Hi guys, good morning. It is October 10th, just going to hit a clock here in London. You can see from picture on my right hand side, it's all going to be about, or potentially all going to be about, the trade talks today in Washington. The two-day, or is it a two-day talk between President Trump and Xi. Just before we go into a bit of detail on that, it's worth bringing up the charts and this morning we've had some decent moves already, not to go into detail on stocks just yet. You can see how choppy they were overnight, but Euro's just coming to an interesting level and worth bringing this in before we go through any points on that. We're just coming to the top end of this trend line, really going back here to, well if we start it on here on the 13th of August, so here looking at a 240 minute chart, then the next high that we had post ECB, if you remember this, the full reversal which made a new low of the year to then go higher up to where we made a high for the 13th. We're now back testing that point. We talked about this resistance level in the briefing for the last few sessions. You can just see here, always struggle to get above. We're now above there, we're testing this trend line, up 36 ticks on the day in the session already. It's a worth keeping a close watch on what happens there and actually just to, I was looking at the trading live chat and Alex, I hope you don't mind me talking through part of your trade here, just on the Euro breaking that high, you can see or you may just be able to see the entry point here to go along and fading in up towards that top end of the trend line and here I imagine this line here is the high that we had from last week as well. So great trade, waiting for that breakout to get in part on the aggressive, I guess maybe some was waiting for the classic or not, but great trade and the Euro strong this morning. So we can see here, it's just testing that trend line. I'd be really waiting to see can we get a confirmed close above there at the moment. It's just testing for now. Also, I mean, if we, before we go on to today's headlines and overnight to an extent, I guess it's worth talking about what a day yesterday was, especially considering it was a data list day other than the oil inventories at half free. We also came in in the morning and we had this headline. Let me just drag this into picture. I've got a, let me just bring this in one second, bear with me. Have it drawn up on paint, of course. We had the headline in the morning. New EU ready to make a major concession and consent by allowing a double majority in Northern Ireland assembly to leave new Irish backs up after as yet unspecified number of years. This saw the pound strengthen as you can see breaking above its pivot, which had been good resistance. However, that did get retracted or denied later on and price came down. And of course yesterday as well, we'd have the big drama between Colleen Rooney and Rebecca Vardy, which I'm sure everyone was interested in. That was a pretty good one, a pretty good spat, shall we say, over Twitter. However, you know, it got a bit more serious overnight. And I remember coming in through the door yesterday and I had football training last night and I can never sleep after football training. I think it's the adrenaline still in my body and I put Twitter up on my phone in bed and here I'm really sounding like Anthony now, checking Twitter in bed and it was all kicking off. And so for an hour or so I was just literally refreshing my feed and having a look at the charts to see what was going on. You can see stocks were really topsy-turvy, pushing to the downside quite aggressively on the futures open before reversing back and literally a full reversal by, obviously I wasn't awake at this time, thank God, but by 3 a.m. we had full reversed and reasons for this. So just before we actually go through those points, a lot of the comments on Twitter around mid-9, 11.30 were just saying how badly stocks are going to get killed following these comments. We pushed higher on the hopes that there's going to be this great meeting and now at that time you can see here just the big push. So this was here 11.15. This is when I really started checking Twitter around 11.15, 11.20. So we did get a strong move to the downside, but you can see that reversal coming back and this is obviously around 1 and then a push higher to 3 o'clock and since then, no real move, no real move. A 10-point zone if you like. Some of those comments that did come through, so overnight we had the South China Morning Post reported that deputies had made no progress in talks before the principal negotiations, so for today. The paper said Premier Li would also cut the schedule talk short by a day. So this really helped ignite the push lower, that talk to literally just going to be a one-day home early on Friday and that was it. And then Bloomberg and other media reported that there was no change in the schedule with talks set to continue Friday. So from a trade opportunity, maybe any clarification or confirmation should we say that there isn't going to be a Friday talk. We already know we're going to see some downside for that, so that's a little one to keep on the back burner there as well. Fox Business reported anew that talks would be one day as well, so if we can get any confirmation of all of this, then expect some downside to come in. One of the positive points that helped rally us or take us back to where we were, Bloomberg saying the White House is looking to roll out a previously agreed currency pact with China as part of an early harvest deal that could also see tariff increase next week suspended. So you scratch our back, we scratch yours and looking for some currency stabilisation for the dollar you want and also therefore the US scrapping some of that tariff increase