I would remind members off the Covid-related measures that are in place, and that face coverings should be worn when moving around the chamber and across the Holyrood campus. The first item of business is general questions in order to get in as many people as possible. I would appreciate short and succinct questions and responses. 3. Evelyn Twitch Thank you, Presiding Officer. To ask the Scottish Government what steps it is taking to ensure that people visiting Rural Scotland, ond y Lachlóman a Llock Ffllachys National Park, yn fawr o'r code gwaith y outdoor Scottish access. Nectar Scott is the primary agency that is responsible for promoting the access code, and it works with key partners on awareness raising. For example, last year, Nectar Scott's traditional and social media activity saw over 15 million impressions, i'r cyffin nhw'n defnyddio caelwiydd o'i gwelio rydwg wedi cyfnodol rydw i'r pethelio yn Daerys Cymru, ond gan ymdilydd y Gŷn yng Ngheilgrifennol o'r Gŷn, gan yng nghymru o'r unrhyw ddod i gyfan hynny arweinio, ac wrth gwrs mae'n cyntafi â'r Gŷn mewn strategi johnibl ac yn ychydig i'r newid arno i ymddilydd i 2022. Felly cwp yn clywed. I think that the minister for that answer has been a notable increase in visitors to rural areas across Scotland, including rural Stirling. While most people enjoy the outdoors in a respectful manner, some do not. Can the minister advise how we can encourage the public to treat rural Scotland with more respect? The member is absolutely correct. The pandemic did see an increase in people spending time in our natural world, enjoying its restorative benefits for our physical and mental health, which is perhaps a glimmer of light in an otherwise very dark and difficult situation. However, Ms Peed is also right that this access must be taken with care, and I would reiterate that with rights come responsibilities, and the statutory right of access is of responsible access. Last year, I mentioned our visitor management strategy. Through that work, we saw a much improved response to countryside challenges, some of which the member has mentioned. Out of that, the centrality and the importance of rangers and the face-to-face work that they do was very clear. I am pleased to say that the Scottish Government is considering what we might do for the coming season, and I expect to announce that very shortly. Cabinet Secretary, I look forward to our meeting next week to discuss this issue, but the access code is nearly 20 years old now, and given the huge demands on the countryside, which became even more apparent during the pandemic, is it time for an update and relaunch? I know that this question has been considered. From my understanding, it is that there is not concrete evidence that revision is required. We have been dealing with different circumstances over the past couple of years, but I believe that education and communication are the key ways in which we will continue to strike that really important balance between a responsible access right and an understanding that our countryside is a living and working one. Education and communication are the keys to that, but I look forward to discussing it with you further. The Scottish outdoor access code also covers access to inland waters. In the context of Loch Lomond, can the minister advise whether she will consider robust restrictions on jet skis in the forthcoming review of by-laws, given the antisocial and often dangerous behaviour experienced as a result of irresponsible jet ski users last summer? I thank the member for a really important question. The national park has got really good track record of utilising by-laws to respond to some of their concerns, for example, with camping. Something like 4 per cent around the Loch is now within a by-law. Of course, it is for local authorities and access forums to develop the plans for a by-law, and of course Scottish ministers will consider them on their merits when they are presented to us. As we move into lambing season, it is particularly important that livestock are not disturbed. How will the Scottish Government support livestock owners to ensure that the outdoor access code is adhered to on their land? The Dogs Protection of Livestock Scotland Act 2021 came into force on 5 November 2021, which strengthened the law around livestock worrying by increasing the maximum penalties for offences. Police Scotland, farming and crofting stakeholders are combining their efforts to address those crimes and behaviours. For example, the Scottish partnership against rural crime, which is chaired by Police Scotland, is launching the livestock attack and distress campaign with the slogan, Your Dog, Your Responsibility. It is intended to educate dog owners about the new legislation through the lambing season in particular. I think that the small minority who do not treat livestock with respect and care can and must be held responsible and the consequences must reflect the severity of the issue. Question 2, Fulton MacGregor. Excuse me, Mr MacGregor. Oh, that's it. You're on now. Thank you. It's all right now. To ask the Scottish Government what support is in place to assist GPs in certifying power of attorney documents. Vacation of power of attorney documents is a private matter between GPs and their patients. GPs may charge fees for providing the service at their discretion and they're not required to provide it within the current contract. Fulton MacGregor. I thank the cabinet secretary for that response. My office in the local citizens advice bureau in Coatbridge has been dealing with a significant number of cases recently where people, many who cannot perhaps afford legal fees, are struggling to get a GP to complete the certification documents, often citing the busyness of GP surgeries. We all know that GP surgeries have been extremely busy during the pandemic and continue to do a fantastic job as we work out of the pandemic, but I would therefore ask if