were an isomorphism, it would just recover Georg's result, but this is a little bit weaker. And yeah, then I already mentioned, we had these strange conditions that the manifold is too connected. We would like to get rid of it, but we don't know how to do it. And also we don't know how to do it for the whole different morphism group and not just those fixing a disk. But this is, I believe, can be done, but not with our proof. It has a consequence. Like homotopy groups of spectra or homotopy groups are difficult to compute, but what is always fairly easy to compute are rationalized homotopy groups. And in this case, you can compute them in terms of characteristic classes like Contralian classes and Euler classes. And they are finally generated a building groups. So it's not so hard to calculate. And one can prove that if the manifold is, doesn't have Pontriagin classes, then this map A is rationally zero. So that's, again, that's very similar to the theorem that the mapping torus of any diffeomorphism of a stably parallelizable manifold has finite order in the group. That's very similar. And one manifold where all rational Pontriagin classes are zero are the spheres. And in this way, you get, we get back the result by Botvinnik and Anke and Walsh and Schick. So that's the corollary. If the manifold doesn't have, doesn't have any non-trivial rational Pontriagin class, then this orbit map has actually finite edge. Even through the pi k of this diffeomorphism group, that's just unknown. I think the only structural thing we know here is a theorem by Alexander Kupas that these are finitely generated groups, that's a billion groups, if k is at least one. So there's almost nothing is known and about pi k of r plus m. We also don't know much, but we know this orbit map has finite image, which I find quite striking and strange. So when I planned this talk, I thought I could explain the proof of the theorem, but I couldn't, somehow it was too long. But I want to give you an impression how such results, so all these results are like of a sort, the action of the diffeomorphism group on the space r plus m is fairly trivial. I just want to say you have 30 more minutes. Yes. Okay. Yes, yes. Okay, just to reassure you, yes, okay. Yes, I still have seven slides. But I want to go into a proof now, but I don't want to go into the proof of the new result. I want to go into the proof of the Abelianness theorem, because there you see, it will be fairly explicit. And there you see exactly how the grammar flaws and surgery theorem comes into play and works behind the proofs of both theorems. This is why I picked this Abelianness theorem as an example. And so let's go through it. So what's the setup? Is we have to simply connect with spin manifold and it's spin null-bordant and high-dimensional and we have two spin diffeomorphisms. And I want to show that the pullback maps of those two commute up to homotopy. So what we do? Okay, let's, so in this M we find two disks. So you remove the two disks and we get a co-borderism from the sphere to the sphere. Well, let's call it W and if you take the union with the two disks, you get back M. So now there's an elementary theorem in differential topology. So if you have a diffeomorphism orientation present, so if you have, so look at it diffeomorphism of M and look what it does with one of those embedded disks and it gives you another embedded disk. And if there's, they have two embedded disks in a connected manifold and a classical theorem, an elementary theorem tells you these two disks are isotopic. Let's see, so we've got disk lemma. And you can use this isotopy of disks, you can use it, you can extend it to an isotopy of the diffeomorphisms. And that tells you after isotopy, after applying an isotopy, you can assume that F zero or that spin diffeomorphism fixes this disk, point wise. You can do it with one disk, but then you can do it with another disk as well because it doesn't change it. So we can assume that our two diffeomorphisms both fix two disks and then you can remove the two disks and you get a diffeomorphism of W, which is the identity on both ends. Now, okay, we have this surgery theorem, now it makes its first appearance. The first appearance is in this, in R plus M, there's a homotopy equivalent to a subspace and it's homotopy equivalent to the subspace of matrix which on both of those two disks are equal to the so-called torpedo metric. So that's torpedo, it's a rotationally symmetric metric. There's the type of metric which shows up in the surgery theorem. By the way, I avoided that word and therefore I introduced the half spheres. Yes, but then you come into trouble with the boundary condition. So I- Not using my theorem with Christiane, I think that's okay. Yes, yes, yes, yes, yes. I mean, the theorem is so surely out of what you formulated, you can deduce what I use here. Yes, I mean, it's the same theorem in slightly different variants, yeah? It's a variant of that. So it tells you the space of matrix which on each of those disks are torpedo metrics that's homotopy equivalent to the whole of R plus M. And then of course, if the metrics are of a standard form on these two disks, you can cut out these two disks. And you see that the space of metrics on the cobaltism W, which on the two ends are G zero, where G zero is the one that's here. So by these two steps, so I firstly achieved that the spindle film often fix the disks and the metrics are of a standard form on these two disks. This means I can restrict two manifolds with boundaries. Yeah, and then let's look at W instead of M. So that was the first step. So I introduced two holes and you see, now how I use these two holes. So let's shorten the notation C means the cylinder on the D minus one sphere and M is the round metric plus the metric, the usual metric in the interval coordinate. Let me write it M. Now, one assumption was that this manifold M is bordered to, is null bordered, spin null bordered. And then it's also a spin bordered to a D sphere. And then you'll see, okay, then you can play a bit around and what you see is you get this. W, which is M minus two disks, you get from a cylinder by surgeries in the interior of the cylinder because that M is co-ordined to SD means you can obtain M from surgeries on starting from SD and you can obtain it by surgeries from that and a little refinement of that would be you obtain W from a cylinder by surgeries. Now I use the surgery theorem for a second time. And it tells me, okay, the space of matrix on the cylinder subject to the boundary condition that you have the round metric on both ends. That's the same as the space of matrix on W with the same boundary condition. And the theorem says there is a homotopy equivalence. You should not try to, you should not try to think there's a map of spaces which takes one point in the space as an argument and spits out the point here. So it's just a map, it's only defined up to homotopy but what you can always do is it gives you a well-defined bijection on pi zero components. And this is what I do. Yeah, I take a metric H zero on this R plus W which corresponds to the cylinder metric on R plus C under this homotopy equivalence, just this plate. So that's a metric H naught that I constructed on R plus. Now this has an important property. Yeah, what property does it have? It's what we call right stable and left stable. So let me explain what these words mean. So you could, so if you have a metric on a cobaltism, this makes sense in full generality but let me, I only wrote it from the situation here. So if you have a metric on a cobaltism W, you can look at any other, any cobaltism V which goes from one end of W to some other manifold. And then I can talk about a PSC metric on the other end call it G1, an arbitrary PSC metric on this other end of