Hey everybody, what's going on? I am Greg Salsman joined today by Jim Sonis of Fandle, which you're going to wrap up our week four DFS preview. What's going on, Jim? Not too much, Greg. A pretty interesting week four sleigh with all these potential shootouts on tap, which means we've got to find access to upside. We can't be going with guys with good floors. Floors are irrelevant in DFS in 2020. We just want ceiling, and hopefully we can find some stacks here that get you access to said ceilings. So would you have any interest in stacking Danny Dimes, huh? With his like negative 15 point implied total, you know, I might want to stay away from that one. That is a very interesting sweater though. I was so excited to show this to you just for your reaction. Not let me down at any point. Ram's defense, Greg. Ram's defense. You got to go with Ram's defense. The biggest surprise today for me isn't that you don't have Danny Dimes as one of your stacks. I feel like Russell Wilson and Tyler Locke are missing here. What's going on? Well, we just had only three slots and I think I've discussed them each of the first three weeks or the two weeks they've been on the main sleigh. So I guess we're taking a short hiatus, but like they're still like Russ, you can make a case that if like Deandre Hopkins doesn't play a Russell Wilson the number one quarterback on the sleigh. So I think the edict here is use Russell Wilson until we tell you not to, which means it's used him once again this week, imperative either Metcalfe or Lockett. That's all I was looking for, Jim. Just letting me know that I could play Russell Wilson with Tyler Locke or DK Metcalfe to stack them up that they may still be the best combination. I'm good now. See, you can play Russell Wilson and you can play DK Metcalfe and Tyler Locke with them seemingly any week. And you can do the same pretty much always with Jack Prescott and Ezekiel Elliott. They are your first stack here this week in week four for the Dallas Cowboys. Jack has been other worldlies. He wasn't great last week. Still could get in the end zone, but you're stacking both of them together here in week four. It's your favorite stack. How come? It's a little bit of a hedge here because, oh no, Beckham is banged up now for Cleveland. Kareem Hunt is banged up too. So we could see a scenario where the Cowboys pull away. Now the bookmaker odds have not shifted too much on this game yet. So it seems like the betters aren't too concerned about Beckham's health and the health of the Browns offense in general. But I do have some concerns if Beckham can't go about the way this game may land. But if you use Dak paired with Zeke, you're benefiting no matter what game script this is. If they have to pass a lot, you're gonna get a lot of production out of both Dak and Zeke. But if they're running a lot, you get the Zeke production as well. And there's also quite a bit of double dip potential here because Zeke has 16% of the team's overall targets to the first three games. He has 17% of the red zone targets as well. So it kind of alleviates a lot of headaches to pair these two guys together. I think that Zeke, like we talked about Russell Wilson among the best players on this slate from a positional perspective, I think it's Zeke Alvin Camara, Dalvin Cook, all at the top of this tier. But I might put Zeke number one. He is at home in a projected shootout. I will always take that for sure. Tyron Smith got in a limited practice on Thursday. That could be a huge boost to this offense as well. So I kind of think that in order to safeguard ourselves from potential game script here with this Cowboys offense and benefit every time the Cowboys move the football, I think pairing Dak Prescott with Zeke Elliott makes a lot of sense once again on Sunday. We're in line for whichever the game script is here on Sunday. If it's a shootout, well, we've got Dak Prescott going ahead with Baker Mayfield. And if it's a game where the Cowboys get out ahead and interrupt big, we have Zeke Elliott as well. Pairing Zeke and Dak for America's team, well, seems like a surefire way to cash on Sunday. As we mentioned earlier, Deodre Hopkins, you may not play this weekend. We'll see the practice report on Friday. But we've paired Kyler Murray and Kenny and Drake before. And as people that have rostered Kenny and Drake this year and used him in DFS, we're still kind of waiting for this breakout game for Drake. We're still waiting for him to show us what he did last year. The touches have been there. The snaps have been there. But the production hasn't really yet. Now Kyler's been awesome. And this week, maybe it's the week where they both go off. Yeah, facing the Panthers can cure a lot of ills because we saw Austin Eckler with kind of similar concerns to Kenny and Drake heading into last week. And Eckler got 11 targets in that game. Part of that might have been Justin Herbert, but it was really good production. And he also did convert on those targets too with 84 receiving yards in that game. Now, Drake is not the same passing game threat as Austin Eckler is. He's been losing routes to Chase Edmonds. But with Deodre Hopkins not at full health, that may increase the odds that Drake gets targeted on the routes that he does run. That's a bump up for him in addition to the match up here. I do think Kyler Murray would get a pretty decent downgrade if Deodre Hopkins were to sit. We can still use him because we're not going to Kyler Murray for passing efficiency. We're going there in large part because of the rushing. This year he has averaged 8.7 rush attempts per game, more than 60 rushing yards per game. Last year it ran just 5.7 times per game. So it's a pretty big bump up for Kyler Murray. And that impacts both his floor and his upside. So yes, I would downgrade Kyler Murray if Deodre Hopkins can't go. If Hopkins is a full go, I would say that Murray is my number one quarterback of the slate. If Hopkins can't go, I'd bump him down behind both Russell Wilson and Deck Prescott among the higher salary quarterbacks. But I'd still be in on Murray because the rushing production has been there because the matchup is so good. So Murray is somewhat between first and third for me in quarterback, among quarterbacks toward this week because the rushing has been so good, because this matchup is so good. I think that pairing him with Drake does alleviate a lot of the concerns around where the targets may go if Deodre Hopkins is not a full hell. Like we said, we're waiting on Deodre Hopkins. We'll see what happens. Obviously we practice this Friday that'll put him in line to play this weekend, but it remains to be seen. So Murray, yes, he won't be as enticing, but it'll certainly be somebody that is worth starting because what he can do with his legs is, well, worthy to put him in your Fando lineup. And can't he Drake? Well, the Panthers care all. So what's the advantage of that here on Sunday? One vital stack to mention that brings us to the Detroit Lions with Matthew Stafford and Kenny Gallade. Gallade returned to the lineup last week for Detroit and found the end zone. Stafford getting his favorite wide receiver back will help the offense in a multitude of ways. Yeah, it's not just Gallade coming back. It's also Michael Thomas being back. We talked about this with the Cowboys blur where we know we like the Cowboys more of Odell Beckham plays. We like the Lions more of Michael Thomas plays because what that does is it increases the odds that this game shoots out. If the Saints score a lot of points, the Lions have to score a lot of points too to keep pace. That is a good thing for Matthew Stafford and Kenny Gallade. And like you said, getting Gallade back a pretty big boon for Matthew Stafford in week number three, he had 0.28 passing that expected points per drop back according to number fires metrics. The league average this year is around 0.15. So about double the league average in efficiency last year when Gallade was healthy, we saw Stafford go deep at a very high rate. Didn't do that in week number three, but I think as he goes back home, we should expect that deep, that aggressiveness to go back up for Matthew Stafford. Gallade himself did look pretty healthy in that game. He had seven total targets, two of those were deep. And as you said, he did score the touchdown as well. And the State's defense, they haven't really been the same force that they have been in previous years. Marsha Latimore taking a step back. We saw Derek Carr go off against them two weeks ago. And Matthew Stafford, I would say is better than Derek Carr. So I do think that Stafford is my favorite among the lower salary quarterbacks. And I think that Ryan Fitzpatrick's probably gonna be the guy who gets the most attention, which is justified. Fitzpatrick is really fun. He runs quite a bit. That's good. It's a game that I think should shoot out as well. But Stafford checks a lot of the same boxes. He is a slight home favorite facing a defense we can target. And that's, I think that Stafford's gonna come in at lower popularity than Ryan Fitzpatrick. Now you could also say similar things about Joe Burrow and Teddy Bridgewater. So it's not a bad week to spend down a quarterback. I'd prefer to go with guys like Murray, Prescott and Wilson, but I think that the lower salary quarterbacks has something to say here too. And among those guys, Stafford is number one for me due to projected popularity and the fact that he's got his star receiver back in the fold. Yeah, Stafford makes a lot of sense in this game that couldn't get away from Detroit relatively early. Michael Thomas is back at Full Health and Drew Brees is cooking. We'll see, but with the combination of Matthew Stafford and Candy Gallaudet, you'll be in a good spot. And you'll save quite a bit of money at the quarterback spot, allowing you to pay out for some of the guys that Tom and I spoke about earlier this week, which should cash you here on FanDuel on Sunday. So we hope. That's it for us here at the FanDuel Hurryup. Jim, we appreciate the time. Good luck in week number four. Thank you, Greg. You as well. And I'm looking forward to wrapping things up on Monday to give the winners of week number four from a DFS perspective. We're all winners here, Jim, because Adam Gase isn't setting our lineups. For Jim Sones, I am Greg Sussman. Have an awesome week four. Enjoy the games. We'll see you back here on Monday to talk about the winners and recap at all. Have a great weekend and we'll see you next week.