there's any further support that can be provided to help GPs to fill the very important task or certifying power of attorney documents for those who need them. First and foremost, I'll explore if there's anything more that we can do in relation to this. It should be said that there is guidance that the BMA has provided in relation to what fees can be charged in regard to this particular matter. I'll also have a conversation with Ash Regan on the eligibility for legal aid in that regard, and I'll come back to the member in more detail. Paul O'Kane. In the course of the pandemic, people who have learning disabilities and organisations that support them raise concerns about the use of blanket do not resuscitate orders and confusion about the role of power of attorney in supporting and protecting people who have a learning disability. What further support can be given to GPs and other organisations to support in particular people who have a learning disability to ensure that their human rights are protected and we never again see a situation like we did regarding blanket DNR? Can I say to the member that we will look to explore what more we can do, particularly as we recover on NHSNO? It's an issue that Paul O'Kane and members have raised to me before, and I think that all of us recognise that our constituents are still saying that they would like to see more face-to-face access with their GPs. Of course, we will look and work with GPs to restore that face-to-face access, and while we still have telephone, video consultation and I know how important that face-to-face access can be, particularly for those who may have a learning disability. So what we will look to do is continue to make sure that those with a learning disability forgive me and their families understand fully what their rights are, so I'll take that away and see what more we can do with a third sector partner in terms of that communication. To ask the Scottish Government what additional funding has been provided to restore and enhance rural health services. Our NHS recovery plan sets out key ambitions and actions to be developed and delivered now and over the next five years in order to address the backlog in care and meet the on-going healthcare needs for people right across Scotland, of course, including those in rural areas. The Scottish Government also remains committed to the recommendations that are set out in Sir Lewis Richie's shaping our future together report, which aims to enhance primary care access across remote, rural and island communities. This year's PFG committed to delivering in this Parliament a national centre for remote and rural health and social care. Scoping work is under way, with an expectation that this will be operational by spring 2023. Community group, the old Lewis Development Trust, my constituents, who are stepping up to the market and planning to build a new GP surgery, which can be caused in the excess of £400,000. The new surgery was identified by the health board in 2015, and although it has contributed nothing financially to the new development, it is my understanding that NHS Dumfries and Galloway has been told by the Scottish Government that it must carry out full auctions appraisals outlined in the Scottish Capital Investment Manual for guidance. This is, of course, for NHS projects. However, two similar projects, Staff and Community Trust in Isles Sky and a new medical centre in Fort Augustus, do not have to follow such guidelines. Can I ask the health secretary to investigate why this is the case in such a discrepancy in Dumfries and Galloway? I will. He will forgive me that I do not have the absolute details of the issue that he raises at hand, but I will take a look at it and I will come back to the member in full detail. Question 4, Liam McArthur. I thank you to ask the Scottish Government what work is being done by Sport Scotland and Creative Scotland to provide opportunities for children and young people. Minister Marie Todd. Sport Scotland works across clubs, communities and education to provide opportunities for children and young people to take part in sport. We are working with Sport Scotland to increase the operational and staffing budget for active schools to drive and sustain the programme's inclusion work with a focus on poverty, additional support needs and care experience for young people. Via Creative Scotland, the Youth Music Initiative provides a years-free music making to every child before they leave primary school. Creative Scotland also supports the nurturing talent fund, which gives small grants to young people to undertake cultural and creative projects. Liam McArthur. Thank you and I thank the minister for her response. In the discussion that I had recently with a headteacher in Orkney, I was reminded of how much children and young people have missed out over the past two years and how important the return to routine in our schools is in rebuilding confidence, reassurance and a sense of normality. The headteacher also talked about the need over the coming months to create wow moments, things for pupils to really look forward to. I am not sure that she was angling for a visit from the local MSP, but would the minister agree to consult with Creative Scotland, Sport Scotland and other such bodies, about the role that they might play in facilitating visits to schools across Scotland by those from the world of music, theatre, film, sport and so on in order to create such genuine wow moments? Certainly, I will. I could not agree more that our children and young people need those wow moments to recover from the harm that the pandemic has caused them and be more than supportive of exploring it. Last year's Get Into Summer programme was a brilliant initiative that aims to create opportunities to socialise, to play, to reconnect. It was in place right across all 32 local authorities. Sport and physical activity and cultural opportunities, which improve