V. And I get a gluing map from metrics on V to metrics on W union V and it just takes a union of H with H naught. And the property that this map has is that it's a homotopy equivalence. This just follows from the surgery theorem in a couple of lines. So it's a homotopy equivalence. This is a property that we call right stable. Yeah, so why is it right stable? So we had to get to distinguish these two sides. So the metric on W is so that whenever you glue a cobaltism V on the right end of the cobaltism you get a homotopy equivalence of this sort. So in this situation, you can also play the game with the other end and it has the same property that's called left stable. So if you glue it the other end, it's left stable. So another metric which is both left and right stable is that the metric and the cylinder metric. And by the way, this notion is we develop this notion and this paper and we proof later to versions of the surgery theorem, which I just tell you it's, if you have a cobaltism from one end M0 to M1 and if the inclusion from M1 into the cobaltism is too connected, too connected means you have an I, you have bijections on pi zero and pi one and you have a surjective map with pi two. And then you can prescribe a PSC metric on one end of the cobaltism. Then you get from the theorem, you get a PSC metric on the other end and a right stable metric in between. That's one theorem. And the other theorem is if both, if the inclusions of both boundaries are too connected, then right stable is equivalent to being left stable. So, but that was only an aside. So we have, so I constructed this metric H0 and I found out it has this property. It's right stable and it's also left stable. So let's go on. And this, now I can look at a spindiff heomorphism, F0 and I can pull back the metric H0 with F0. And I take the union with the round metric and because this H0 is left stable, I can, I find out that this metric, is in the same path component of the space of PSC metrics as a metric MF0, union H0 and MF0 is a certain metric that I just constructed. So that's what we get from H0 being left stable. And now I do what I need to apologize like, I make a diagonal trace. I have W and I glue cylinders to both ends. So here I have, here I glue the C to the right end and here as well and here as well and I use the metric M, the cylinder metric to do it. Here I have the pullback with F0. Here's also the pullback with F0 but I extend F0 over the cylinder. This is the square as commutative and here I glue this M0 from the left side. This is also a commutative diagram and here I glue the H0 and all maps are homotopy equivalents. So that's clearly a commutative diagram and I want to find out something about this map F0 stuff. But now you look at this diagram and you compute the right hand column. What does the right hand column do? And the right hand composition, what it does is I take a metric on a cylinder, I glue on H0, I threw it over the manifold with F0 and I glue on this M. But now that's going to be the same as taking the union with M and the union with F0 star H0 because this metric here is in the same path component as this metric. I see that the two maps are homotopy. So that means the right hand column is the same as taking the union with H0 and then taking the union with MF0. But now these maps are all homotopy equivalents and then you see this map F0 star is essentially the same as taking the union with MF0 on the right hand side. That's what I get from this argument. So here's the conclusion. So if I first apply F0 star and then I glue on this cylindrical metric M, this is homotopic to the map that I obtained by gluing on this metric MF0 to one side of the cobalt. But now I want to talk about two different morphisms and the other one is F1 and I played exactly the same game but I used the other end. So it says F0 star is given by taking the union with MF0 from the left and F1 star is given by taking the union with MF1 from the right. But if you take the union from the left or from the right, it really doesn't matter in which order you do it. And this shows that the two maps are commute up to homotopy. So that's the proof of this ability in that theorem. So you see, I presented it because it really shows you how the surgery theorem can be used to manipulate the action of the diffeomorphism group and to obtain interesting results. Johannes may ask something. So my intuition is that, of course, if you apply these two diffeomorphisms, one after the other, each of those effects, basically the whole manifold, more or less. And so if you pull back the metrics, it's completely unclear why these two actions should commute up to homotopy, but why is it possible? So is there a kind of a rule of thumb explanation or giving an intuition why it's possible to still separate the kind of the regions where the positive scalar curvature is affected by the... I mean, that's a surgery theorem. In a sense, it's a set. I mean, the real intuition is, what really happens is here, this step. This H naught is right stable. So you see all of the topology of R plus W, I mean, W union C, it's essentially W, yep, it's diffeomorph to W, but it tells you all of the topology of R plus W is somehow concentrated on this cylinder around the boundary which is not affected by F at all. That's how, this is really the intuition. The intuition is it's all the complicated topology of R plus M, it can all be compressed into little disks. That's the reason. But we don't get, I mean, we don't get that the action is trivial. You don't, this doesn't follow from that. And it's also, it's not true, yeah. The action is non-trivial. One can concoct examples of manifolds where this is non-trivial. But it's somehow, this is the best you, the most you can trivialize. So it commutes up to homotopy. So it factors for the abelianization. And maybe I should say, maybe I should say that you should say this explicitly. This map A, which goes from pi naught of the spin diffeomorphism group to pi one of empty spin D. This map is some, for some, for some even dimensional manifolds. But it is actually the same as the map as the abelianization. So that's really something one can show. Galaxius Rendeweim really proved this. It's part of their big theorem. For some even dimensional manifolds, this map is actually the abelianization. But that's somehow, you can't make the action completely trivial, but the fact that you can compress, that you can compress all the non-trivial topology into disks makes it possible to prove such a thing. You can't prove more, but this is exactly what you get. So we can also, then later, we also showed it for manifolds with arbitrary fundamental groups. And then the role of the disk is then played by somehow the unions of all the two handles in handle body decomposition and things like that. It's a very similar result there. Yeah, this is a basic argument.  