Hi, I am Dr. Lohit Shetty Raju, consultant HVB and liver transplant, Manipura Hospital Bangalore. So today we are talking about liver diseases, which are the conditions which affect the liver. The most common condition are infections, which we commonly come across in our OPD. There are few viruses and parasites which infect the liver cause damage to the liver function. The most common ones are hepatitis A, hepatitis B and hepatitis C. There are some uncommon conditions which cause liver diseases like amoebic liver abscess, pyogenic liver abscess and some parasites. The second condition which damages the liver is genetics, where one abnormal or both abnormal genes are inherited from the parents. Some of the examples are hemochromatosis, Wilson's disease, half-hour antitropism deficiency. Coming to the third conditions, that is tumors or cancers which affect the liver. What we call is the liver cancer or the hepatitis cellular carcinoma and the tumor affects the bile ducts. It is called cholangio carcinoma or other benign conditions like liver adenoma, FNH that is focal nodular hyperplasia. The other common conditions are due to alcohol intake causing cirrhosis, which is the most common conditions where we come across in the OPD. Or liver damage secondary to drug intakes like Ayurvedic drugs or increased accidental poisoning like rat poison, paracetamol poisoning. The other category of liver diseases are autoimmune, where the body's immune cells affect the liver. Such conditions are like primary biliary cholangitis, primary sclerosis in cholangitis and autoimmune hepatitis. So these are the common diseases. Next disease which is also called as the next pandemic is obesity. Obesity affecting the liver disease which is also called as non-alcoholic steatohepatitis or NASH which is almost overtaking the alcoholic liver disease and is also called as the next most common cause of cirrhosis. Thank you.


Thanks for coming back to the last lecture on the Advanced Topics and Higgs Bundles. What I want to do today is I want to tell you about some correspondences between Higgs Bundles and other Higgs Bundles or Higgs Bundles with other objects in maths physics. Before I get started, just a couple of comments about the question sheets. So you'll see that the question sheets are all related to each of the lectures, but they're not in any order, particular order. So they're not from easy to hard. You should definitely not start by the first one just because it's first. Take a look at them and start with the one that you feel most comfortable with. There are all problems that come from papers in the area. So there are all things that are not that trivial that will require some thought and that, ideally, it will take you to read those papers that are mentioned and where these things are done to see the methods a bit further. The methods are the ones that we described in the lectures, but they're a bit further developed in those papers. So don't feel upset if you can't solve something in half an hour, it's not supposed to. But if you want to solve things that are a bit easier, so there's some lecture notes from something I did in Singapore a few years back. So if you look at the archive, there'll be some lecture notes on Higgs Bundles and that wasn't advanced topics. That was a very, very introduction and there the exercises are much more simple and to do just in a few calculations. What I thought here since I was asked to do advanced topics was that I should challenge you just a bit more. But you should just, don't get stuck, don't get upset if you can't solve it and if you want to carry on thinking about these things later on, you can email me. So feel free, any of you, to email me. My email is in the website. Okay, so Higgs Bundles and Correspondences will be doing the things from the fourth chapter in the lecture notes, we'll see how far we go and also I'll have to go back to something that we skipped in lecture one since parable Higgs Bundles are related to what we want to do today. So we'll introduce parable Higgs Bundles and see some correspondences with Quivers. So let me just put here the plan. So we want to do Higgs Bundles and Correspondences and Correspondences. Yes, I left this for the last lecture since it's what I've been working on in the latest times. So I've been working with different collaborators, looking at correspondences, correspondences coming from a few perspectives. So I want to look at correspondences via three different directions and there's probably many more. I just want to start with these three. So the first one comes from dualities. So this could be Langland's duality or any other duality that you know between groups or between modelized spaces that you could apply to Higgs Bundles. Then I want to look at group homomorphisms, or group homomorphisms. The group homomorphisms or maps between groups that satisfy certain properties will induce maps on the modelized space of Higgs Bundles for each of those groups and it's interesting to ask what happens with the hitching vibration, what happens with brains inside this vibration, how do they transform with respect to these homomorphisms? And lately, I want to take, borrow some notation from graph theory, use quevers, which are graphs which carries some information on each of the vertices and arrows and look at correspondences between these objects and Higgs Bundles. So I'm going to be talking about work that I've done with David Baraglia, this paper published this year on SOPQ. I'm going to be talking about work that I've done with Bradlow and with Bradlow Branko. So this in terms of group of homomorphisms and I'm going to be talking about work with Steve Ryan involving quiver varieties and polygons and hyperpolygon spaces. So I want to start by looking at some of these. Let's talk about the dualities one first since we've talked a little bit already and we're not going to take it that much time today. So for Langlands duality, Langlands duality is a duality that we have between groups, they're Langlands dual groups. So if I have a complex league group, we're going to be working just like before, I haven't fixed them here, but just remember we used to have here in blue the things that we have fixed, complex league group, Riemann surface of genus at least two. Today we're going to just relax this condition but for now let's just fix them here. So given a complex league group, I can form its dual league group and the ones that you should keep in mind are the following. So if I take the general linear group GLNC, I'm going to come back to GLNC as the dual. If I take SLNC, I'm going to go to PGLNC, and if I go to SO2NC, SL dual SO2NC, and if I go to symplectic one, SP2NC, I'm going to go to the orthogonal with odd SO2N plus one C. So this is the correspondence that we're going to be considering and we want to understand what's happening with the hitching vibration in the modular space of Higgs panels for those groups. We mentioned just as a motivation in the last lectures that there was some correspondence and the correspondence is between the two modular spaces of Higgs panels for a group on its Langlands dual. What one can do is one can look at the hitching vibration that we defined before. Remember we're going to be taking a Higgs pair here so we're going to take a representative of a class here and what we're going to do is we're going to send it in particular for instance to the characteristic polynomial and its coefficients. So I'm going to send this to the coefficients of the characteristic polynomial of the Higgs field. So that phi minus lambda identity here. If I do the same taking Higgs panels for the Langlands dual group, I'm going to arrive to a modular space AGCL that one can show just because it's formed by the characteristic polynomials, invariant polynomials is isomorphic to our original base. This isomorphism is not always the identity. It is going to be the identity for most groups but for instance for G2. So these correspondences also work for exceptional groups and when you look at G2, the isomorphism is not trivial. If you want to know more about that correspondence you should look at Hitching's paper from 2007. So what is the conjecture that appears when considering modular space of Higgs panels on their Langlands dual? Well, Ströminger, Jao and Zaslo, Jao and Zaslo conjectured that the duality between these modular spaces, the historic fibrations should be a duality between the fivers, duality of fivers. Which means we take the fiver over a regular point and we take the dual abelian variety in the other side and that should be what the fiver is in the dual side. So let's, quality of fivers and here we should emphasize this is regular, regular fivers. So when we were looking at the Hitching fivration we said in the Hitching base there's going to be regular fivers and there's going to be some space that's not regular. So there's going to be some discriminant locus and this duality is for all the fibers that are over the regular points. Remember over the regular points our fibers are abelian varieties but over the singular points there'll be spaces that are not necessarily nice or as nice and for those spaces this duality is still not well understood for the groups, for these groups and more generally. So back in 2002, so 2002 Housel and that is of proved that this is the case. So it proved that the duality between the fivers is indeed appearing for SL and PGL, SL and case. And soon after Donaghy and Pantheb and Kapustin and Witten around our six they completed the study of the regular fivers for these groups. If just as a little exercise for your head remember that for instance, for GL and C Hickspanos we mentioned that the regular fivers are Jacobian varieties. What's the dual space to that Jacobian variety? Any thoughts? Is the Jacobian itself? So for GL and C the regular fibers are Jacobians of curves and the dual space to a Jacobian. And the dual variety is again Jack. So we have a duality between the fibers, the fibers are Jacobians and the duals are also Jacobians and it agrees with our little table here that says GL and C goes to GL and C and they're like those duality. When you look at SL and SL and C then the regular fiber is the prem variety. You said we constructed the prem variety here in the lecture. And actually for the dual space the dual fiber is the prem variety of S sigma quotiented by torsion and points which agrees with the fiber in the dual side. So you can carry on and look at the duality in general for groups for any group that has a Langlands dual group or you can actually just do