wellbeing, were right at the heart of it. We intend to build Get Into Summer 2021 this year to deliver a summer 22 offer for children and families in low-income households, and that will provide co-ordinated access to food, childcare and rich-experience activities. Brian Whittle I know that the minister agrees with me that children having access to sport, music, art and drama can have such a significant impact throughout the rest of their lives. She also recognises that Covid has such a negative impact on that. Does she agree with me that it will take significant input from the Government to redress that balance and what steps will the Government put in place to ensure that our children have access to all those essential services? I absolutely agree with Brian Whittle. Our work on adverse childhood experiences has shown us pre-pandemic just how important rich, cultural and sporting experiences are and how protective that can be against adversity and how that protection can last a lifetime. I have absolutely no doubt that we will use that learning to invest going forward. Everyone's responsibility is not simply Government, but Government certainly. In my portfolio, we are doubling the investment over the course of this Parliament in sport and physical activity, and I hope that we will see the benefit in the future. Jamie Greene To ask the Scottish Government what its position is on whether a mix of energy sources, including renewables, could facilitate a reduction in energy prices for consumers. Cabinet Secretary, Michael Matheson. Scotland has had the good fortune to be blessed with huge and varied renewable energy generation capabilities. Unfortunately, Scotland's ability to take full advantage of those resources has been curtailed by an unfair transmission charging regime that has directly disincentivised investment in generation in Scotland. Renewable energy presents better value for customers than nuclear energy and does not present the same safety and environmental concerns. The latest contract for difference auction delivered offshore wind at £39.65 per megawatt, our substantially below the £92.50 award for Hinkley Point. Jamie Greene The only thing that is putting off investment in Scotland is the minister's moratorium on even the exploration of new nuclear energy that is putting companies off right now from investing in Scotland. The reality is that renewables do not account for 100 per cent of energy. In fact, today 30 per cent of it is coming from fossil fuels. A fusion power facility using less than one ton of fuel could create as much energy as 10 billion tonnes of fossil fuels. So I ask quite simply why won't the Government drop this ideological opposition to nuclear fusion? Why won't it work with companies to support a sustainable energy source that will actually drive down consumers' bills once and for all? Let me address the point directly in relation to fusion power. The reality is that fusion power is at a very early stage of development and at the very earliest it potentially would be deployed in 2040, not something that is going to add to our energy mix in the short to medium term in a substantial way in any shape or form. It is misleading to try and give the impression that fusion energy, in some way, is part of the solution to the very significant challenges that we have in the energy market today. However, the reality is that nuclear energy is one of the most expensive forms of energy generation that it can pursue. That is why, at the present moment, it is actually forcing consumer prices up because of the cost associated with nuclear power. What we need to do in Scotland is to maximise our renewable potential. Will that be in wind and marine, but also in storage around battery and hydrogen, and to make use of pump storage alongside making use of CCUS, if the UK Government can get its act together and support the Scottish cluster? To ask the Scottish Government whether it will provide an update on the action that it is taking to prepare for Ukrainian refugees arriving in Scotland. Tomorrow, I will chair the first meeting of the community integration partnership, which will bring together key partners across Scotland. I will also meet tomorrow with the international non-governmental organisations of Scotland to discuss how they might contribute to the UK Government community sponsorship route, given their experience from the Syrian refugee resettlement scheme. That will build on the incredible partnership work that is already under way. I want to thank Scottish Government officials, who are meeting daily and sometimes hourly, and their partners in local government, public and private and third sectors for their work over recent weeks. We continue to work closely with the Home Office, COSLA, local authorities and other partners to provide people with the safety and security that they need to rebuild their lives. The UK Government proposals remain insufficient, given the urgency and gravity of the situation, and we will continue to urge the UK Government to follow the examples of Ireland and countries across the EU and to waive visa requirements for all Ukrainians and develop a comprehensive resettlement programme to ensure that Ukrainian citizens can provide with the safety and security that they need to rebuild their lives. I thank the minister for that answer. Further to the statement that was made yesterday by the First Minister, can he confirm that work is going on to ensure that the Ukrainian people who will come here will have access to GP, dental services, childcare and even language support services, to add to the warmth of the Scottish welcome that they will surely get when they arrive in Scotland? Yes, and I thank Willie Coffey for his interest and raising those critical issues. We are engaging with a wide range of partners to ensure that wraparound support is in place for all displaced people arriving in Scotland. As the people who come here from