It's very similar to the classical Eckman-Hilton argument which proves that higher homotopy groups of spaces are commutative. And that's not very much, not different. I could also, no, maybe I shouldn't say this. No, no, that's not true. Okay, let's go on. So you see that the surgery theorem really allows us to prove things about the differential morphism action. Let me also say that this is a key lemma in this work with botvinic and random variance because it allowed us to use knowledge about differential morphism groups to conclude finally things about R plus of the sphere. So it also tells you, this is also a theorem which tells you that this action of the differential morphism group, it's not just a random action of some topological group on some topological space. There's very distinctive, very interesting and rigid features. So that's, I found this very interesting when we, and I still find it mysterious. So I promised to talk about a little bit about the higher dimensional version for higher homotopy groups. And then we don't do it in a way that we look at homotopic groups. We look instead at a certain vibration. So there's a standard construction in algebraic topology. If you have some topological group which acts on a space X, you can form a fiber sequence with the base space. It's a classifying space and the fiber is X and the total space, that's the so-called homotopic quotient. Yeah, X, yeah, it's EG cross over G with X. And for such a fiber sequence, you get a long except homotopy sequence and it has a connecting homomorphism. The homotopic groups of BG are the homotopic groups of G shifted in degree by one. And then you apply the homomorphism and the map is exactly, I mean, things are exactly done in such a way that the connecting homomorphism is exactly this orbit map. Yeah, that's exactly true. When you want to say something about the orbit map, it might be better to say something about this vibration and to see, for example, why is the connecting homomorphism this vibration? Yeah, so the theorem that we actually prove makes a statement about this vibration. So here we need to talk about the group Diffen that's a whole of a big group from a group theoretic perspective, but it has a nice geometric model. So it's like, you know, what is BOD for the orthogonal group? It's this, you know, it's a Grasman manifold. The Grasman manifold is the space of all linear subspace of r infinity of say, dimension D. And here, Bdiffen that can really be modded as a space of all submanifolds of r infinity, which happen to differ morphic to M with a, of course, that needs to, you need topology to make sense out of it. But that's a nice model. So you can really think about points of Bdiffen as some manifolds, which are differ morphic to M, but not equal to M. And similarly, this homotopic quotient has a nice description like you take such a submanifold which is differ morphic to M, and you take a PSC metric on it. Yeah, that's the, there's homotopic quotient. And that's also what one knows as a modular space of PSC metrics. It's very close to what Bernard calls the observer modular space. It's the only difference is I apply this usual trick. So the usual trick here is the action of Diffen on R plus M doesn't need to be free, but you make it free by introducing this extra EG, this contractable free G space. And then you get, then you get this. So that's a modular space very close to this observer modular space. Now let's, let's return to the situation where you have a general group acting on a general space. And you look at this vibration that I just introduced from the homotopic quotient to the class frame space. And now I suppose that I can induce this vibration from another vibration over some space set. Yeah, suppose I have a vibration over some space set and I want a commutative diagram which is homotopic Cartesian. And that's, what does it mean? Homotopic Cartesian means the following. It means the following if you turn this maps Q and P into vibrations, you can always, there's a standard way of doing this. Then you get an induced map on the fibers from Q, fibers of Q to the fibers of P. And you want that this map is always a V-comotopic equivalence. So that's the meaning of being homotopic Cartesian. It's the same as saying that the, that the vibration Q is induced from a fluctuation P over some space set. So assume that this, and then you, then you make a little diagram trace and what you see the action map, the action map is from the homotopy of G. It's the same as the homotopy of BG, but drifted in degrees. You take connecting homomorphism and you make a little diagram trace. The fibers are the same. And you see that this connecting homomorphism factors over F. And that's exactly the theorem of the sort we want to prove. Yeah, that's exactly how we do it. So instead of looking at individual homomorphisms or individual homotopy classes of diff M, you look out for such a vibration over some space set. And that's what we want to do in this. And you can play a similar game. So we have two versions, one for the orbit map, the other one goes to this, that looks more fancy. So the homotopy automorphism, but you can get the same deck. Yeah, so they both of these maps factor through the homotopy groups of set. And then what we do here, okay, we look at the action of B diff M on R plus M and we do such a diagram. So what are these spaces there? Explain the left-hand column and the right-hand column is looks very scary. The infinite loop space of the spectrum. That's a very big thing. Its features are the homotopy groups of this looks infinity empty spin B are exactly the homotopy groups of the spectrum that I just talked about half an hour ago or 20 minutes ago. And then there's a map alpha. And this really, so I should say what are the hypothesis? The hypothesis are that W is one connected and spin and the boundary is also simply connected. And those hypothesis you get such a map alpha. And that's a very, that's a very important map has been, this was introduced by Eben Watson and Michael Weiss 20 years ago and Ulrike Tillmann, they did it. Yeah, these three people introduced those maps. And there are many firms saying when this map is some sort of equivalence, it can't be a homotopy equivalence because the right-hand side is a loop space and it has a billion fundamental group whereas the left-hand side, the fundamental group that's pi naught of B this delta W and that's, as I said, a big non-nabirian group. But sometimes for some manifolds, it's known to be a homological equivalence in small degrees. And it's, I gave you one example where the statement is literally true. It's if you take connected some of many copies of S3 cross S3.  I don't know. Is it microphone? Yeah, I mean, we can hear you but it's sometimes distorted. If he stays a little back, it's not distorted. Okay, yeah. Okay, so this map, these are really well studied and have been well studied in the last 20 years. So it's not a random construction, not something we came up with. But it's some standard thing. It's like a, if you know the comparison of cobaltism groups with homotropic groups of the term spectrum, it comes via this so-called Pontriagin-Turm construction and it's exactly the same in a parametrized way. And that's how these maps alpha come into life. So that, an important thing here is that this infinite loop space is the classifying space of the spin cobaltism group category. So what is the cobaltism category? The topological category, objects are close D minus one manifolds, morphisms are D dimensional cobaltisms, both have spin structures and then you take the classifying space. It's a general construction homotopy theory and then Galatius-Machin-Turman-Weis proved that this classifying space is homotopy equivalent to loops infinity, I should say minus one to be correct. Loops infinity minus one of empty spin D. So that's it. So this space here is a classifying space of the cobaltism category of spin manifolds. And then the idea was, what is this mass cal X? It is a classifying space of the cobaltism category of manifolds except the metrics of positive scalar parameter. It's not exactly that, it's a variant and then we get a diagram and then it's quite a bit of work to show that this is homotopy cartesian. There we need at several places, we need the surgery theorem in a very essential way to do it. So that's how it goes there. It's really the use of the surgery theorem here is really hidden in the construction of X or rather in the proof that this is homotopy cartesian. But I think it's a good time to stop here. I hope I convinced you that the surgery theorem can be used to prove powerful results about the different morphism action. Okay, I think I stop here.