for next week. This is a positive, but we are exactly where we were on the open last night pretty much. New York Times saying that Trump administration would soon issue licences to US companies to supply nonsensitive goods to Hawaii, so another good one there, and the Financial Times saying the US is weighing options to crack down on shipments or contraband goods from China, so slightly negative on that, but overall all things considered, back to where we were. Let's have a quick look at the other reactions that we saw, gold as you'd expect on the one-day talks and on the sort of the futures open, if you like, pushing higher, pushing higher by 15-20, snap back on the more positive and exactly where we are trading. So it looks like it's going to be a pretty interesting day, not to even go through the data yet, the data calendar actually looking like it should be a pretty good one, but certainly these comments are looking to come out quite often you'd imagine now and especially as once Trump starts waking up, although he was tweeting two hours ago, so a late one for the Donald. Euro, of course, pushing on here, a couple of comments this morning or headlines saying that the Euro is pushing higher because of the trade talks and of course that link between the Euro and the Chinese Yuan effectively the dollar index, but on the Chinese side the Euro is a large weighting of that, so really positive put moves to the upside for trade talks, you can also get the Euro pushing on and one to keep an eye on, so if it was to go negative there may be this trend line on that 240, you can see it looks like such a good opportunity to sell. The dollar index is, as you could imagine here, slightly weak already down a quarter percent, quick look over at the pounds, you can see at the time, the Euro push, we did just get above that pivot, relatively important resistance zone yesterday, just where we found almost a top today, so again one to keep a watch on 12258, the higher the day on the futures or previous higher the days as a potential support, and as usual with these moves I always like to have trend lines on from those lows, which you can see not that respected but potentially later on maybe something to have on as well. With this week of dollar gold is just trying to get back above the pivot, so just putting this on to a five minute chart, you can see worth having on even just a little trend like this, you can see one, two, three, four, five tests of that, if we can get a further pushing the dollar to the weakness, so you're a dollar higher, gold you'd expect to break through this resistance trend line as well, so one to have marked up on the charts for the future, so those talks taking place today really going to be the main driver for equities you would imagine, we do have US CPI and we'll come on to the Fed for minutes in a second, there's some of the reasoning behind the majority wanting that cut was to do with the previous CPI number missing expectations, so it will be quite an important reading but with the trade talks today and potentially tomorrow that's really going to be the main driver of things, so I like on Bloomberg here they always do sort of go through the key events coming up for the week and the day and things to look out for and obviously we do have the ECB minutes to come as well and then the inflation numbers on Thursday I would still say there's some other important things to come but certainly from a Euro dollar related market, it's going to be all about the trade talks, the dollar and the Euro side of things, we've got the ECB minutes and then those inflation numbers on Thursday so that will really determine where we finish the market or not, moving on to the FOMC minutes a good tweet here in just clarification really of those minutes last night, very limited reaction as usual, as usually is the case here so this tweet here is from Michael Brown many cited inflation and economic risk management and justifying rate cut, debate emerging a winter and policy easing, officials generally more concerned about risks relating to trade and global economy, wherever you heard this one before, every single central bank meeting it seems, labour market and overall economy readings are strong, although I did see an interesting tweet from someone yesterday saying the unemployment figures in US are skewed and are fake, let's not talk about their GDP readings I guess, also continued a couple of policy makers said rate cut may be too much insurance, others saying factors keeping rates steady, clear a picture emerging a weakness in investment as well interesting remark, several favoured keeping rates unchanged may make further easing more difficult, the next meeting the next favoured meeting on October the 30th so one to just under three weeks we'll be doing that live on YouTube as well covering it, the day later Draghi is leaving the day after that is non-farm payroll so that week should be pretty key and also actually I was going to talk about this later but considering we're talking about that week there of course October the 31st isn't just Draghi's leaving do, it's also the current date for when we will leave with a deal or no deal, I haven't got my phone on me but I got a text from someone and I'm not going to name names to put them in it and I'm not going to say who sent them the text actually it's an email but they may or may not have had lunch with Stephen Barkley yesterday and he was just confirming that they would be leaving on the October the 31st with or without a deal, they think the press have looked into the consequences of a no deal too harshly and in fact they are getting off the trade deals every single day of course he would have to say this as well, he's not just going to tell anyone you know what actually we're really worried we have no idea what's going