Ukraine have a right to work, benefit and public funds will be ensuring that people are aware of and get access to such services such as those Mr Coffey mentions, we are rapidly working to establish welcome hubs which will help to triage people and find out what support they need. Multi-agency teams are lining up support, which will cover a range of areas from healthcare to clothes and food, welcome packs and information leaflets translated into Ukrainian about how to access support, including social security, will also be provided and translators on hand to help. Scotland is a long history of welcoming and supporting people displaced and asylum seekers, and we stand right to support the people from Ukraine, as we have other countries as well. To ask the Scottish Government what support it is providing to Ukrainian communities in Scotland. Scotland has a proud history of welcoming refugees and people seeking sanctuary from war and violence. The Scottish Government and Scotland's local authorities have made clear to the UK Government that we stand ready to offer refuge and sanctuary where necessary for those who may be displaced. I look forward to chairing the first community integration partnership meeting tomorrow, which will consider how to ensure that we are effectively supporting Ukrainian communities in Scotland, and we will build on the work already under way. We will continue to engage with our Ukrainian communities as we work to ensure that all those arriving in Scotland, as well as those already here, receive the support that they need. I was pleased to meet with the acting consul general, Yefhian Markovsky, when he was in Parliament yesterday to discuss those matters directly. Fiona Hyslop. The minister will no doubt agree that it will be so important for Ukrainians seeking refuge from war to connect with the Ukrainian community here in Scotland and to be supported by local community support hubs. Can the minister confirm what measures have been taken and at what pace to set up Ukrainian support hubs across communities in Scotland? Perhaps, as the Ukrainian and Polish consul generals have suggested, with cities and towns twinning with other cities and towns in Ukraine so that communities can be together. Will the minister join me in thanking all the Scottish families who have offered their homes for support and refuge? Fiona Hyslop raises very important issues around twinning, which has been explored. We very much welcome the generous office of people to open their homes and their hearts to the people of Ukraine. I will absolutely join Fiona Hyslop in thanking families for offering their homes their time making donations and for the messages of solidarity and support. As the First Minister said in Parliament yesterday, our priority is to ensure that we are ready to welcome displaced people from Ukraine to Scotland by the weekend when the first visa, I hope, will start to be issued. The welcome hubs that we are establishing will provide a warm welcome safety and any immediate assistance. We will also be funding the Scottish Refugee Council to provide support for the Ukrainian family scheme and humanitarian sponsorship pathway in Scotland, which includes planning for increased protection and integration support.


Thank you, I want to thank the organizers for the invitation. It's been a great week. So this is joint work with Hayroboki And Rafael Potri So just so we know we are talking about the same thing. Let me recall the classical Morse Levin So when you have a negative record of space You have some quasi-sodesic So provided the quasi-sodesic is long enough it's going to be about the distance from a true ishodesic This is the classical Morse Levin negative curvature. So this is obviously false when When you look at flats, right? Because when you're in R2 some spiraling thing is actually a quasi-sodesic, right? So it turns out that recently Kapovic The Ivan Porti in 2014 I think So they stated they proved a very nice version of the Morse Levin for symmetric spaces of higher rank. So symmetric spaces of semi-simple groups of non-compact type So what we did With Hayroboki, so we actually found a new proof of their theorem I believe this is essentially a different proof So this is what I would like to talk about So I'm going to actually talk about the proof of the state of the theorem and not why it is important Or why is this is this relevance? So let me so the actual statement requires some Knowledge of the symmetric space. So the statement is going to come later in the talk not at the beginning So let me start by saying By explaining the main tool we're going to use This is called the what's called the mediated splitings So what is this? So when you have some fiber band on Over some compact base and you have some bundle of tomorphism So this is so this is linear on fibers and this is over some dynamics on the on the base So T here could be in could be discrete time or continuous time could be a flow or So we say that it has a dominated splitting if well the bundle splits Into two continuous invariance of sub bundles and what else so we're we're going to ask some conditions So which is vectors here are contracted more than vectors here So this is some sort of very weak condition in some sense. So I'm not requiring that vectors actually contract They could both be contracting they could both be expanding. I'm just saying that here goes It's contracting more than here So let's just put it this way Okay, so if I pick a vector on E if I pick any vector on E and any vector on F if I flow long enough So this is this gets smaller So this is actually a given this is very strong, but it's actually equivalent So actually just the limiting going the limit going to zero So this is what I'm saying. So these vectors here are contracted more than vectors So the so the basic example of this is when you have some some sort of an also some hyperbolic dynamism So this is flow was