We're going to spend the next 20 minutes or so just talking to you guys about School of Physical Sciences. I'm Andrew McKinnon. I'm an actual physicist, so don't hold that against me unless you love physics and then you'll embrace the whole idea. Good thing is I won't be talking for the full 20 minutes. I've got three students from the School of Physical Sciences who are at various stages of their journey here at University of Adelaide who will be talking to you about their experiences. And that's part of what we're going to talk to.  A few things there. University, why University of Adelaide? Well, we're the leading university. We're ranked in the top 1% worldwide. I'm going to talk a little bit more about some of those details and these guys will as well. So physical sciences, that incorporates physics, chemistry and earth sciences which is a geology, geophysics type of area. As I said, we're going to hear for three students. They all have very unique journeys and I think that's the important thing.  And one thing is it's a journey that should be challenging, should be rewarding and also it's a journey that has to lead somewhere. And that's one of the really powerful things about science is it does lead somewhere, it does open doorways. Now when you sort of consider what is in physical sciences, there's a lot of different variants and sometimes people can get confused about this or the different degrees, the name degrees. I'm not going to go into the huge detail behind these. We've got set up in the tent next door. We've got people there who will be able to spend some time sitting down explaining some of the nuances. The main thing I just want to point out is the things the Bachelor of Science or the Bachelor of Science advance, when you do those you end up doing a major. So the main thing we're going to be talking about is the people who lead on and end up with a major in chemistry or geology, geophysics or theoretical physics or experimental physics. Then we've got the advanced degree. You also end up with a major. The only difference is the advanced degree has a research component attached to it. They are very similar programs but it just has that research component in the first to second and the third year. So you actually can spend time with some of the researchers potentially doing some research yourself which is a great opportunity. Then we have the name degrees. The ones I have up there are the energy geoscience, the mineral geoscience. They're from the geology area. So they end up, they're very similar to a normal Bachelor of Science with a major, for instance, in geology or geophysics. But some of the courses which they encourage you to do and you need to do lead into that slightly more focused area. Then we have the physics ones, space science and astrophysics, high performance, computational physics which is actually an honours degree. It's a three year and honours is already embedded in it. Normal degrees you'll do a three year degree and then honours after and laser physics and technology. Again, they're very similar to a Bachelor of Science with a major in physics but the courses or the subjects, what you guys would call subjects we call courses have got a focus in those areas but they still end up being effectively a Bachelor of Science with a major in one of the discipline areas. Why study physical sciences? A lot of reasons. You love it. Okay, you like asking questions and finding out solutions. I mean that's one reason why I really love doing science. Studying something new, this is a great opportunity to try something new and a Bachelor of Science, especially in the physical sciences you've got a broad range of things you could actually pick. You want to be a scientist or not and I talk a little bit more about that because it's the skills you get doing science and in the physical sciences can transfer in so many different areas. You want a job. Okay, everyone wants a job, hopefully. If not, this is probably not the pathway for you. If you're not exactly sure what you want to do and this is a really common one, you're not sure what you want to do and you'll find there's a lot of people who get quite far into their degree and aren't yet sure what they want to do but where these degrees are fantastic they let you delay that decision. So if you're still procrastinating or you may know what you want to do, basically this is a great opportunity. Now, some of you may have gone to the talk that Sandy gave this morning which was about the broad science degrees. I'm not going to talk too much about this but the main thing I want to pick up, this was actually, it was a survey which was done in 2015. It was the office of the chief scientist. Top three things, active learning. This is what basically skills that employees want. Active learning, critical thinking, complex problem solving, creative problem solving. That's in a scientific area, not like creative accounting, okay, science, creative problem solving and it's only when you sort of get quite far down you start getting the discipline specific skills. So this is the critical thinking skills, the ability to solve problems. It's the skills you get doing science. That's what employees want. They do sometimes want those discipline specific skills which gives you this fantastic opportunity to study something you really enjoy doing and then get the skills that will get you a job. It's a fantastic combination of the two. Job mobility, this is something which is very different to people of my generation or older where nowadays people are turning over jobs. People are changing career paths. You'll actually find what you think you want to do or what you start out doing. You'll probably find 5, 10, 15 years later you're doing something very different and so that's where at university it's not the skills, it's not the job specific training you get that counts. It's the skills that you actually get, the skills that can be transferred into a lot of different areas. So it is something where it's very unlikely, unlike your parents where they may have had the same job for a very long time, it's very unlikely that people will actually have that in the future and also we don't know what some of the jobs will be in the future. Okay so this is a little, it's a one or two years old this information here so just bear with this for a sec. Physical science graduates, okay what do they earn? Well starting salary for a science graduate in 2015 was about 60,000. That's not too bad. That's not bad. You come up, it's on par with what you get for medicine when you first come out. 47% of people go on to do further full-time study.  