on and we're getting no trade deals but yeah worth just looking into that, just seeing a couple of comments come through now China Foreign Ministry, China the applause US smearing China on protects or religion and rights a couple of comments coming through the pound actually just coming under a bit of weakness but I did mention that it's a pretty key resistance level from yesterday so it seems more technical there and Euro just having a slight bounce back towards those highs on the subject of also I wasn't on the chart so I was just talking about the pound resistance level from yesterday and the Euro on that trend line as well so it seems a bit more technical than anything there is well to have marked up, worth having a look while we're talking about the pound and whether you want to believe those Stephen Barkley comments or not is up to you if they're that confident they're going to leave on the 31st of October without a deal then yes there would have to be some more downside priced into the pound but ultimately six months time I see as higher than where we are now to be honest so today we have UK PM Johnson meeting with Baraka, the Irish PM around mid day UK time which you know the few times they have met has nothing really happened has it has been just been shot down just like most times he speaks to people in charge within Europe so not expecting too much in the way of positivity from that a couple of headlines overnight from the times and confirmed in the sun has bring this article in Brexit latest no extension without new referendum or election the EU insists and then following on from that Corbyn is willing to grant Johnson a general election on November the 26th if Brexit is delayed so I did a I did a tweet a couple of four days ago on if there was a general election and it was confirmed is the pound a buy or a sell holding trade for at least couple of weeks so you know more just going with what is your general view on the the medium term direction of the pound and 52% of course 5248 was the result but 52% saying buy 5248 saying sell and it really is a tricky one going through that because I guess on the the buy side you're getting well if conservatives and also Stephen Barkley was saying to this person they really do believe they would clean up in a general election my view is I think they would as well and so on the general election side of things you've got positive idea that they're going to have more sway more opportunity to get a deal through parliament last person to say that of course was Theresa May in 2017 and that didn't end too well but this could be seen as a positive but also on the flip side if they're going to be more hawkish and you know even favouring a no deal or whatever then that's kind of got to be a negative as well and you flip it around to the other side and you know if Labour were to get through or the Lib Dems were to provide the shock of the century and you know these are going down the route of more remain than the pound has to as well so I think you know that finished 4 votes or 2 votes either way it would have been 50-50 and I think that's almost fair enough to be honest looking at that but today mid-date you've got Johnson Veracca meeting one to to keep an eye out on as well and these talks of a general election as well to come through November the 26th the rumoured date there as well hang on election November the 26th elections are always on the Thursday so I don't quite know why they've said that's a Tuesday interesting interesting we'll look into that data calendar wise you can see yesterday was obviously you know incredibly quiet here there was just literally hardly anything out it was just that that crude oil number let me just bring in the today's calendar one second just open that up for the 10th of October here we go Thursday so yeah coming into the morning actually the morning is a pretty good one you've got GDP out of the UK as we know not expecting too much in the way of movement from these UK numbers with the Brexit still the main driver ECB minutes at half 12 we're not expecting too much from that and then we get into the afternoon we have the US CPI numbers obviously the weekly initial jobless claims as well and we've all got the speakers here Carney at 1020 and then Fed and ECB speakers making up the afternoon post EU as well those inflation numbers you can see here the straight inflation coming at 1.7 a bit of a miss hasn't been at 2% since April that was a miss expected last something to consensus for that was around 1.8 a slight miss on that we're now expecting it to rise again to 1.8 so potentially a bit of dollar strength and it would be a this could really confirm or let's just get the Fed watch to have a look at October this could really sway this quite drastically so at the moment we're at 82.8% priced in for a cut in October I saw Anthony on his Instagram did a poll recently saying how many are expected this year and the majority from what I saw anywhere getting to confirm we're saying they expect two and at the moment you can see 82.8% but if we were to have a really strong inflation number if you've got a member citing their reasoning behind the cut in September because of a poor inflation number well if you get a good one that 82% isn't going to be 82% much longer and it will come down and get closer to that 50 so quite a good potential opportunity there of a good number as well just having a look actually at that dollar again it's just having a further leg down on the Dixie which means obviously the euro is now back above that trend line can we get that confirmation push in terms of resistance levels above where we're trading we've got quite a few highs on the 25th that are one 1090 so another 30 ticks to the upside I think that's not out the question to be honest the euro has obviously been such a