something negative record. This is actually what's called hyperbolic, which is This is contracted and this is expanded Also, but this this comes in the family was called the weaker versions of hyperbolic So for example, so that's that was one example of the main splitting other another example Which we're not going to use but I just gonna I could just state it like that so that People are talking about So if you have some representation of some hyperbolic group into PSL DR say So this is going to be an also in the sense of Francois if only if The associated flat bundle has a dominator Okay, so this is another characterization characterization of being another representation in the sense of Francois If you don't know what this means, it doesn't matter where I'm going to use it Okay, so what I wanted what I'm going to try to use now is there is some very nice characterization of having a dominator splitting like this Which is due to Bucky and Grumbelon, so let me introduce some notation So when you have a She has a map going from some linear map Well, it between two to norm vector spaces, we're gonna call Sigma one of a These are called the the singular values. Yes, so this is what is this so? Your matrix a takes a ball and sends it into some ellipsoid So the singular values are just the size of the axis of this the match of it, right? Let me just introduce another notation, which is I'm going to look at here So for example, if say the piece Similar value is greater strictly People's one for example, if you have some sort of gap which is singular values Then I'm gonna we're gonna then all by you P say of a Which is the the vector space by the by the first P axis of the ellipse Greater the greatest P. Yeah, yeah, yeah, yeah Metric spaces in metric in a product of B and a product on W So what is the characterization that Bucky and Grumbelon found it's actually W some day much Yeah, so I know thank you for so when we're gonna also consider Like the image of this the pretty much of the smallest axis sometimes the pretty much is like this And here we're gonna have some other space We're gonna call it SD minus P So the statement Is the following so you have some Some Automorphism familiar automorphism of some vector bundle then it has a dominated splitting Say of dimension P say say for example that one of them has a mission P if I don't leave Then when you look at The pay plus one singular value of your matrix of your automorphism and you divide by the The pace the P1 This is contracting. Okay, so if you have if you have some some gap on the singular values after time T That is contract that is contracting with tea Then you you will find some dominated splitting you will find some invariant sub-bundles So the The straight direction is actually sexually sexually forward is nothing to do It is the backwards direction. That's a little harder. And so let me just say a few words about the proof So what they actually what they do is they actually find who is the splitting is going to be So if you want to find a splitting like this, right? inviting splitting So How is it? How is it gonna? How do they found it actually they show the following? So you want to take this you P say of Psi T Into the time minus T. Yes, so this is this is some vector that's living on the fiber over X, right? I go backwards t times and I look how this map expands the first P vectors Look at what I get. This is what it is Awesome ellipse some ball here Look at the image here.  You look at the biggest The biggest P axis of the ellipse So what they show is that this is this is convergent and This and the limiting is going to be some invariant bundle but to show that this is convergent. It's not actually very hard Some tricky computations and very clever computations using this actually give you that this is a Cauchy sequence That that's actually the distance in T is decreasing exponentially on T This actually is this actually is the problem was hardest when you when you look at the other guys Well, if you want to find the other one, you're gonna look at the other space that's standing here What it contracts the most to the past and what they show okay? This is also conversion just because because of the same but the hard part to show is this is that these guys are in the next Some that these guys actually don't intersect So this is this is the actually this is the to show this is the non-trivial input of the statement and What they do is They use some some old machinery what's called which is called the city that's theorem Which is such actually a measurable a measurable theorem. So in some sense using some Measurable theorem from the 60s called the city that's they can show that this is true almost everywhere for anybody a measure That's always true for every point something like some sort of argument Like that Okay, so let me explain Let me know we're gonna leave that theorem there We're gonna come back to it like in half an hour or so And let me explain you Let me say something about the metric spaces of let me just always stay in SLDR. So it's simpler if we have time We can say something about the general case afterwards, but let me explain something about the symmetric space of SLD So this is gonna be very basic so that everybody follows So what are we gonna do? We're gonna define the symmetric space I'm gonna be consider the space of inner products on our D up to a home of three Okay, so this is gonna be our space It's just a point here is an inner product up to a home of three So this is a contractable space, of course. It's a convex space convex set some some vector space So so this this guy has some action, right? So SLD acts here or PSL DX here. So it acts transitively So we're gonna this will give you some way for example to understand what what is the tension space to this guy? Yes, so for example, if you pick some inner product up to home of three then And then this induces some involution only as you're