They enjoy the research and the benefit of that is they're starting salaries over 80 grand, okay. By 2019 the level of employment of physical sciences is predicted to grow by 11%. That's actually gone up. That's now up 14%. So there's this demand for people who have got the physical sciences skills to actually get jobs. We realize there's a huge focus on the government in STEM related areas and that's where you get the physical sciences are at the core of those areas. And 22% of physical science graduates are employed before they graduate. We get people who haven't even finished their degree and already have a job lined up which is higher than what it typically is for most university broad graduates. Okay, that's enough of me talking. What I'm now going to do is I'm going to hand the floor over to three of our students. They're in their summer at the beginning, the middle and the end of their PhDs and they're going to talk about their journey. So first off I'd like to ask Jason if you'd like to come up and talk to us about your journey. Step one, figure out the microphone. Is that all right? Hi everyone, my name is Jason Oliver. And today I am speaking to you with a goal in mind, right? And the goal that I have in mind is to share with all of you my experiences over the last five to six years, right? So in keeping with that goal, something I'm not going to be doing is going into huge specifics about what I've studied, right? You'll have loads of people who can do that. I'm going to try and keep it simple and I'm going to try and just be general, right? So with this in mind, I need to talk about where I'm from, where I move to, what I studied and what I plan to do, right? So unlike a lot of people here, I imagine, I'm from a rural town, Waala. You've probably all heard of it. It's well known for its manufacturing of steel and mining and these sorts of related industries. This is a picture from the jetty in Waala, which is probably one of the nicest pictures from the town. The rest is red. That's the secret. And five years ago, I moved from Waala to Adelaide, which, as you can see, is quite different. The reason I moved from Waala to Adelaide is university, right? In year 12, I was a bit unsure what I wanted to study. I knew that I was interested in physics and I knew that science was sort of where I wanted to go. But I think like lots of science students are sort of tempted by the dark side. And in this case, the dark side is engineering, right? And one steel there, when they offer to pay for tuition and things like that, it can be a very tempting sort of offer. But I sort of thought about it. I did my year 12. It's a very difficult time. And then I sort of censored around doing a degree in physics. So the degree I did was a Bachelor of Science Advanced, which is a very research oriented degree. So moving on, I've sort of summarized my undergrad into some highlights. So when I look back on my undergrad, the things that I think about are making lots of friends in like my first and second years. I was founding the Science Society of the University, which is called OSCA. There's like 400 people in it. And going on exchange to Copenhagen, Denmark.  To probably like, off the top of my head, I actually don't know how many places that you can go on exchange to. But it's a lot. So if you can think of the country, you can likely get something arranged. And it's that experience in particular that really affected the rest of my degree. It really changes the way that you look at things. And you become a very sort of internationally minded individual. In particular, I really liked my third year of course work. You don't often have people say, yeah, I really like study. But my third year was like really something. The courses that I did were all very well designed. And they all sort of coalesced around specific ideas in physics. And in particular, I also had exposure to research culture, which is sort of summer research scholarships, exposure directly with professors and things like that. And after I think, I think that's really what we want. We want to do a degree, but then also have exposure to what it's sort of really going to be like. Because there can be a disconnect between a degree and the actual job that you're going to do. So because I had academia in mind, this sort of let me sleep well at night. So when I thought research culture, I thought lots of people don't really, when you're just coming into university, that doesn't really mean much. Right? Because it's, it's, you don't have experience surrounding what academics do every day. Right? So I thought a good way to sort of explain what research culture is, is, sorry, yeah, that's better. A good way to explain what research culture is, is by just telling you what I did in my honors. So I chose a project in an area of my choice. For what I did was sort of like a mixture between theoretical physics and experimental physics. I also did coursework. So I did seven courses along the side. And along the way, I learned a lot of different skills, like particularly like programming, which is really transferable. Looking up, being able to read articles and things like that. And at the end, I wrote like a 50 page thesis that I, that was all like mine and what I really understood. And it was titled Chargino Polarization in the MSSM, which is like a really specific thing. And if your eyes glaze over, that's good, because these things are supposed to be specific. Right? You're not supposed to be able to understand at day one. So what I'm doing now is working on the Atlas experiment. So I've started my PhD. How many of you have heard of the Atlas experiment? Just check your hands up. Yeah. Okay. So the Atlas experiment is a cathedral sized detector that's located about 100 meters below Geneva, around the Large Hadron Collider. And for some context, that's a EU citizen, right down at the bottom. So it's a huge detector and it's awesome. And the Large Hadron Collider is this big. So it's 27 kilometers along. Thousands of people work on it. And it's really like cutting edge research. So if you're interested in a PhD, some of the things that are really good about it, it's self-directed. You get direct exposure to research, culture and academics. You can be a part of an international collaboration. And I think the next one's really something I like. There's lots of travel. So in a month's time, I'm actually traveling to Geneva to work for eight weeks. And I'm really excited for that. And you also get coffee machines, which is awesome. And I did have something to say there, but I think I'll probably leave it there. But just say that a lot of the time, you don't know what you want to do. And that's okay. I think if you invest in skills and in yourself, then those skills and that investment in yourself can pay off in many other jobs and things like that. So I'll just leave it at that. Because true to my nature, I spoke too long. That works, I think. Yep. I'm Laura. I've actually just finished my PhD in metamorphic geology here at Adelaide, which is quite a nice feeling because it's always a bit of a long journey to get there. But sometimes I'm really surprised that this is where I've ended up and what I've ended up doing. Because when I was at school, I had absolutely no idea what I wanted to do. My career choices varied almost on a weekly basis from things like architecture to meteorology to diplomacy, which I thought sounded very glamorous. And eventually, by the end of year 12, I still had no idea. So I knew I wanted to go to uni, and I enrolled in a combined law science degree with a diploma of language in Spanish, just to cover as many bases as I possibly could. I didn't even really know what I wanted to do as my science major. And when I got to uni, I started doing geology in first year, and I really enjoyed it and kind of just kept on doing it. Throughout my undergrad degree, I did work experience for a mining company. I did work experience for Santos. I did a law clerkship, and I spent two months living in Spain, learning the language. But somehow throughout all of that, I just kept on doing geology. So I thought I'd share some of the reasons why I started and why I kept on going. Geology is really broad-based, and it gives you an opportunity to study lots of different things. So when I was at school, I liked geography and I liked chemistry. And I get to use both of those things a little bit in my day-to-day work in geology, and also a little bit of physics and a little bit of creativity. So my role is to get what evidence I can and then to try and make the most logical, most simple story I can from the evidence I've got to try and understand specific processes in the earth. I've always been interested in how the world works, and I think lots of people probably fundamentally are, because you look at the earth and you see these patterns that need explanation. So for example, why are some places really safe to live in other places or not? Or why do some places have mineral resources, and why do others not have them? How do we find them? How do we make the most of them?  