it for these classical groups and for that if you are curious about how to look at it I would suggest the work of Hitching O7 G2 curves and Langlands duality where he does very explicitly the correspondence between spectral data for these groups. The work of these other people is much more broad reaching but a bit more technical. The other thing that happens with Langlands duality and mirror symmetry is that once we have mirror symmetry between the fibers giving us the mirror symmetry of the two spaces we had also brains inside the mod light space. So brains brains here inside this mod light space and homological mirror symmetry also should give us a duality between brains so through conceivages work there should be some dual brain related which we talked already about when describing brains. So anytime that you study the mod light space of Hicks panels you should keep in mind that there is this duality there is this duality between fibers and there is a duality between subspaces and you should ask how does that fit into your research or your picture and in particular we can even ask how do those dualities fit with group homomorphisms or with graph theory and that's what we're going to do that's why I started with this one because I want to also mention some open questions that appear when you look at these two other correspondences together with the duality. Any questions about this? Yes, as dual, so when you construct a dual abelian variety looking at the exact sequence on the annihilator that's what we're getting, yeah. There's a bit more explanation I think in the notes about just more general. That's a great question also because when you look at brains inside the fiber so you look at the brain inside the fiber and you want to construct the dual object in the dual fiber you'll have to consider first the full fiber look at the dual space and look at the annihilator on the other side. Yes, yes. Because if you think about it what you're doing is you're taking your spectral curve you're pointing the base given by the zeros of this polynomial is your spectral curve which is generically smooth and it has the same linear system defining it. So you can calculate the genus that's a nice exercise to calculate what's the genus of this end cover of the Riemann surface and using that you get the Jacobian dimension, yeah. Any other questions? Okay, so let's take a look at the other dualities and see what happens. So I want to keep this Langlian's dual group here because the other correspondences the next correspondences the group homomorphism correspondences appear or I started studying them at least because I was wondering what else I mentioned some of these before what else can I put here which moduli space can I put here over the same base of the hitching vibration such that there is a correspondence which might not be the duality which shouldn't be the dualities there's a correspondence between these two vibrations these two moduli spaces and then there's a new correspondence between brains. So in particular from Langlian's duality we know that we saw yesterday that what we call BAA brains like brains for real hexpandos correspond to what we call hyperholomorphic brains, BBB brains. So I want to consider these new spaces these blue spaces here such that brains don't satisfy the pairing that appears from Langlian's duality in particular like BAA brains to correspond to BAA brains I want to keep the same type of brain if I can and that appears from group homomorphisms very naturally so let me tell you about it a little bit about what we've done with Steve Bradley and this is what actually how the lectures start in the notes here so I want to consider group homomorphisms group homomorphisms so these are maps between a group some G and some G prime I can look at morphisms between real groups I can look at morphisms between complex groups let's look at complex ones first and then we'll go to real ones once you have a group homomorphism between groups you can define a homomorphism between the representation space so this induces a map so I'm going to call it just the same between the representation space for your fixed Riemann surface and GC to representations of pi one again for sigma and GC prime and just by the non-abillion-hodge correspondence we talked before about we can then look at a map induced on Higgs bundles so induced map on Higgs bundles map on Higgs bundles from these finally what we have here is going to be the following so I'm going to take principal Higgs bundles so P let's recall that we're working with a complex group GC and P phi is going to go to so the same P GC but tensor through the morphism of groups with GC prime and the Higgs field will be a transformation of our original Higgs field and we're going to get through the action of our oh what's the name of this letter? Psi, okay thank you we're going to get through the derivative of Psi with phi so what are these objects? this is what we're going to call the new P GC prime and this is the derivative of so this is through the derivative of phi of Psi under the identity so at identity giving a map from the adjoint bundle of GC to adjoint of GC prime so once we have that we can ask what are Higgs bundles once we have particular group homomorphisms if you have your favorite group homomorphism we can check those ones and it's actually not been done very much so a few years ago we started doing this kind of thing with isogenes so we'll consider isogenes I'll put here a few so you know but if you can think of other morphisms that you're interested in or that you've seen and give you some nice property of groups then it would be very good to try and do it for the Higgs vibration it would suddenly be a new result I'll talk today about isogenes the other ones that I'm looking with Sebastian Schlöss so he's a student of Andi Naitzke actually we're looking at triality so how does triality influence the Higgs vibration? I won't talk about that today I'm going to focus on this isogenes isogenes are maps between groups of low rank that give you some unexpected equalities or or congruences but that are not there for higher ranked groups so the ones that I'm going to talk today about are going to be rank two and rank three so instead of putting all of them I want to just put the ones that we're going to use today so for example SL so I want to do SL2 C cross SL2C this is isogenes to SO4C and I want to do SL4C and SO6 so SL4C and SL, SO6C these are the two that we've considered both on the regular locus and on the singular locus I'll tell you about the regular locus today there are many other isogenes so if you look at page 36 you're going to see a long list of isogenes for instance SO5C and SP4C so another one that's here not mentioned which is what would arise from Langmuir's duality SO5C and SP4C so that's from Langmuir's duality the correspondence but these other two are not from Langmuir's duality and we want to understand what is the homomorphism for Higgs bundles what does it do to the hitching vibration and what does it do to brains in the hitching vibration the way that we're going to study this map is by considering the action of Higgs bundles will be coming directly from this map so if we apply it to Higgs bundles for each of those two groups then we get the following so for our particular cases let's put the cases one and two here that we're going to be considering so one and two for the cases one and two that are going to give us some of these blue correspondences so case one and case two we're going to apply the map to get from SL2 cross SL2 Higgs bundles and a natural SO4C Higgs bundle and the same for the second one so we need to say what we're starting with if we're starting with the SO... so the SOgene is going to send here so we're going to call it I2 the SOgene in rank two is going to send SL2C cross SL2C Higgs bundles into SO4C Higgs bundles which means we're going to apply it to a pair E1, phi1 and this is why I was telling you you can actually define Higgs bundles not necessarily for just groups of type A, B, C, D you can put other groups so like this product and we're going to get an SL2 cross SL2C Higgs bundle you can show that it's actually just two SL2 pairs so E2, phi2 and we're going to build the next Higgs bundle the SO4C Higgs bundle by doing the product of the bundles and doing the product of the Higgs fields with the identity so this is what we get we get E1 plus E2 and then for the Higgs field we get phi1 cross identity plus identity cross phi2 one can show that this pair actually belongs to the moduli space of SO4C Higgs bundles so it's not too difficult to check that the properties just carry through that the product of two Higgs bundles to do vector bundles from the SL2 group are going to give you a vector bundle that has an orthogonal structure and whose structure is compatible with that Higgs field now the I3 isogenic that takes SL4C Higgs bundles into SO6C Higgs bundles you might wonder how am I going to get a higher rank but we're just actually going to apply the same correspondence that we wrote there for the psi we're going to start with a pair now it doesn't have any number it's just E5 in SL4C and we're going to do is we're going to look at the Higgs pair twisted with itself so we're going to use the bundle will be the exterior power of E so this is a rank 4 vector bundle from SL4C and when you take the watch 2 you're going to get a rank 6 bundle and here the Higgs field will be very similar to that one but just itself taking both times so we're going to put just phi identity plus identity times phi but what we're interesting most on is not just these maps these maps just carry on naturally from what we explained here but we're interested in these correspondence with the hitching vibration so as I mentioned before I want to not only see the map or the new mod light space over the same space so here what we're showing is that we have SL2 cross SL2 Higgs bundles when you look at the bases for these two groups and for these two groups they're the same so we can put one here and one here and we have these correspondence between the bases but we need to understand what the correspondence is between the fibers so I want to mention in just a few minutes what the correspondence between the hitching fibers are since these fiber product construction could possibly have some other applications in other areas so what we're going to do to understand to understand the correspondence between hitching fibers so the hitching fibers for SL2 cross SL2 Higgs bundles corresponding to SO4 and to SO4 corresponding