right just the edge of the pollution transposing So this involution pleads the vector space into eigenvectors and vectors that are sent to its opposite. So this is Again, okay, so this is very simple So it turns out that okay, so this is this is what is this is the algebra of of the compact group is stabilizing So if This is some compact group stabilizing all and there the other is what so the other is just a set at the space Matrices are going to lisable on a all or turn on set. Okay, so this gives you the tension space to this guy Just because you have XD Here you have some points Disacting here KO The derivative of the stabilizer of this point, so this goes to zero and PO goes with the tension space and So the thing is that here is LDR and you have this you have the killing form This is what the killing form of AB is simply the trace of AB Okay, so some so this is very silly, but if you consider some some metric which is actually on P so if So this matrix is diagonalizable So this trace is just the sum of the of the eigenvalues, right? so This is just a sum in particular, but this is positive definite and not a generator, of course, right? So the so the metric The metric on the symmetric space there are many methods we're going to choose is This is killing form restricted to this space Yes, so in some sense in some sense the metric is in changing what changing is the space what you what you measure so it turns out okay, so Okay, so what's so you have some point say you have some point on it on XZ you have some times on vector This is just PO This is what this is just some matrix which is diagonalizable on a All-Orthogonal set so you can look at for example the set of all matrices that are Deagonizable on this same orthogonal set So for example consider and we can consider the set of matrices Deagonizable on this special particular set. Okay, so what happens with this set? So this is an abelian the algebra And so what is this so when you what happened when you look at the orbit? Oh, this this is simply the set of All inner products that make this set orthogonal. Okay, so There is something this some very easy computation that you can do actually if you restrict the metric of this of the symmetric space to this set Trivial computation tells you this is a metric to a In fact, but this is this is a little harder is that this is actually a totally scholesic flat so so the intrinsic the intrinsic geometry is flat right because it's just a vector space with some inner product but The fact is it is scholesic. So it's actually in a better flat so maximum in dimension and the scholesic flattas flat so So for example, what you get from this is that this time from all to each of the some vector It's simply the sum of taking values. Okay But so what happens for example? You have some some matters like that. So So this is one flat that's going through through P and this and this tension vector, right? This is just some flat there, but there are probably maybe there are more flats That goes through this point and this vector, right? So what could happen? So what do we do? So we pick T. We looked at the basis where it was diagonalizable and mattresses diagonalizable Inner product that make this special set orthogonal are the flats. It's a flat through that goes through this point So maybe there are more because maybe T could be a good diagonalizable on several other bases The fact that they could be going on many bases is saying that T has some condition is an eigenvalues, right? What are we going to do? We're going to consider the following. So if you take U and V on E I'm going to consider the following function linear function the eigenvalue minus Okay, so if this is zero then there are several flats through T because this is diagonalizable on on many on on many bases that That are contained in the vector spaces by U and V, right? Okay, so this is a finite set of of linear forms So this finite set of linear forms is called the root system of A. Okay So what do you have? You have A and you have this finite set of linear form and when the forms vanish It's saying that there is some trouble in the vector So you're going to look at all the possible kernels of all these possible linear forms So if you have a vector that doesn't lie on any of them Means that there is only one flat through that point on the vector because it is only one There are no coincidences in the eigenvalue. So we're going to choose an only one Orthonormal set So the so connected components of this of this complement is that's called a white chamber It's picking one of these connected components. Okay, so now if you pick some white chamber just pick one pick this one for example So this is picking what about chamber is exactly the same as picking some order on the set E So just fix one of them So now now that we've picked one we can choose an order So we're on right now. Now we can write this as this Yeah, and the white chamber is going to be vectors such that all of these linear forms are positive which means that the vectors are A Okay, so what happens now? Let me just record for later that this is special now that we have this order of this special linear forms here are called the simple roots Okay, so what happens when you when you have two points now? We just study what happens when you have a point and a vector So what happens when you have two points in the symmetric space? You want to understand if there is some flat going through them and you say so what do you have to do? So these are two in the products and you want to find a set which is orthogonal for both That's a flat through them So if you write so So how do you do that? So We're gonna write Q as some the image of some matrix times all so direction of the group is transitive And so we have we have this method and also we can look at this carton the composition of the matrix with respect to So this these two guys are okay, and this guy here It's a it's a