Why is Mount Everest the highest mountain in the world, or why is there a great big rock in the middle of central Australia? And all of these things are things that geology helps us to answer and to understand. So that's what I really liked about it. It's also a good way of making friends. So when I walked into my first year math class on day one of uni, I knew absolutely nobody. And I was a little bit concerned that I would be a bit lonely. But science in general is a great way to meet people because we have prior sessions, we work in groups and we spend quite a lot of time with contact hours at uni getting to know people. Geology as well as has got quite a strong social scene. So we've got a university geological society who have barbecues. And they also run pub crawls with varying degrees of geology puns on the shirts. So that's always a bit of fun. But because geology's got such a strong field component as well, that was another way of meeting people and getting to know them. And I think lots of students have never done things like field trips before. So at first perhaps it's a little bit out of their comfort zone. But by the end, almost all of them find it a really rewarding experience. And the friends they make on those trips are friends that they keep for a long time. So that was a cool part of geology as an undergrad. I also really like travel, like lots of geologists I think. And so I've got to visit some amazing places that I probably never would have been to otherwise. So even as an undergrad, we visit Central Australia and the Flinders Ranges. And then when we get to honours, there's a trip to New Zealand, which lots of the students really love. But when I started my PhD, that's when I got to visit the really cool interesting places. So I spent two months in Antarctica doing field work, which was obviously a fairly unique experience in one of the highlights of my PhD. I've also visited parts of India that I never would have gone to as a tourist. And last year, I ticked off my seventh continent when I went to a conference in Namibia. So it's kind of good because it's partially paid for, so it's subsidised travel. But it also means that I see the world and I visit places that I wouldn't see as a tourist and I see it differently because I'm there to understand how it works. The recurring theme of my life is pretty much indecision. So the good thing about geology was it left so many doors open and I didn't have to decide right away what it was I wanted to do. So obviously you can work for a mining company or a petroleum company, but really you can also become an exploration geologist and spend time in the field. You can go into teaching, you can work for the government, you can even go into policy and things like that or financial analysis for big finance companies. All of these things, the options that the doors are open to you when you when you do geology. So I really like that and that's sort of why I kept on going. But kind of lost and it sounds a bit lame, the reason I really stuck at it is that geology becomes a lifestyle, it's not just a desk job. So I love being outside, I love travelling, I love going to new places and doing things that are a bit different. And so I get to do that as a job. It's really a kind of unique job I think in that sense. And for me, I've just finished. So what's next for me is that I'm starting a three-year postdoc with the Geological Survey and the University. Next week I'm going out to do helicopter field work in Western Australia. And although I never really expected to end up here, I think what happened was I just took advantage of all the opportunities I had and kept an open mind. And I think that's probably what's really important about your trip at university is just to see where you go and do the best you can while you're doing it. Hello. Hello. How's it going? So my name's Lobby. So I'll just be wrapping up the student talks. So I am a chemist by trade. I'm doing my PhD in chemistry. And I just want to talk a little bit about what I actually do on a database basis and a little bit about what my research is about. So I work in a bit of hydrogels, which is a kind of material that's made about 95% of water.  But it's also using things like tissue engineering and drug delivering. I don't really want to focus too much on the chemistry per se, but I do want to kind of mention what this really means as a researcher. So I brought with you one of the hydrogels that I made today. So I've got this orange gel in a vial here. And what this represents is actually one of the rarest and most unique compounds in the world. And I know that because I made this one. This is the only one in existence in the entire universe as far as anyone in this known earth actually realizes. And that's kind of the essence of what a PhD is. It's discovering new knowledge, it's uncovering new facts, and kind of seeing the world before anyone else does. If I sort of thought to myself you know ten years ago when I was sitting in a position similar to yours, I probably didn't think to myself that I would be doing this kind of research, kind of looking at things that no one else had known before. And so 2006, that's when I was in year 12, I got my 10-year school reunion coming up which is quite scary. Like many people in year 12, 17, 18 year olds, I had a bit of a teenage crisis. I didn't really know what I wanted to do in life and I kind of felt like this frog here just kind of hanging on the ledge not knowing where I wanted to go. Yes I liked chemistry and science, but I like maths, I like drama, I like singing and I like painting and all sorts of stuff. And I was kind of confused as to what I wanted to do. There was so much pressure when I was in high school to kind of pick a direction. And I felt that everyone around me knew what they wanted to do and I was the only one that was sort of struggling. I wish someone had told me that this was the reality of the situation, that nobody knows what they're doing. We're all scrambling to kind of figure out what degree we want to do, do we even want to go to uni, do we want to take a gap year or whatever. And yeah that was a difficult time as I'm sure many of you can recognise. So after year 12 I decided that you know going to uni wasn't really a good idea for me. I was too confused and I just need a bit of break after studying for 12 years. So I took a gap year. I deferred university, I worked for the first half of the year and then I saved all my money and went to USA working in one of their summer camps. It was a great synergy for me. From an all-knowing experience to meet all these people, from all these different countries around the world, from the Netherlands, from America obviously, from different parts of Asia, Asia from the Middle East and kind of opened my eyes up into what the world is and also the kind of person that I wanted to be when I you know left and kind of went on with my life. Not necessarily the job I wanted to do but what I wanted to contribute to the world and I think after that gap year I was in a better position to make decisions about my life and so I involved back into uni and I involved in a double degree in both maths and chemistry and I enjoyed both those things and kind of just wanted to see how it went. However, after the first year I decided to drop maths. This was me kind of in a nutshell. In primary school what's one plus one? Two. Awesome. I am amazing at maths. In high school you know