to SO6 we need to consider fiber products of curves so we need to consider fiber product of curves so fiber products are products that we do over the Riemann surface for instance if we have for one curve so we're going to have the curves given by eigenvalues over each point of the Riemann surface and the fiber product of the curve with itself it's all of the combinations of those eigenvalues repeated so we have a higher rank cover so the fiber product we're going to be looking at in the first case so in the first case we're going to be looking at the two cases that we have there in the first one we're going to have two spectral covers because we have two Higgs bundles E1, phi 1 and E2, phi 2 and these two Higgs bundles have spectral data we saw already spectral data for SL Higgs bundles so we know that spectral data here is a curve S and a line bundle in the print variety so L1 and here there's an S2 and a line bundle 2 in the print variety in the regular fibers so for regular fibers we saw then the same for the spectral data of SL4 we know that there's a curve and a line bundle in the print variety so we want to do something to these curves and these line bundles in order to arrive to data for SL4C one thing to note is the following so let me put a remark here because this will be something interesting remark you might have seen it in the problems if you got to do something about orthogonal Higgs bundles when considering SL2NC Higgs bundles your characteristic polynomial so Higgs bundles define a curve S a curve S through a characteristic polynomial which is the zero of our lambda to the 2N plus a1 lambda to the 2N minus 2 plus a2 lambda to the 2N minus 4 plus our last coefficient which is not really going to be an A and N but so this is going to be A sub N where A sub N here so A sub N remember this is a section of K to the 2N and it's not just any section it's the square of a Fafnian so it's a Fafnian square so now your linear system has base points the base points are the zeroes of these differential because those zeroes appear twice so your curve is always singular so whenever you look at Higgs bundles for SL2N you are always on a singular curve so this is always singular what's that? of a Fafnian yes of a Fafnian sorry so always singular and what you have to do to define spectral data is you have to separate those points and define the normalization so you have some normalization S hat normalized and then it's the prime variety of this S hat that you're going to be looking at so what you're going to be doing for the spectral data in this curve is you're going to look at the map that's a little involution that sends lambda to minus lambda in the original curve has fixed points the fixed points are those base points but when we normalize and we separate them our new cover S hat doesn't have any ramification points and our new involution doesn't have any fixed points and the data, the spectral data in this case is going to be coming from a prime of S hat and S hat quotiented by sigma so this is a very very quick explanation of something that took hitching many pages in his paper to describe so you shouldn't worry if you can't deduce it right away I just want to give you the gist of what's going on for orthogonal heat expansions and in particular the fact that spectral data has to be coming or comes from a normalization of a spectral curve so if there's any way in which you could recover the normalization automatically that would be great because you don't have to normalize the curve and that's what happens when we do our method of fiber products so through fiber products we can show the following so the image so the image let me put it here the image of I2 has spectral data I'm going to call it just trying to follow the notation from the notes so you can go back to them S4 hat and L4 for S4 being S4 hat being the fiber product of S1 fiber over the Riemann surface with S2 and these two spectral covers are given over the Riemann surface so there's a pi1 and there's a pi2 from each of these two covers and L4 the line bundle for the rank 4 orthogonal bundle is just going to be the pullback of of each of these line bundles on each of the curves so let me write it like this L4 is going to be if pi1 is the projection from the first one to the first factor so let's not call these ones


Welcome to Sister Power, I'm Sharon Thomas Yarbrough. The topic for this segment, Coronavirus Beyond Surviving to Thriving, Lessons and Blessings. So what's the role of Sister Power doing this strange in different times? Today, Sister Power special guest, Dr. Patricia Jones-Blessman will be sharing ideas worth spreading. Licensed clinical psychologist from Chicago offers insights into the COVID-19 pandemic, discussing when a traumatic event occurs we are challenged to grow, change and adapt. With over 30 years of experience as a consultant and administrator of mental health problems, her vocational experience encompasses a diverse array of clinical settings, public and private, private and not-for-profit as well as academic institutions. Although now retired, Dr. Blessman maintains a limited consultation and private practice. Patricia, welcome to Sister Power. Well, thank you Sharon. It's so good to be talking with you. You know, you're such so inspirational and thought-provoking and just, you know, just it's just wonderful to be to have some intellectually stimulating conversations. So I know this is going to be a powerful segment here and I'm just ready to dive in. Where should we begin? Oh, I just, I just want to know, I'm excited as well. You know, under these circumstances, we're dealing with this pandemic and coronavirus and we've been speaking about this over the phone and you were telling me about some of the conversations you're having with your clients during these challenging times. So yes, let's jump right into it because unfortunately, Hawaii has approximately almost 300 cases and unfortunately, Illinois is approximately almost 7,000 cases. So, yeah, yeah. I mean, those are, anyway, we're going to get through with this. We're going to get through it and we're going to come out ahead. And my question to you, Patricia, what is your radical plan to stay healthy physically and emotionally? Wow. You know, this one of the things that's happening with COVID-19 is that it's really challenging us to really think about and pay attention to our health. Most of us, the first plan most of us have is, what are we going to do to try not to catch this bug to begin with. And so, in some ways, we've had to spend some time thinking about our bodies and thinking about, you know, there are things I know I should have been doing, but now being much more consistent and much more intentional about drinking water, which is very good for us, right? We all know we're supposed to drink more water, taking our vitamins, making sure that we have good vitamin C, making sure that we have good rest, sleep habits, you know, all those, you know, destressing, all of those things help us to ward off disease and infections. And now it's all making us pay attention to what are we doing, how are we treating our bodies and not taking it for granted anymore. And that's a good thing. It is. So, sometimes a radical plan is just simply, you know, all the five things that I know I should be doing, I'm now doing all five of them for sure every day. Daily, religiously. Religiously, like being consistent, like, ooh, you know, I don't take that multivitamin like once a week. It's like, every day I got to make this a routine and a habit to get my vitamin C, my vitamin D, you know, and anything else that, you know, my body might need in order to ward off or fend off any kind of infection. There's also, you know, we've also had to think about, well, how do you know, the ways in which we eat, how are we using food? Are we using food to stress eat? Or are we using food, are we eating to stay healthy? And there's a difference between stress eating or emotional eating or eating for pleasure as opposed to looking at food as fuel for our body and as medicine for our body. And so COVID-19 is going to be challenging us to rethink our relationship with food, you know, and that can be a good thing. It's also challenging us and probably, this is probably an issue that goes over and beyond just, you know, a radical plan to stay healthy. But just in general, you know, I want to go back to something we said in the very beginning about when an event occurs, we are challenged to grow, change, and adapt. And I just wanted to say that, you know, with diligent effort, it usually takes about six weeks to learn a new habit. But in this present universe with coronavirus, we now have to learn and consistently practice multiple habits religiously and consistently. We have to be vigilant all the time. There can be no lapses. Yeah, this is a life and death situation right now. And I think that is the challenge that we all are facing daily. Well, really every minute of the day, we're facing it. Okay. So can I tell you a personal story that just happened today? Absolutely. My husband and my son and I have been diligently social distancing for the last three weeks. We celebrated three weeks, so we've had no contact with anybody. You know, we've done our shopping or gotten our little food or whatever we take care of the family needs. And we were like good. We were all good, right? Okay. And nobody had any symptoms and we're all good. My husband went to the grocery store today. He had a list. He bought some things. He bought a little bit more than he had planned to. And so he couldn't, everything that he had, he couldn't carry back on his own. Rather than call me, he called an Uber. I heard the old, yep. That's exactly how I went and he called me from the Uber.  No, I haven't killed him yet. Thank you. I'm staying in prayer. I'm just staying in prayer because I'm like, the clock has not started again. You know, and so we've had to have, so we're all struggling with this. We're all struggling with, this is a new habit. Now I understand he was trying to be helpful.   That's that fierce independence. But it was an old habit to just call an Uber. But it's that old habit that we now have to rethink in this day and age. Does this make sense? And is this a safe thing to do? Now I'm not saying that in a time of crisis or a time of, you might need to call an Uber, but there's a way to call one.  