small mover all year a big day here and there but even so this looks like it's a massive move but it's only 38 ticks still quite small but a break by that trend line you should see maybe even a bigger as well to come through on that as well just having a quick run through the final bit of that of that Canada there you can just see those speakers are coming through but the main points that I would say to focus on today obviously we have the numbers out of the UK in the morning not expecting too much from that then we go into to midday we've got PM Johnson and America speaking interesting to see what comes of that into the afternoon we've got the US numbers which should be pretty important we've got the two-day talks in Washington is it going to be two-day are there going to be the suspension of tariffs next week all these things will influence where the S&P actually finishes up as well any questions as usual please do let us know obviously be on the mic throughout the day and going through some set ups midday which I'll put on to YouTube or Twitter or something as well but I hope you'll have a good trading date and I'll catch you in the chat


Thank you very much. It's a great honor for me to give a talk on this workshop celebrating Kodaka Shibara's birthday. So, Kodaka Shibara developed many important theories, but I cannot, so I can produce only new spaces, new varieties, and today I also send my recent construction of new syntactic varieties and its contentation. So, this is based on the joint work with Braver and Finkaba. So, the paper appeared just this, today. Okay, I first reviewed mathematical definition in Coulomb branch. So, Coulomb branch is originally for serving mathematical physics, but we try, so then the definition is, in mathematical point of view, it's almost clear and you cannot justify the physical definition, I believe, but we give some alternative mathematical reverse definition. So, let us take reductive complex data, reductive group. Then I consider the affine plus manual. So, this is modular space. So, this is a pair of bundles and trivialization. So, P is a G-bundle over the risk and phi is a trivialization except the origin. So, D is a formal risk and D is the puncture risk. And you have the action of G-o. So, I did not do this by all. And so, you have the action of G-o, affine plus manual. And so, I will later use geometric satake correspondence to respond when I just recall. So, you consider the category of power sheets, G-o equivalent power sheets on affine plus manual. And then you can define convolution product. So, then it becomes a monoidal category. Then, this monoidal category is equivalent to the category of representation of Rangran's DR group. And this convolution plus corresponds to the tensor product. This is Rangran's DR group. So, G is also we take N. So, this is a finite momentum representation G. So, this Coulomb branch is defined for a given pairs of group and its representation. Then, I consider a variety, which is a kind of certain space which lives over affine plus manual. So, this is a modular space of triples P and phi and S. So, P and phi is the same as affine plus manual. So, this is a section of associated bundle. So, you consider, so since you have representation G, so you can consider vector bundle twisted according to this P. And then, you import this condition. So, you send section by phi, the distribution. Then, phi is a ration just, just, triplication outside the origin. So, phi of S may not be regular at the origin. But, we require this to be N of O. So, this is regular at 0. So, this is a closed condition. If you don't put this condition, then it is a vector bundle over affine plus manual. But, because of this condition, this is just a closed sub-variety in the affine plus manual. And, do you have an action of G of O? Or R? This is good to wait. Maybe I'm confused how to use it. So, this is fine. So, we consider G of O is equivalent to Borelmua homology of R.  For the left end is a product of affine plus manual, and the right end is affine plus manual. Single copy of affine plus manual, and you pull back and push forward. So, on this variety R, you have similar diagram, and you can define a compilation product. So, this is a ring.  So, this tensor product is, of course, commutative. So, this is again, basically the same reason, this is commutative. So, we just define Coulomb branch, MC. So, this, as I said, this depends on MC of G and N as its specter. So, we show that this is finitely generated, and this variety is affine algebraic scheme, but in fact, this is affine algebraic variety, no normal affine algebraic variety. And, so, this, this construction, for various choice of G and N, you get many, many spaces. And, this includes many interesting spaces. For example, slice is in affine glass manual. It's rank of G. Demention is equal to twice, twice. Slice is in affine glass manual. So, this appears, if you choose G and N from those, you take quibagase, quibagase. I will explain later for very special example of finite type. And, but even for affine, if you take quibagase or your affine type, then you get so-called Chex bo variety. So, this is a new kind of variety, which was introduced to Chex several years ago. And, this, this variety has a natural quantization. Yeah, that I will explain now. So, you consider the C star action on the disk. So, you consider the equivalent homology of larger space. So, this C star action also affine glass manual, and R, space R. Then, so, this, this becomes non-commutative. And, you can consider this to be a deformation, non-commutative deformation of the Coulomb branch. So, deformation parameter H bar appears like this. You consider this equivalent homogenous additional C star. So, this is a polynomial in one variable. So, this, this is non-commutative deformation or