it's still a little bit difficult. They started introducing algebra and things like that. Still a challenge but it was something that I felt that like yeah I really enjoyed that. That was really fun but then when I got to university things just spiraled out of control. There were all these like symbols and numbers and I didn't know what they meant and for me it was just too hard and that's when I decided to drop it and quit maths and I think for me that was a really good decision. A lot of the time we think about don't be a quitter just stick with it but for me I could have gone on with maths tried really really hard but in the day I just didn't have it and so I decided to focus my attention to chemistry. A subject I still really enjoyed but I was ultimately better and would kind of like find more satisfaction from that and that decision paid off for me because in the next year I went on a semester exchange to Hong Kong. I think you're kind of seeing like a general travel theme that our students really like to not be here and that's a good thing you know there's very few times where you get the opportunity to spend six months living in another country experiencing another culture meeting people from all around the world and seeing phenomenal views like that and I look back at my time in Hong Kong as some of the greatest times that I ever had. After my third year I decided that I really still did enjoy chemistry and so I went on and involved myself in honours. So honours is a time to do a little bit of research and also to try and figure out is research for me do I like this research life and there was a lot of emotions that were going through my head throughout the year and if you are doing any research you'll probably feel the same thing. There's disbelief when things never work out there's anger when your experiments don't work a lot of depression when you put so much energy into research and it's going to work out a lot of frustration but there's also joy and happiness when suddenly you figure out something a problem that you've been working on for six months and you suddenly crack it. I decided that yes research was pretty good so I decided to involve in my PhD and I sort of wish that when people told me to do a PhD that they kind of explained the whole commitment idea of it and for me a PhD is very much like a marriage it's a commitment to one other person for x amount of time often very strenuous relationship at times but yeah it is a commitment so for those of you that might be thinking about this in the future just bear that in mind but it does lead to a lot of opportunities as well and so in two years ago I got to go to a conference in Germany again traveling seeing the world learning all about other people that brings me to today and the future and what I want to perhaps do in the future and for me I absolutely have no idea what I'm doing and I am not stressed about that idea I think it's okay because if you see my track record it's quite a non-linear pathway that I've taken but it's all sort of worked out in the end and I have kind of faith that with all the things that I've learned throughout my university degree the fact that I have these degrees and have these opportunities but in the future something will come up for me that will work with what I want to do and that's what I want to end with thank you very much okay we've pretty well almost ran out of time so we just ended just in time what now well what now is a big question for you but in the immediate future we're actually going to be running three tours leaving right now so the people leaving the tours Jason will be leading a physics tour and will be leaving from the bottom and heading out those doors chemistry Nobby will be leading a chemistry tour and these are tours that will go outside of what you can normally see and have a look at some of the facilities focusing on physics chemistry and also earth sciences Alan who will be holding a sign there's Alan there actually if you guys lead from the top so chemistry geology leave from the top the last thing I'll leave you guys with is it's a quote that Jane Lomax Smith said when she was given a graduation speech pick a passion not a profession it's the skills that will give you a job thank you very much


I think the box looks different than last time but overall I felt pretty similar. I think that fourth inning was kind of a one strike one pitch away from getting out of there and you they put some good at bats together and you know hit it where we weren't kind of a little bit. Other than that I felt I felt pretty good about you know executing.  Did you feel as though that was not quite as consistent as it was last time out? I did. I think the Frazier ball was a change up and the Mariznik pitch was a slider that he just kind of got to. I felt that like the location was decent. Maybe a little further varied might have been better obviously hindsight there but yeah that's probably accurate. And how much of a challenge is it facing the team same team in a short period of time? Yeah I mean you try not to overthink it or at least I try not to overthink it and I try to attack and get strike one. And again for the most part you know take away a few at bats but you know I also give them some credit you know they started making some adjustments and that's kind of what I saw. It seemed like you guys had this game won but obviously not the end result you would have liked. What's the overall frustration level at right now with this team considering all that's going on in the last week plus. Yeah I think you know we probably do feel like we let this one go. I think more often than not we definitely get that that game. But I think we bounce back we got to tomorrow we don't have much time to to dwell on it. You know we got to we got to recover and come ready to play and I think we'll be ready to do that. Thank you Jen.


Hey, this is Brett, and this 2021 Ford F-250 Crew Cab Short Box XLT is stock number 13017Z. I am here at Summit Automotive in Fond du Lac, Wisconsin near new and used heavy-duty truck headquarters. This 2021 Ford F-250 has the 6.7-liter Power Stroke diesel engine, 475 horsepower, and 1,050 foot-pounds of torque. This truck has been fully-safetyed and inspected by our service shop, has a fresh oil and filter change. All the fluids have been checked and topped off, and this truck is 100% ready to go. I'm going to go all the way around in this video, inside, underneath, start it up, and take a look under the hood. Carbonized gray metallic is the color. I shoot all my videos in 4K, so if you have HD capabilities on your computer, tablet, smartphone, or television, I highly recommend turning them on right now because it is your best way to check out the quality, condition, options, and cleanliness of the vehicle before seeing it in person. And if you like the video and how I do things here at Summit Automotive, consider clicking the subscribe button to my YouTube channel, the lower right-hand part of the screen, and then click the bell notifications, and you'll get updates every time I do videos here at Summit Auto. This one comes with the 18-inch chromed alloy rims, and it has Goodyear Wrangler all-terrain adventure tires. These are LT27570R18 tires, and they have right around half the tread left on them. Framing underbody is an exceptionally nice condition. This is a one-owner outer South Carolina. Front fender is an excellent condition, no dents or dings, headlight lenses are nice and clear, and it does come with the factory fog lights. Front bumper and lower valance are an excellent condition as well, and you do get the chrome-trimmed grille. I didn't see any dents, I didn't see any dings on the hood. Looks really good. Passengers