Make sure they're wearing a mask. Keep the window rolled down so that there's air circulation and only called if you absolutely, you have no other choice. He had other, you know, my husband had other choices. He's going to call me. We've got a clean car. He chose not to do that in that moment. And so, you know, everybody's going to struggle with that. Everybody's going to have to rethink, you know, their habits, the way that they used to do things may not be the safest way to do it now. So that takes us immediately to how do we keep, what is the plan to keep our homes disinfected? Girls. That's a big one. That's a real big, a very big one. Because there's a whole lot of stuff that's changed in terms of how you disinfect your home. Now, I tell you, one of the advantages that people in Hawaii have is that they're accustomed to taking their shoes off before they walk into their home. This is a new habit for people in Chicago, but it is, you know, people are learning that you shouldn't take your shoes into your house unless you disinfect at the bottom of them. And so now you see more people keeping their shoes outside of the home, cleaning the bottom of the home and disinfecting the floors. But just paying attention to, and then just paying attention to all the things that we commonly touch, whether it's light switches, the refrigerator door handle, door knobs, the water faucets, all the handles in our kitchen, in my kitchen. Like right now I can count in my kitchen if there must be 20 handles, at least if not more. And just in my kitchen alone. And that including the light switches. And then, you know, and so that has been a real chore to just go around the house every day and wipe off the light switches. And even when we get into our cars, I'm wiping down the steering wheel. Yeah, the keys. Yeah, your car. Sure. Yes. You know, anything that any place where you sit and yet so the car in your house. A lot of people are not trying to use public transportation, which is good, but just just just your own personal space. So, and thinking through how people use things like, you know, I had to talk to my child about well you know, when you use the bathroom.  But you know what, whatever, you know, whatever you did with your hands, you have you almost have to go back and then rewash the flush handle, because there's stuff on that from when you use the bathroom. He's like, yeah. Oh, well, you're just a germaphobe. Life and death situation. And what I love about, you know, what we're doing, we're educating our children. This is a new norm now for the world to follow these safety steps. And so let's even touch on another subject about what is your plan if you get sick. You know, that's something that we don't really want to talk about, but it may happen. And I talk with my clients about that when I carry them through the steps, you know, in terms of, you know, being radically healthy, sanitizing your home, but also having a plan for if you should get sick, because you do have to think about it. So everybody should have in their home right now today, a thermometer, a 30 day supply of whatever their favorite Tylenol and whatever their favorite cold and flu medications is, are. And there should be enough for each member of the family. When you start thinking about how much medication it is, it's a lot. So you shouldn't be surprised that the Tylenol is out of stock right now. It is here. It's out of stock. Because in order for anybody, one for one person to have a 30 day supply, that's 180 Tylenols right there. And most of us don't usually have that kind of, you know, that amount of medication in our cabinets. You know, I'm working with a client now who is, she has not been tested for COVID-19, but she has all of the symptoms.  So she didn't, she wasn't thinking that she needed to have that much medication on hand. And I was talking to her about, well, you know, if the theraflute says you can take it three or four times a day, then that's how much you need to plan for 30 days worth of your theraflute three or four times a day. That's how much you need to have on hand to aggressively treat your symptoms aggressively. And this one is different. What she used to do with a normal flu, you might have, you might have worked, but not, not for this one. Patricia, we're going to take a quick break and we're going to come back and continue our conversation about coronavirus. Thank you. Hello, I'm Lillian Cumick, host of Lillian's Vegan World, the show where we talk about veganism and the plant-based diet located in Honolulu, Hawaii. I'm a vegan chef and cooking instructor and I have lots of information to share with you about how awesome this plant-based diet is. So do tune in every second Thursday from 1 p.m. Aloha. Welcome back to Sister Power. I'm Sharon Thomas Yarbrough. And my special guest today is Dr. Patricia Jones Blessman. And we are discussing coronavirus beyond surviving to thriving lessons and blessings. And before we went on break, we were talking about what do you do if you get sick? Okay, so not only do you have to plan for what if you get sick, but what if each member of, any member of your family gets sick? For example, in my family, there are three people, my husband, myself, and my son. Okay, so, you know, I don't know what they're going to do if I get sick. I'm the one that holds everything together, so I don't know. But I can just pray. But no, no, that's not true. I do have a plan. I've got some girlfriends that I've already told them you will have to step in. And I've already given them the list of medications, the doctors, and how they might need to work with my son and my husband in case I get sick. But I also have a plan for when if either one of them gets sick. I've had a plan for where does if my husband and I get sick at the same time, I have to make a contingency plan for when my where does my son go? Who's going to take him in if the two of us get sick at the same time. So those are the things that it's important to have those to have thought that through and to have thought about what what that means for your family. If you are a single private number of people who are single who had not even thought about what what happened or what they would need or what you know what their environment or what resources they could get from their own network. If they should get sick, who could they call on to even just drop meals off at their door. But those it's important to do that. It's also important to take a look at what happens if the cook in the family gets sick. How is the rest of the family going to have food and who's going to do it and who's going to prepare it and to have some idea what that means. Now, you know there there's food services out there like farmers box and real eats and freshly. So there are options out there that do deliver meals right to your door but it's important to have have thought it through.  The other thing I want to touch upon is that women are typically the caregivers and families. Yes. And they're usually the ones on the front lines in their homes. And one of the things that I'm seeing is that you know women to take will end up taking care of other family members. But then not taking care of themselves. And I think it's important that we step back and make sure that we are also taking care of ourselves in the process. This is a situation where it's important to you know like they say on the airlines put on your own oxygen mask first before you help somebody else. We're in that kind of situation. If you know you know who the people are that are typically the caregivers who help you know in the family.  You know protective gear or protective clothing or you know and what are the rest of the family members want to do to support the person who is the who usually takes care of the sick people in the family. So, so there we have I cover. Medical plan to stay healthy with my clients, keeping their home disinfected and there's that can be a whole number of things that people need to consider what he could be about to make that they have in their house, you know, paying attention to your home environment. What is your plan if you get sick. And the last thing that I talk about, or I try to get to with my clients is what is your plan to help others while you are still well. And, and it's not necessarily meaning helping your.  Can you offer to the world out there during this time.  In Chicago we're doing stuff like having a nightly sing out sing out from our balconies and our windows in honor of the health care workers. You know it doesn't have to be major it can be a community for other people but it makes you feel good when you know that you're doing that you're not just thinking about yourself but you're thinking about the community around you. Well you feel good when you're giving back, you know, and then while we're still healthy. We invent and thriving to survive that we can give a smile and and before you go on Patricia I just want to make a note that I think it's time for people to start picking up the telephone and calling one another and checking on them. I know text is good. I text I email, but it's just a sound of a voice we're not able to hug one another any you know at least for another 45 days. But the sound of a caring warm voice I just that's my two cents I want to add with your know what knowledge about expertise. That's more than two cents that's at least a couple of hundred dollars. Let me tell you. So one of the things that I've done for as an example is I have a list of elders, elderly people that I know are not getting out of the house. So I have a list of them and I call them on a regular basis. I touch base with them. You know if I at least every couple of days. And you know who else I have a list of I have a list of single people. People are living by themselves. Yes. Yes. So my mind I have two neighbors on my floor. They both live by themselves and I check in with on them to make sure that they're okay.  