quantization. Which object in the blackboard is called the Coulomb branch? MC. So, it's just upstairs. MC. MC, this spectrum, this commutative ring. This, this is usually called the quantized Coulomb branch. So, then, because of this, so, if you have F and G functions on the Coulomb branch, you can define Poisson bracket. So, first you lift it here, and then you take commutator. And, this, this vanishes at H bar equal to zero. So, you can divide by H bar. And, then, you specialize to H bar equal to zero. So, this is a definition, usual definition of Poisson bracket, once you have this non-commutative deformation. And, you can also show that this, this, this gives, this is coming from symplectic, symplectic form on regular locus, the Coulomb branch. Coulomb branch is in general singular, and we conjecture that this singularity is so-called symplectic singularity. In the sense of volume, but so far we don't have proof of this statement. And, there are, I mean, in some case we can construct a resolution singularity, but that's, that's not so often. And, we do have an example which is known to be, that, which is known to not having a symplectic resolution. So, you really have some singular varieties. Okay, so this is just to review any question. So, when you say, symplectic singularity, do you mean? So, this is in the sense of volume. So, if you take, there's some resolution, not, so you, you can pull back this symplectic form defined on regular locus. Then, it extends, but not necessarily non-degenerate. So, if it is non-degenerate, this is a symplectic resolution. So, symplectic singularity says that the existence of such resolution. And you, I mean, there are some, some, some general theory about this structure of variety having symplectic singularities. So, you can use some, some result. For example, the number of symplectic leaves are finite. So, it's a kind of nice space. Yeah, maybe in this example, so you can directly check the number of symplectic leaves to be finite. So, I'm not sure that this is useful or not, but I think it's a, it's a little optimistic, but it's a natural conjecture. Okay, now I just start new construction. So, from this definition, you have map from space R to to affine glass mania, just for getting section. So, instead of considering Brouwer-Hommology of this space, you just consider objects, sheeps, sheeps on affine glass mania. So, I denote this by a. So, this depends again by g and n. So, this is pi star omega r. So, this is a deriving complex on r. So, you can recover the, so, this is, I take everything in the equivalent category. So, pi is not proper. Pi is, I mean, so, the pi, pi, pi is in fact infinite dimension. So, infinite dimension vector space. So, you must be, but it is, you can approximate when, I mean, I don't give a precise definition of this homologics, but you can always approximate it by finite dimension of space in practice, if you fix the degree. So, fiber is a vector space. And, but the dimension of the vector space changes if you change the point in the finalize mania. So, this is a complex. So, this is not, I mean, you must take in the completion, but basically this is complex on the affine glass mania. And, if you take homology of the affine glass mania, then you recover this the original. So, in that sense, you can, you can, instead of working on this, you can consider this properties of this shift A. Then, you can show the following. So, this is the first method. In fact, this is not so difficult. So, A is a commutative ring object in D. That means, you have multiplication. So, as I said, on the category of fiber shifts, geo equivalent of affine glass mania, you consider the gene geometric, you consider the convolution product. That extends to this category. So, this is a convolution product A itself in this. Then, you have a morphism to A.  So, this is 1. So, this is skyscrapership at the unit. Maybe I should say that this skyscrapership is a unit for this tensor monoidal category. And, satisfies this usual property. So, this unit under associativity and commutativity. So, commutativity means that, for example, commutativity means, so, you have, so, this in geometric sattake, in the proof of geometric sattake, you construct commutative constraint from here to here. Maybe I need a little bit. Yeah, I cannot really distinguish the two A's, but, so, you swap two factors. And, there's natural isomorphism between them. And, you have map, maybe 1, 2. So, this is commutative diagram. This is commutative. So, the derived category is of what kind of, which kind of coefficients? I cannot hear. For the derived category, you take which kind of shapes? Constructive shapes. Constructive shapes. Geo equivalent constructives. Yeah, complex. Yeah, complex. Yeah, you can work on by integers probably, but we are not sure that what kind of space we get.  That kind of thing, I don't know. Yeah, in fact, I said that the proof is easy, but, in fact, our proof is so far not satisfactory, and we at some point, some, that argument there is. So, observation. So, there are other examples of commutative ring object. Yeah, in fact, there are not so many, as far as I know. So, one is, of course, unit. Unit is 2-3, but another one, important one is this, what we call regular shape. So, this is, this corresponds under geometric satake to, to regular representation. I think it's a great G check. Ah, let me see. Yeah, maybe you are right. Regular representation. Yes. So, we want to have objects in our fine glass veneer. So, it's really confusing which, we should put the check. So, natural question is AR appears as A of G prime for some G prime and N. And in fact, yes. So, this is a very, two different construction. I mean, this is not really construction. So, we have to make this construction and we just ask this old example can be constructed