it's an element of the on the white chamber. Okay, so which is which is now the orthogonal set Who's gonna be now the orthogonal cell which is? The cell which is gonna be orthogonal for all and Q is gonna be simply the image of the of E by this guy So this this set of D lines is going to give you exactly the flat That's good. That's going to that's gonna go through all and Q Okay, so again as before There could be many flats through on Q and that depends on whether this guy some cohesiveness on eigenvalues Because if this guy some has some cohesiveness in eigenvalues means that there are many choices of this vector of this element So so what you're gonna do? Let me just write some definition We write K of P as destabilizer K of this of the a vector space Be so remember we had a preferred basis here, and we had an order on it. And so let me write down See all the simple roots. Let me put it this way to see the numbers P That's that So this is this is this is this is telling me where there are no coincidence of the eigenvalues of of a of g and so Let me just find this is a set. Let me just find a defined K of theta as the intersection of all of these Let me write this as depending on G or more better depending on all and Q Okay, so finally what's happening what I'm saying is that any element any element of H a K theta So all of these or all of these sets are simultaneously orthogonal for all and Q So this is telling me all all the plots are going through all Okay, just just for the record So we instead of considering the the basis We can we can stick with it with a little less information which is called we're gonna go We're gonna consider the flag the flag But this is a complete flag touch that the which is So I'm just considering the flag which is This vector then the sum of the first two than the sum of the first three Yes, this is telling me what where it can jump So this is defined up to up to the moment you jump it you can choose anyone So this is exactly saying so you consider this complete flag And so so now what I want to do is instead of considering all these bases all these different bases I'm going to consider the flag So this was a complete flag, but this may this may kill some some vector So this is now going to be some partial flag partial flag So why is the interest is the interest of this partial flag because I'm gonna think of this flag as a pointed infinity on the symmetric space from For the flats that go through all and she and she so let me let me make this picture So in some sense was what's gonna happen is if I look at flats that go from oh and she all if I look at Not plus but by the cons I mean The image of the instead of looking at the whole flat I'm looking at the image of the by chamber only if I look at all this all this flat that go through all on this guy Do in some sense that they're gonna have this flag at infinity They want to share this flag at infinity in the following sense. So let me write it this way So this flag is contributed flag which was gonna call you you of she I'm gonna call this flag you she of she because exactly This flag is corresponding to where G has its biggest axis as we had at the beginning And so what I what I'm going to say is that all these guys share some this flag at infinity. So I'm not I'm not defining a boundary I'm not looking at the visual model. I'm just saying we have to think think about this in the following way So when you in in H2 for example, if you have a point Inside an appointed infinity you can you have only one should I see great as going As I say to these two So here you can do something very similar, which is if I have this flag if I have a partial flag and a point in sign I Can choose a whole family of flats that that go through this point and at infinity go to the flag This is simply want I have my flag. I have my inner product. I Apply Grammys meet to this flag so obtain an orthogonal set and then I complete this orthogonal set as I come with Orthogonal sublines this this is going to be all the flat is going from this point to this to the point at infinity So this is actually very this is actually very important the fact that The flag at infinity that you get from all to see all is the biggest axis of the ellipse of how Is the biggest axis of the ellipse when you when you look at the inner product? So let me just say again a quick Formula that follows from the captain the composition which is Distance from oh to see oh This is going to be if I play the captain in composition. They both stabilize. Oh, so this is going to be exactly The norm of she and this is going to be the square root of the log So when you have oh to see oh This distance here is going to be something like the log of the norm of she For the inner product. Oh, it's going to be comparable to that So the distance from oh to see oh is what is the norm of the matrix with that inner product? and at infinity what what what is it associated flag at infinity is The flag that that explains you how the biggest axis of the ellipse of the image ellipse are So just one one last statement and we can we can actually state couple which lives for this theorem The following following observation which I personally like very much If you have say now say now that you have two flags Is a is some partial flag? Index on some numbers It's on some numbers bi and you have some other flag in general position again a partial flag So so they're in general position are in general position if when you take complementary spaces they They don't intersect So now you can do something very similar to what we did right, but we didn't know so if we had a point and the flag at Infinity we could reconstruct This is the image of this while chamber here Simply by so this is this is a flag with the inner product you order gonna you apply garbage meet and you obtain an Orton and set and then you consider all set of lines that expand the same sets at the same time So now you