Yeah. But you know but they appreciate it that somebody is that on their floor. You know and I usually don't even you know it's funny I'm getting to know my neighbors better. You know but it's you know in this day and age you know this is what we must do it and then I have some younger friends that are you know that is younger and single friends that are. You know just a part of my social network I've got some little millennial friends and I call them and you know make how you doing make sure we have everything you know. Some of them you know they would I mean they're just so delightful. So but they're also appreciative that somebody is cares enough to check in on them on a regular basis. Yeah. Because you don't want anybody to be in their apartment by themselves isolated and getting sick or not feeling well. Or maybe just having a rough day and just maybe somebody to talk to because isolation in and of itself has its own psychological and emotional challenges. It does and you know. Listen to you speak so calmly and reassuring before we close. I want to you to leave Dr. Blessman with what is on the other side of this. What do we have to look forward to after this pandemic. Leave us a few words of encouragement and motivation and in this these times we need something to chew on this that feels good. Well you know you're going to leave a personal legacy whether you want to or not because at some point your children are going to and your grandchildren are going to remember. This is a historic event and people are their children grandchildren are going to remember how they experienced this and who you were in this during this time. So it's important to think about how you show up in the community and in your family and in the world as you go through this. Now we don't have any control over this virus that's perfectly clear but we still have agency over our life. And we have the ability and we make the decisions around how we're going to show up for each other and how we're going to live through this moment. And maybe in the process of thinking about what's on the other side and also looking for the blessings in this moment looking looking for the gift in this moment.  I mean you or your children being much more thankful or maybe just and just maybe just being more appreciative but you will there are if you look for the gifts in this. And I know that's a hard one to think about like because right now people might be calling like this like this sucks and this doesn't feel good at all. But it's important to look for the lessons and the blessings because they're there every experience has them and they may be different from person to person. You know yours will be different from mine but they are there and we have to we have to keep an eye out and look for them as well and not just focus on the rough stuff or the tough stuff but look for this the silver lining in the clouds. Dr. Patricia Jones bless my dear friend. This is so wonderful that we've had this chance this opportunity to let us know that there is a rainbow at the end of this tunnel. There's something to look forward to and I want to thank you so much for participating and and speaking about coronavirus beyond. Surviving to thriving there's lessons and blessings yet thriving we're definitely going to thrive and I just want to leave the audience with this note that I received from a friend of mine on Facebook. One last thought we isolate ourselves so that when we get back together. No one is missing. That's how my friend put it so isolate yourself people so we can all get through this and come back together and hug each other again. And I want to thank the health care workers as well. We're in this together. Please take care of yourself and others Aloha. Aloha.


So let us start. OK, it is my duty to introduce the winners of the ESRB research prize in memory of Ike van der Berg. Ike was, in a way, a colleague of us. I mean, she was a member of the ESRB Advisory Scientific Committee from 2011 to 2014. She was also a member of the European Parliament until 2009. And unfortunately, she died towards the end of her mandate as a member of the Advisory Scientific Committee. And she was a great colleague to have on the Advisory Scientific Committee. And this prize is dedicated to her memory. And since Ike very much held very high the notion that finance should serve society and not the opposite, this prize was created by the Advisory Scientific Committee in this spirit. And so it's dedicated to excellent researchers who do work on systemic risk on macro prudential policy and also to consumer protection in finance. And in fact, last year, which was the first edition of this prize, the prize was won by Celerier and Ballet with an excellent paper on retail products complexity and, therefore, consumer protection issues. And this year, the winners of the prize are Sergei Czernenko. So these are execual winners. Sergei Czernenko from Ohio State with a paper joined with Addis Sundaram from Harvard University. And Matthias Effing with a paper. I mean, both papers will be presented very soon. It's a solo paper, instead, in the case of Matthias. Now, I also want to say that there were two runners up whose papers, as well as those of the winners, are already part of the SRB working paper series. So without any further ado, I give the floor to the winners for a brief presentation of the key points of their paper. Who should start? Well, let's go go in alphabetical order, so Sergei first, and Matthias next. If it's OK, otherwise we can. Oh, it's fine. And this is, OK, all right. Oh, why do we do this here? It's here. Thank you, Marko, for the great introduction. And thank you to the selection committee for picking my paper with Adi to be the joint winner. Very honored to receive the prize. So the paper is interested in measuring and understanding liquidity transformation and asset management. We know that liquidity transformation or the creation of liabilities that are more liquid than the underlying assets is a key function of many financial intermediaries, banks being quintessential examples. Since the crisis, there's been an increasing realization and a spirited public policy debate on the extent to which liquidity transformation by asset managers can cause similar financial stability issues. And here, the concerns basically center on the interaction of what we might call performance flow relationship and fire sales. Was the basic concern being about negative performance by a manager leading investors to withdraw capital, forcing the manager to sell some of the assets at fire sale prices, and basically creating this loop. And these kind of concerns are especially prevalent and plausible, given that a lot of the growth since the crisis has been in strategies that invest in less liquid assets. So here's one example from the US. It's the growth of loan mutual funds. These are open and mutual funds that effectively promise investors next day liquidity, but invest in syndicated loans. Which basically an interesting fact about this market is that these loans basically settle T plus 14. So it takes two weeks for them to settle while the fund promises next day liquidity to its investors. An example closer to home might be the UK property funds that had to suspend redemptions following the vote about Brexit. Now notwithstanding anecdotal cases like this, a key empirical challenge in this debate is really the difficulty of measuring liquidity transformation in asset management. For banks, things are relatively straightforward. Maturity mismatch is a fairly good measure of how much liquidity transformation a bank is performing. For asset managers, things are more complicated because in principle, the assets are tradable securities. Also, the price impact can be at least partially passed on to the investors. Nevertheless, asset managers such as open and mutual funds do perform some liquidity transformation. And effectively, the way that it works is that the pool transaction costs across investors. And so if you're an investor in an open and mutual fund, you can in principle withdraw unlimited quantities at the end of day net asset value without internalizing the transaction cost and the price impact that you're basically effectively imposing on all of the remaining investors in the fund. And that's what basically effectively what it does is that it flattens the price quantity schedule that you face as an investor and makes the assets more liquid for you to trade in the mutual fund than potentially trading in their underlying securities, which might be corporate bonds or properties, like an example of UK property funds. Now, so how do we gonna try to measure how much liquidity transformation funds are really performing? So the key idea in the paper is to take a revealed preference approach and to argue that the way that mutual funds manage their own liquidity helps shed light on how much liquidity transformation they're performing. And specifically, how aggressively funds use cash to accommodate investor redemptions and subscriptions, so net fund flows, and the level of cash holdings are gonna be measures of liquidity transformation. So the first one should be relatively intuitive. If a fund was investing in perfectly liquid assets, there would be no need for cash and it would be simply transacting in the underlying securities immediately whenever it receives net fund flows. The second one might be a little bit more counterintuitive from the perspective that if you force a fund or an asset manager to hold more cash, then mechanically it's gonna be performing less liquidity transformation. The extreme would be a fund that holds 100% cash, while it's not performing any liquidity transformation at all. But the key to recognize here is that funds are gonna be, asset managers are gonna be setting their cash holdings optimally and they are gonna be doing this to mitigate some of their expected liquidation costs. And so the funds that invest in less liquid assets and provide more liquidity to the investors, so have more volatile fund flows, are gonna be the ones that are gonna hold more cash in equilibrium, although their cash holdings are not gonna be fully enough to upset the higher expected liquidation costs. So that's the basic idea. We take it to the data using data on U.S. open and mutual funds and basically find results that are consistent with sizable amount of liquidity transformation taking place in mutual funds. So first of all, from the dynamic perspective, even at a one month horizon, which is fairly long in asset management, a big fraction of net fund flows is accommodated through changes in cash as opposed to trading and the underlying securities. And it's more so the case when the fund invests in less liquid securities. Also the level of cash holdings is strongly related to proxies for liquidity transformation, the ones that I mentioned before, asset liquidity and flow volatility. And there is an important interaction effect between the two that basically for funds that have their liquid assets, the volatility of investor fund flows doesn't matter for their cash holdings. So these funds are kind of close to the frictionless ideal. The typical fund however is relatively far away from that and so for the typical fund in the data, flow volatility is gonna have a substantial effect on its cash holdings. Now this is kind of like validation of the basic idea of what can we do