in our new way. What? Yeah, yeah, G, the group must be changed. So, you need also luck to map it to the same glass veneer. Yeah, same glass veneer, but G, yeah, it's a little bit complicated, more complicated, I will explain. In fact, the answer is yes. I'm after this modification for type A. So, G prime has a map to G, but G prime is much bigger. I mean, this is not, in general, not pervasive. So, this is just complex. It's okay. So, but it's not in the direct category of pervasive. So, it can be in the direct category of representation of the complex. Not, not, it's, I think it's a little bit more complicated. It is a variant, derived category, which is much more complicated. So, it's not just derived category of pervasive. It's just a, it's a, it's a, it's not a project with grand, derived category, which is considered, which you can also describe on the little side, but it's, yeah, there's some discussion by Bezo Kashnik, think about, but the object, yeah, this category is much more complicated. So, you don't know, you don't know what it becomes, is there some category? I don't know. Yeah, we don't know. No, it's absence is the whole point that they don't know this. Otherwise, if we construct this common branch, it's completely algebraic. And what do they want to say? So, so, I know, I mean, at least after there's some modification of this construction, we hope to get this regularity for classical groups constructing similar, but, but we are sure that the exceptional groups for regularity, for exceptions, you cannot construct by any choice of G prime Y. So, this is really new construct, new, new, combining. And once you have this commutative ring object, you can take a tensor product, that is also commutative. I will explain it. The column branch is simply a very small dimension for a place rank, yeah? Uh-huh. And suddenly, is it, is this group of, the influence, don't group on it, what, what, what do you think? It's an object, what? I don't quite understand the question. So, this is object, A, A, A, are you asking about A? Because the spectrum of this, I think you get some variety of section G check, yeah? No, no, there's no action of G check. G check only acts on the model of the previous chief, and this is a model of something, well, it's not, it's equivalent to a model, which is, I already take a problem for me, no, no action on G engine. Okay, so, so, now from now A is just commutative ring object. Then, as I said, so, then you can h star of G of O, O equal G of A. So, this, in the original case, you recover the, the model, so this is commutative ring again, and also you can slightly modify, you consider x of skyscraper shift at the origin between A, then this is also commutative ring. So, in the original case, I mean, this becomes trivial, but in general, if you consider some case, I mean, for example, sorry, I will consider, let me see, maybe I need to expand it a little bit. What? Is it graded commutative ring? That is, is it graded commutative? Graded commutative ring, yes, yes. But there's no, no auto-homology group, so it's really commutative, not super commutative. And so, if you take this regular shift, so this is studied many years ago, like hop, there's a crack new and Ginsberg into 2004. So, this, maybe I start with this example. So, spec of x group of one A. So, this is near potential for the Lagrange-Dier group, and the spectrum of h star of G of O, F, R. So, G check times G divided by double. So, this is basically constant size. So, you get, let me see, this, yeah, you get some symplectic varieties, and from our point of view, you can consider this to be construction of symplectic variety using regular shifts, but of course, in this particular case, you get some old friends. But it always says something, I mean, this kind of construction might be important in, because near-potent comm are very important in geometric presentation theory. So, this kind of construction may give us important varieties in geometric presentation theory. So, I slightly generalize modified construction. So, this is the notion of flavor symmetry group, which is just used quite intensively. So, we consider larger space G children arc theme. So, any representation larger group which contains G as a normal subgroup, and I take GF to be quotient. So, this is called flavor symmetry group in physics literature. Then, we have pi. So, I consider the larger group. So, this is pi. So, group of G children. But since G of F is a quotient of G children, you have a map to group G of. So, I denote the composition by pi. Pi children. So, you can just mimic pi star of omega of RG children. So, if I take this to be A. So, then this is the object in G of GF of Grassmanium G of F. And this is again commutative ring object. So, in order to recover, as I said, for type A you can recover this regular sieve. So, we take the following construction. So, this is a query of type A. So, n minus 1, n minus 2, and 2, and 1. So, this means G. So, maybe I put out G is product of GLI up to this circular vertex. I want n minus 1 and G children is basically you add GLN or additional one times G. But you divide by all scalars, diagonal scalars. And n, n is just all linear maps corresponding to ROTS. So, if you know the definition of quiva varieties. So, you consider n direct sum of n and its real space. Then you have a symplectic form and you just make symplectic reduction by this group G. Then you get nilpotent cone of type A of GLN. And so, this is some miracle guess. It doesn't happen usually, but so, Coulomb branch of this quiva gauge, sorry, coincides with this quiva variety. So, this we proved in earlier paper. So, this Coulomb branch for this example is also n. And in fact, we can make a refinement of this. So, this above construction, pi children star of omega RG children. So, this is you get