side front fender is in nice shape as well, and the passenger side rim, no major scuffs or scrapes on there. Carbonized gray metallic, it's got a lot of metal flake to it. Really a cool color. I think it was new for 21, I was the first year that you could get this. And as you go down this side of this truck, take note of how clean the body is, how reflective and mirror-like that paint is. I take all these HD videos, so if you're far away or even if you're close by, you just cannot make a trip down, but you're still interested in purchasing the vehicle, you can see the truck here, the truck, and have confidence in the vehicle that you're looking at before you even get here. So when you do get here, there's absolutely no surprises, and you can make a smart and informed buying decision from wherever you're at. And if this video helps you make that decision, let your salesman know that you saw the video, that it was helpful, and that Brett sent you. And if you helped you out at all on this video, give us a like and subscribe on our YouTube channel, the upper right hand part of the screen. Back rims in excellent shape, and these back tires are brand new, they still have the little wear knobs on there, so you can see what a brand new tire looks like. Frame and under body is in excellent shape once again, and has all the remaining factory exhaust, so it hasn't been altered in any way. And it comes with the very nice wheel-to-wheel side steps, so they go all the way up to the box, which is nice to get into the box. Pass in your side box, no dents or dings, it does come with the FX4 off-road suspension package, and it does have the chrome package, which gives you the chrome-tipped exhaust, as well as the chrome-trimmed mirrors. Coming around to the back of the vehicle, rear bumper is in excellent condition, no dents or dings on there. It does have the backup parking sensors, and the full towing package, which includes a receiver hitch, four-pin and seven-pin wiring. The tailgate is in fantastic condition as well. Does have the tailgate step assist, backup camera, and a very nice line-ex spray and bed liner. You can see that was done in Spartanburg, South Carolina, so I wasn't kidding when I said this is a one-owner from South Carolina. Fifth wheel and gooseneck prep package, you get some side box tie-downs, and then seven-pin and four-pin wiring back here. Comes with a nice northern tool and equipment toolbox. Tailgate shuts nice and solidly, and you can go down the driver's side, just as clean as that passenger's side. No dents or dings on the box here, looks really good. And for full disclosure, this back room is in excellent condition as well, and this back tire is brand new too. So the back tires are brand new on this truck. On the rest of this side, doors and cab all look really good. And this one does have the driver's side door code entry. We do have the code for this truck. And if you ever wanted to figure out what your code is for your 17 to 22 Super Duty and the upper right hand part of the screen guide video is showing you how to do that. Blind spot monitoring, built-in directional signals. These power fold in, they power scope out as well, I'll show you that in a second. Inside the XLT package gives you the gray cloth interior. There are no rips or tears on the seats. They're in fantastic condition. You get factory floor mats, power pedals, auto headlamps, tilt telescopic steering wheel, power windows, power locks, power mirrors. Like I said, these mirrors power fold in. I was like showing both sides, so you know that both sides are working properly. And then they do power telescope out and in. And one more time, both sides working nicely. Take a quick look at the back seats before we check out the miles and radio. Back seats are just as clean as front seats, no rips or tears. Back here it does have the latch. Child safety system for any child car seats you may have. And the fixed glass rear window headliner is in very nice shape. These seats do fold up for extra storage. You get a storage bin under there that also collapses down into a flat surface. The back flooring is also flat as well. Back here you get a USB and USB-C and then a 110 volt 400 watt plug-in as well as another 12 volt power point. These seats come down like so. You get side curtain airbags, child safety locks on the back doors, and the bottoms of the doors all look really good as well. We'll take a look at the VIN sticker as well as the tire and loading information sticker right here. Looks really good. People always want to know the gross vehicle weight ratings and stuff. We'll hop inside and check out the miles, the radio, and everything that this truck has to offer, and then we'll start it up. This truck has 37,000, 29 miles on it, I'll dim it down here. You get a digital speedometer and compass display. Instrument cluster is very nice and clean. Here in wheel you get cruise controls and information center controls on the left, Bluetooth and audio controls on the right. This one does have the 10-speed automatic transmission with the optional tap shift, and this one does come with the sync 8-inch radio with the factory navigation system. You get AM, FM, and Sirius XM radio capabilities on here as well as Bluetooth capabilities. You get all your different settings in here. You have the Ford Pass, you also have Android Auto Apple CarPlay that you can project your cell phone to the screen, and then this is also where your backup camera is going to show up when the truck is running.   Here's my magic trick for the day. You get two cupholders, now you have four cupholders. Pretty cool. Dual gloveboxes, passenger side, floor mat and seat are in excellent condition, and once again that headliner is in nice shape. You do get six auxiliary up-fit switches up there. Map lights, and we'll start it up and take a look under the hood. Starts right up, no-check engine lights or anything like that. I would personally like to thank you for checking out the video today, and hopefully from this HD video you'll be able to verify the quality, condition, and options and cleanliness of this truck all the way around, inside, and out, and under the hood. We have the 6.7-liter power stroke diesel engine. Engine-based, very clean ones, very smooth. Once again, this truck has been fully safe to inspect by a service shop, has a fresh oil and filter change, all the fluids have been checked and topped off, and this truck is 100% ready to go. There is your emissions sticker. And I would highly recommend this 2021 Ford F-250 Crew Cab Short Box XLT from a quality and condition standpoint, and to see more pictures of this truck or one of other 450 new-news cars, trucks, SUVs, minivans, Wranglers, half-tons, decoder-tons, one-tons. To name it, we've got to go to that website right there, summitauto.com. Full pictures and descriptions of every single vehicle from two locations, all at summitauto.com. If you'd like to check out more HD videos, you can go to youtube.com slash summitauto. Remember to like, subscribe, and share on this video and all the videos that you see there. Click the bell notifications. You'll get updates on the videos we do each and every day here at Summit Auto. In fact, any second you see, link to subscribe to our YouTube channel in the upper left. Link to more F-250 videos like this one in the upper right, link to this vehicle on our website in the lower left, and a link to one of our latest YouTube videos in the lower right. Click those. I'm super excited to help you with this Ultra Clean 2021 Ford F-250 Crew Cab Short Box XLT FX4 Power Stroke Diesel in Carbonized Gray Metallic. Thanks again. Remember to like, subscribe, and share on the YouTube channel. I really appreciate it. Thank you.