with this? One thing that we can think about is the extent to which funds internalize their price impact. So in the paper we have a simple model but also both are the simple model in the paper and most theories would suggest that funds will not hold enough cash to fully internalize the price impact that they're imposing on other market participants, right? And that is basically the counterpart of the more standard leverage fire sale externality. Now what we're gonna do empirically is look for settings where there is likely to be more internalization of the price impact, right? One setting you can think of is that the monopolist would fully internalize own price impact. If I own all of the security, I fully internalize any price impact in that security. And so what we find is that funds that hold a larger fraction of the outstanding amount of the securities that they invest in, either equities or bonds, hold substantially more cash than other funds. The second setting, second idea is that funds may partially internalize the price impact that they impose on other funds within the same mutual fund family. So we measure overlapping holdings between the fund and other funds inside the family and funds that have greater overlap with other funds in the family tend to hold more cash, okay? Consistent with them worrying about the price impact that they might be imposing on other funds, on other related funds, okay? Now one implication of this analysis is to say that since most funds do not fully internalize their price impact, like the special funds that we're looking here, the kind of like the monopolist idea and the overlap idea, since most funds are not close to that, they're gonna hold too little cash relative to what an agent coordinating across all of the funds would have them hold, okay? The second sort of like extension of this kind of idea is to look at the effects of cash holdings on stock fragility, okay? So the idea here is to measure at the stock level the cash holdings of the funds that hold the particular stock. And if the stock is held by funds with abnormally low cash holdings, it's potentially gonna be more fragile because if investors withdraw capital from the funds holding the stock, the funds might have to sell it, right? To liquidate it and gauge and force fire sales as a result of potentially introducing excess volatility in the stock, okay? So in this analysis, what we do is we first of all at the fund level calculate sort of this adjusted cash-to-assets ratio which is tells us how much cash you have relative to like sort of our model relative to other funds within the same objective sort of size, age, et cetera. And then at the stock level, we calculate the average cash-to-assets ratio of the funds holding the stock, okay? So we do this at time t and this is what you see on the x-axis. On the y-axis is the daily stock return of volatility over the subsequent quarter. What you see is that stocks that are held by funds with lower cash holdings are more volatile and this is especially the case where the stock has a relatively high mutual fund share so relatively high fraction of the stock is held by mutual funds, okay? And another extension that we're working on is using this revealed preference approach to think about corporate bond liquidity. There's been a lot of concerns about deterioration in corporate bond liquidity since the financial crisis. Now if you look at kind of like standard measures that academics have of liquidity in the corporate bond market, they are basically similar to pre-crisis levels. So you see these measures of liquidity spiking during crisis but then they come down and they're similar to what there were before crisis if not even better. The caveat to the standard measures of course is that they're based on transactions. You can only measure them for bonds that do trade. It's difficult to say what's the sort of latent liquidity for bonds that do not trade. And the fraction of bonds for which you cannot measure standard measures of liquidity has actually been trending up, okay? So this is where the revealed preference approach can help, we can look across bonds and the relationship between cash holdings and flow volatility. This relationship should be stronger, the more illiquid the bond is, right? And we can construct these measures and see how they change over time and for different bonds, right? And so kind of like a couple of nice things about this approach is that we're not limited to looking at the transactions.  So basically to conclude, we take a revealed preference approach to measuring liquidity transformation and mutual funds. We find evidence of a sizable amount of liquidity transformation and kind of two implications that I wanna touch on. One is that liquidity transformation and asset management is dependent on liquidity provision by the traditional banking and shadow banking systems. And that's in a sense that in order to provide liquidity to their own investors, asset managers such as open and mutual funds that we're looking at hold large amounts of cash and equivalence and a lot of these assets are basically short-term liabilities of the banking sector. So things that affect liquidity provision by the banking sector will potentially have effects on liquidity provision by the asset management sector. And other implication that I already mentioned before is that despite their size, cash holdings of mutual funds might not be large enough to completely mitigate their price impact externalities. Thank you. Thank you very much. Yes, so yes, we'll present, okay. So both papers are about macro prudential stuff more than last year's paper, which was more about consumer protection. Okay, so let me also thank the scientific committee for this honor to be here today. I'm very grateful to share the price with Sergey. So this paper is going to be about investments into the securitization market or in what I use as an umbrella term, asset-backed securities. And I'm going to look at investments by banks in Germany. And more specifically, I'm going to look at how considerations for regulatory arbitrage are going to influence these investments. So the regulatory framework for asset-backed securities came under fire during and after the financial crisis. And it has been reviewed by academics and the media, but importantly also by regulators. So for example, the Basel Committee on Banking Supervision looked at its own regulatory framework under Basel II and tried to identify weaknesses or shortcomings in capital requirements for asset-backed securities. And one important weakness that they identified was the mechanic reliance of capital requirements on external credit ratings, as those issued by Moody Stunner and Poznan Fitch. And there are four different lookup tables. Well, it depends on the approach, but basically you have a mapping of the credit rating of the asset-backed security into risk weights, which will then be mapped into a capital requirement. And the fear was that these credit ratings, and hence the capital requirements, would not be sufficiently sensitive to risk. To make this point more clear, let me show you these box plots, where on the horizontal axis, you have different rating buckets that roughly correspond to regulatory buckets. So securities inside one rating bucket have similar and often even identical capital requirements. But still, if you look at the distribution of yield spreads in these different boxes, you see quite a lot of dispersion in the market price for risk. More importantly, or not more importantly, but also to note is that the relation between the credit rating and hence the capital requirements and the yield spreads is not even monotonic. So for example, a bank could buy a high-yielding A-plus rated security rather than a security with a similar yield spread in the A-minus or even triple B-bucket. And without incurring higher capital requirements. Overall, if you take the correlation between capital requirements and yield spreads, the correlation is only 0.5. And if you compute an approximation for the return on the capital required for an ABS investment, you also see a lot of dispersion. If you use the ratio of the yield spread and the capital requirement for one euro invested as an approximation for this return on the equity required by the regulator, you see a lot of dispersion and especially at the higher end of the rating scale. So especially A-plus rated securities can have very high returns on equity. And the question now is whether banks will exploit that and which banks? Maybe those that are constrained by the regulator more than others. And then what does it tell us about the effectiveness of the regular framework that was in place for an asset class that was at the core of the financial crisis? So the way I tried to get at this question was to look at data maintained by the German Central Bank, the Bundesbank, that records exactly how much a given bank in Germany has invested into one specific asset-backed security. So security-level data. And it allowed me to estimate the probability that a given bank would buy a given asset-backed security as a function of the yield spread and the capital requirement. And this figure summarizes the first result of the paper. So on the horizontal axis, you see the cross-section of banks ordered by how constrained they are by regulation, by their capital adequacy ratio. Banks with low capital adequacy ratios over here have relatively tight regulatory constraints. For them, regulatory capital is scarce. And banks at the right-hand side, they have less regulatory constraints. From the regulatory perspective, they appear better capitalized. And then here on the vertical axis of the figure, you see the effect of an increase in the yield spread on the probability that the bank will buy a given asset-backed security, conditional on its regulatory treatment. So take, for example, a constrained bank with a low capital adequacy ratio at the boundary of 8% and take the green dashed line, which is the A-plus bucket. And you see that if you increase the yield spread of an A-plus rated security by one percentage point, the probability that the bank would buy the security goes up by four percentage points. And this is similar for the orange line that's for A-rated, for the brown line, which is for double A-rated, and for the blue line for triple A-rated securities. That corresponds roughly to these rating buckets that I showed you in the previous figure. So it's consistent. Second, I would like to take away from this graph that the effects disappear as you move to the right. So