object in the flavor symmetry group, the PGLN. So, this is regular shift. So, this we proved in this paper, appeared in this morning. So, in the remaining time, I will explain the application of this to the understanding Coulomb branch of star shaped quiva, right? Coulomb branch of quiva gauge. So, we combine, we take several copies of this example and then combine at the center at the vertex n. So, this is the star shaped quiva gauge, sorry. So, you can have l legs, l legs. And Philippe explained that, so, in this case also, G is product of all GLs and divide by again by central scale. So, Philippe explained that corresponding quiva varieties are open subset in the space of flat connections on S2 minus L points and with some monodomy fixed around this punctures. Maybe I just said character variety. No, in this example, no. And this correspond to, as I said, regular near-potent orbit and it correspond to taking semi-simple, regular semi-simple conjugacy class at f, at those points. Then, so, you can const, you can first make n this central vertex to be flavor vertex. I mean, you don't take the linear group and you just take push forward and to this affine-glass manual for this central vertex. Then, you just, from this theorem, you just see this, this a of G and n is just i of delta shrink of a r to a r. So, you take l copies, right? So, this is basically Q-ness for me. So, as a corollary, so, this spectrum, Coulomb branch, is the variety which Ginsburg and Kazdan introduced recently. So, this is one application. And so, Ginsburg's Kazdan's paper is still in preparation, so maybe nobody knows their definition. So, I must recall what it is. But basically, this is the right-hand side. You just take right-hand side for any group. This is the spectrum. So, this is, I mean, they use some algebraic construction, but by a lot of, I forget his name, but some student of Ginsburg saw their construction is same as this. So, this is for generality. And in this case, as I said, AR is something, I mean, by geometric circuit. Again, this is a regular representation. So, everything you can do by explicit construction. But, so, once you have, as I said, a regular, so, this commutative ring of, you don't need to take the same one. So, you can take any, any, any commutative ring of which you can make the same construction. So, you get really much more examples of this kind of construction. And, so, the remaining time is, maybe I should explain this. The motivation of Ginsburg has done construction and why it may be something to do with star-shaped quivers. So, that is what I want to explain. So, that is based on the conjecture of Mu and Tachikawa. In fact, this is, so, this is a physical fact. And they just translate it into a statement, mathematical statement. And so, for them, it's not really conjecture. So, from physics, physics perspective, so, they expect, there's a functor from two Buddhism categories, two Oromax and Plectic varieties, category of Oromax and Plectic varieties, this group action. So, to S1, so, if you, you first take complex reductive group, that is first fixed. And, so, this construction gives long runs dual. So, I just, I take G, G check, corresponding to S1. And, so, for sigma, so, this is some lemur. So, this is topological one. So, some, some, too many for this boundary. Then, it associates M sigma. So, this is Oromax and Plectic action. And, you have an action of G check of number of boundaries. And, what is the composition of homomorphism? So, if you have sigma1 and sigma2, then, so, this is sigma. M of sigma is a simplectic reduction of the diagonal. So, at each boundary, you have an action of G.  So, you have a corresponding group. You take the simplectic reduction by this group. And, there is some normalization condition. Before that, the first, the first one is G check. Yes. Thanks. So, if you consider the cylinder. So, this is the identity in this Buddhism category. So, this should correspond to identity object in this category. That is just the quotient bundle of D check. And, so, if you take this disc, then, it should correspond to G cross constant slice. And, so, from this action, so, once you have this three boundary, then, by, by this gluing, you, any, I mean, two manifold can be constructed by gluing. So, by this action, gluing action, so, this is what I call gluing. You can construct variety for anyone. But, so, we don't know what it is. There's no problem of isomorphism or, or, or your actions. Only have a symmetric group of actions. And, I, I don't know. You don't, you don't put this, and there's no symmetric group of acts. Your variety at sigma, everything is canonical. You can make everything canonical. When you do the composition of cobaltism, it's, ah, so, this is non-trivial statement.  So, you can divide this or this, and you must get the same isomorph. Yeah, that I don't, I'm not quite sure. And, in fact, this is based, even for, for, for g, g check is sl2, then, this m of this, this one. Maybe I just write m3. m3 is just c2, tensor c2, tensor c2. So, this is easy, but this, this, this checking of this is non-trivial statement. And, g check, ah, for sl3, then m3 is, ah, minimal nil potential for e6. Minimal nil potential. So, this, this we proved.  So, when sl3, for sl3, we consider this, this star-shaped quiver. So, you, you see this e6 link integral from this, and you can really show that this is minimal nil potential for e6. But, this is some non-trivial. From the definition, I don't, it's not so clear. So, anyways, I just explained the physical intuition why this, this, this, this construction, for type 8 is something to do this quiver geyser, star-shaped quiver geyser. So, if you have some supersymmetric quantum field theory in three dimensions. So, you can assign the so-called Coulomb branch, which I just explained in the case of geyser. But, you can also consider the Higgs branch, which for the geyser, this is, this is m, mc of gn for geyser. And, the Higgs branch is just n plus n star divided by g, for geyser. But, physicists recently consider another construction, different construction of supersymmetric quantum field theory. So, they start with 6d, some mysterious theory in 6d, and you're compacted by Riemann surface. Riemann surface, or this, this is too many times this one. Then, you get some supersymmetric quantum field theory in 3d. So, this is example. Geyser is another example. And then, from this, you can get Coulomb branch and Higgs branch. So, expectation is, if you consider the Coulomb branch of this theory. So, this is open subset of character variety. And, Higgs branch is this, just I described, m of gn. And, this gluing property is also consequence of this construction. But, this 6d theory is something mysterious, so nobody quite understands. And, physicists say this in the category of this supersymmetric quantum field theory, you have involution called 3d millisymmetry, which says if you have a theory A, which have Coulomb branch and Higgs branch, and if you apply millisymmetry, you get another theory whose Coulomb branch and Higgs branch is swapped. So, as I said, if I start taking the Quieberg Geyser, Starship Quieberg Geyser, it's Higgs branch which I just explained. And, Higgs branch is this open subset of character variety. So, if you just make change, then you get this correct answer. So, Starship Quieberg Geyser theory. And, this 6d, compact with s2 minus n points times s1. So, this is 3d millisymmetry. And, so the 3d millisymmetry is some new phenomena. But, people somehow started to understand some relation between the, some mysterious relation between the quantization of both sides. So, I think, so it may say something about some quantization of character varieties. That is, I think, a very interesting problem to study. Thank you for your attention. So, medically, the duality is implemented as what? As a symplectic duality. But, I mean, what does it mean? Well, but mathematically, so this, this category of supersymmetric quantum fields in 3d is very difficult to make real. But, in this example where you know, you know the mirror duals. So, they just naively say that in this 3d millisymmetry, Coulomb branch and Higgs branch are swapped. That is only, I mean, physical definition of this 3d. The quantum level as well, yeah?  So, if you, you, you have two, it's something similar to this usual mirror symmetry. In the usual mirror symmetry, you have two u1s and you exchange two u1s. And, in this 3d manager supersymmetric field, you have two SL2s and you swap this. It, it, it's all homomorphic, like, categories of coherent shifts on one or exchange with categories one. Not something like that. So, so, at this moment we only understand the, the statement in symplectic duality. I mean, you can see, symplectic duality, you don't need a 3d mirror symmetry, in fact. So, you can say it's a relation between the Coulomb branch and Higgs branch. But, you have both Coulomb branch and Higgs branch have natural quantization. And, those, and you have, ah, a notion of category O's. And, then, there was category A, C, U, D, R, D, R to each other. That is a statement of a symplectic reality. Maybe just, you, you, you started to speak about Gisburg-Karstner variety and then said it should be related to this moral, uh, conjecture. But, you didn't explain how, what is the relation between Gisburg-Karstner? Ah, so, this, this satisfies, this is just- M3, okay, yeah. M, M, R, yeah, so, this is just, I mean, I, I just only consider the case of, uh, sigma, this, uh, two sphere, but it can be generalized arbitrary, arbitrary surface. So, it's just sphere with L branches, yeah. So, on the Gisburg-Karstner, Kazdan proved that this growing, most important growing property is, is satisfied. So, is there an expectation, uh, uh, what happens to your 2D, uh, sphere theory, if you're quantized, if you're on place M3 by, uh, its quantization, does, is there a three-dimensional theory or something, is that, I mean, physically, is there something like that, or? M3, I'm not. Because M3, M3 comes as a, as a, whatever, as a Higgs or Coulomb branch. M3 is a Coulomb branch, uh, from this, I mean, you, you must, otherwise you must start with from this. And this should, this should have a, a quantization, uh? Other countries, what do you mean by other countries? There's one, I mean, uh, so there's, uh, upgrade of this, this construction. So, instead of a simplistic variety, you can construct the vertex operator algebra. And, uh, so this simplistic variety can be, uh, reconstructed from this, uh, vertex, algebra associated, associated variety. And I heard that Aracawa recently succeeded to construct vertex. I mean, the quantization, so you, your construction of, of the Coulomb branch comes also with a quantization? Yeah, this I explained. So, but can you, what, what if you, M3 is not the, if you replace M3 by it, by the quantization, I mean, what, what should you get? That is some new, I mean, even in the classical level, this is a new variety, not known before. Except two examples. What, can you make a field theory by replacing M3 by the quantized, uh, M3, by the quantized version? I, I don't quite understand what you mean by. If you replace simplistic varieties, uh, by, uh, by quantizations, uh, is there, is there an expectation that this also, that there is a field theory like that? Like, I mean, you could upgrade from dimension two.  I think if you take a group, you can, uh, naturally associate a 2D theory, but with a quantum group, you can get a 3D theory, topological theory. So is there something similar here? That's my question. I see. That kind of thing, I don't know. Other questions? Okay, so thank you.