banks that have lax regulatory constraints don't appear to reach for yield. They do not seem to exploit the low yield or risk sensitivity of capital requirements of ratings. Now the question is, what does it mean for the effectiveness of the regulatory framework? How big is the problem? And I would like to discuss this figure in this context. The horizontal axis is the same. Again, you have the cross-section of banks. On the left-hand side, you have the constrained banks with low capital adequacy ratios. And on the right-hand side, those banks that appear better capitalized in the eyes of the regulator. And this brown line here is an estimate of the yield spread of the average asset-backed security bought by a given bank. So for example, a bank with low capital adequacy ratio here on average buys asset-backed securities that have a yield spread of 110 basis points. And what you see is that constrained banks tend to reach for yield. They buy securities with higher yields or higher market price of risk than unconstrained banks. And now next I'm going to plot the risk weight of the average position taken by the banks. And you see that constrained banks, even though they buy securities with higher yield spreads, they buy securities that on average have a lower regulatory risk weight. Whereas unconstrained banks, they incur higher capital requirements. It might not be bad for them because regulatory capital might be abundant in these institutions. They might attach a different shadow value to capital. But the takeaway is that the securities bought by these institutions appear riskier, at least if you interpret the yield spread as some proxy for risk that is compensated by the market. But nevertheless, they have lower risk weights, which is against the idea that riskier investment should have higher capital requirements. In that sense, the regulatory framework seems to do less well than for other asset classes, let's say. Coming back to this approximation for the promised return on the capital that the regulator requires for a given investment. So not return on equity for the entire bank, but what's the return on the capital that you need to use to fund one specific ABS position investment? If you compute this approximation, you see that a relatively constrained bank on the left can have a promised return on equity of 46%, which is very high and which can be realized due to the extremely low capital requirements and the systematic choice of the highest yielding securities in the buckets. This relatively unconstrained bank has a four times lower return on equity on average for the average aspect security purchased. And the conjecture is that if you can increase the return on the equity required by the regulator for an investment by a factor of four or let it be a factor of three or two, that still maps into a significant increase in risk of the position. So then in the next step, I looked at the exposed performance. What are the implications of this behavior? And I see that the constrained banks on the left-hand side here, they tend to allocate more of their portfolio to the lemons in the market in the sense that they buy more securities whose collateral will perform worse exposed. Nine months after investment, I see that the ABS bought by these banks here have a higher delinquency rate. So more of the collateral that backs the ABS is delinquent, then the collateral here, the ABS bought by the relatively unconstrained banks. Okay, so I don't know how am I doing on time? I have the impression that I was really fast. Subjective bias. So to conclude, this is a paper on the buy side of the securitization market. To be sure, there are other papers on the demand for SAP X securities, but either they look at aggregated data or they look at other investors. Sergei has a paper. For example, he looks at funds and investment companies. But for banks, we know very little what determines their investments into this asset class that became very famous during the financial crisis. And we see that banks actually exploit the low risk sensitivity of rating contingent risk weights for asset-backed securities.  And what this may be worrying is, in particular, those banks that appear fragile at least from the perspective of the regulator. So those with low capital adequacy ratios. That they are evading the very capital requirements that were designed to limit their risk taking. I believe that the extent of this, what I call regulatory arbitrage is economically large. And the question is where we go from here. So I just found out yesterday that the BASA Committee redrafted revisions to the securitization framework. I think it became public in July, 2016. And they reiterated that they are going to move further to internal credit ratings, rather than using external credit ratings to determine capital requirements. The question is, will they be more risk sensitive? Alternatively, people have brought forward other ideas like calibrating risk weights to market measures of risk, yield spreads, for example. Rochet did that very early in 1992. The question is, of course, how liquid are prices and how easily can the speed shift? Okay. Thank you. Okay, just a few words about both papers. First of all, basic recommendation, read them because they are worth it. I read them several times in, you know, I was part of the committee within the ESRB picking them among a vast set of people who submitted work and they're really good papers. And they're good papers because they look at new data and they provide new pieces of evidence on issues which are highly under-resourced. The paper, by itself, yeah, belongs to an area of research which is very important for the ESRB and for all prudential, macro prudential regulators because he looks at issues which are relevant for the prudential regulation of non-banks, which is an issue that we have already discussed yesterday, they came up yesterday, and which is increasingly important. So the question is whether, for instance, mutual funds or other financial intermediaries which are non-banks are holding sufficient buffers in general, in particular in this case, liquidity buffers or not. And this is an issue, for instance, on which the ESRB has already done a study based on questionnaires to asset managers to ask, first of all, what is their perception of their own liquidity, of their own liquidity buffers in response to possible market movements and so on. And then there is a second questionnaire which I don't remember if it has already been done or not on second round effects and stuff like that. So it is stress testing in a way of these institutions is increasingly important in prudential regulation. The paper makes a claim which is very important from the point of view of a macro prudential regulator. It says that they have evidence that funds do not fully internalize the effect that providing investors with daily liquidity has on the prices of the underlying securities. I'm not completely convinced that actually they show this but to the extent that they can actually substantiate this point, this is quite important because, of course, it opens potentially the role for intervention by a macro prudential regulator in the form, for instance, of either recommending or forcing mutual fund managers to hold more liquidity than they currently do or other interventions. But I would like to make sure that really, really in the paper there is evidence for this. There is another piece of evidence that Sergei actually mentioned just at the end on his last slide of his presentation which I think is very important from the point of view of a macro prudential regulator. And it is that the form in which this liquidity is held by these mutual funds is essentially deposits with banks or with shadow banks or money market funds. And this belongs to another area which is under the spotlight of the ESRB which is essentially interrelationship between a non-bank and a bank intermediaries in the provision of liquidity. So imagine that, for instance, there is a shock to bank solvency or to shadow banks solvency, then this is telling us that these guys, these mutual fund managers, we have problems in drawing upon their liquidity which they set aside in order to face possible shocks to their net inflows or outflows. And so essentially there is a potential interrelationship between liquidity of banks and liquidity of these intermediaries. So it is all very interesting stuff from the point of view of macro prudential regulation. The paper by Mattias is also very important because it provides the first piece of evidence based on micro data as he mentioned regarding banks on regulatory arbitrage of risk weights. And he explains very well the fact that the way risk weights were set, at least, I mean, looking at this data for German banks, pushes or induces or lets, at least, banks which are more constrained by regulation to actually engage in purchases of riskier securities because these provide, promise them, a return on required equity which is about four times as large as for unconstrained banks. Yet exposed, they had the lowest exposed performance within each risk weight bucket. So essentially, risk weights appear to be utterly counterproductive when they are set because they both increase or at least allow an increase in risk taking by the wrong banks, so the constrained banks, the riskier banks, but also exposed these banks do worse with them. And then towards the end, Mattias was going already in that direction, these banks, the policy question, what to do? I mean, these risk weights are clearly not well set, so should we scrap them, should we base them on more like finer, you know, on basis of finer measures than credit rating agencies ratings, but then which ones should be the actual yields or should be the CDS premium when they're available? This also had a problem, he mentioned, should we go for limits to large exposures? Of course, these are very hot issues, not only for micro prudential regulation, existing one, but also for future possible one. Imagine that we, as we were mentioning before with in the previous session, we have positive risk weights or known as Zelly zero risk weights for sovereign bonds, you know, this all becomes highly relevant also in that case. So of course, this begs a lot of questions, but at least we know that there are things that don't work over and above the prosyclicality, which is generally the issue, which is raised above risk weights based on credit rating agencies' ratings. Okay, let me finish here. I wish you best of luck with the publication of this work. Thank you.