have two flags What are you gonna do they enjoy a position so now when you consider? You can consider all inner products that make these two flags or tunnel This is what's called a parallel set So this gives you some sort of sets inside It's a union of flats If you have some more time I said and then what and then you look at all the lines that Expand the same guys and you look at all those when a person and make this nice orthogonal. So this is a union of flats so actually you using Using the order I had in my set. I can actually interpret as this as Going somewhere like starting here and going there Okay, so what what is the name I want to state for you is that if you have any a product here? Yes, and you want to understand what is this distance for the statement is That this distance is what you're gonna do. You're gonna you have you have these two guys, right? So you have these two spaces which are complementary You're going to measure their angle with this inner product And you're gonna take the smallest of that and the log of that and this is this So what do you do you take the angle between e? I You take the scenes Hello, you take the minus you take the mean take the minus you get something positive And this is the detail is going to be comparable to this comparable in the following sense That you will have some numbers some constant numbers L and C and the same on the other side So if you want to understand that this I'm from this this point all to this Spell of the set of what you're gonna do is you're gonna see you gotta measure the angles of Distro guys from this point for this inner product What's the statement? So let me just let me just take the the simplest version of the statement so Yeah, otherwise we won't have time to do just playing how the proof finishes so so what you're doing you want to consider some I'm gonna consider some cone say that we have picked this one for example consider some cone inside this by jump Can't touch the walls. I don't know. It's just some cone in there Consider some position some position is So let's make it by infinite so to simplify the statement, but we can also get the other statements Stronger statements So we're gonna say that the position is is C regular if what if When I look at the carton of them this carton projection from one point to the other right, so this was what this was this was You pick a matrix has to go from here to here and you look at its singular values. This is this vector If this belongs to C, okay, so you have this question. So desic and then So this is saying something about the distance So it goes further away in distance comparable to n for example, but also the vectors that we had you get a Relay inside this some some given comb This can be make or see that's that's that's not a problem So what's the statement? this one of this one of the statements, so if xn is a C regular position desic Then what there exist? two flags partial flags In general position So the type of these flags depends on where on the walls the cone intersects or not such that Is it bounded from the parallel set? Okay, so actually it's the actual table is a little bit stronger because you have this position desic Have this parallel set here, but actually you can pick a point and you look at the white chamber that goes At infinity to this guy and so infinity to this guy So this is not actually the whole parallel set you can look at some images of course So let me let me try to give you the proof that we found So what you're gonna do is you're gonna consider sequences of matrices that explain you how this guy is moving so Say that you fix them all here, right?  These guys have bound the norm bounded norm Respect to this this whole point here and more over So what happens when you multiply them? So this is going to give you the map When you multiply all of them you multiply some fix the amount of them Sorry from n to m. This is going to give you the map that goes from here to here and this The fact that this lies in the cone And the fact that the norm is growing As my n-m because it's a quasi-scholesic It's gonna tell you that you're gonna have the exact same relations work for the again for the singular values that that depend on them On the for the walls that for the walls that doesn't intersect the cone C So let me just write this So this is very straight. This is very very straightforward, which means that This is very straightforward I literally follow from the definition of quasi-scholesic and being away from certain walls And this is this is this whole for the P, right? Okay, so now let's go back to our usual sort to our first statement When we're going to build ourselves some co-cycle and apply the dominated splitting condition. So it turns out that Actually very strange You consider the set of sequences Perhaps they have bounding norm fix some norm And that verify that condition over there So as long as you fix this contents L C and Nanda This is some compact set and you have you have the shift on this composite because it's some set of sequences So you're gonna be the co-cycle, which is just this set times V And who's your who's gonna be your? your bundle automorphism just so this is a bundle automorphism and And by definition of the actual of the base they verify Bokey-Gormelon's criterion, they have the hypothesis And so it splits. So the Bokey-Gormelon criterion is saying exactly the same century one when you look at the This u vector is going to converge to something look at the complementary guy when you do it backwards This is going to converge to something. This is the Bokey-Gormelon criterion and they are in the exam But these are the sorry so in particular, so then the exam and the base is compact. So in particular the angle between these two guys is bounded below Because the base is compact. So what's happening is you have your O and you're supposed to do this going through O So when you look at this flat from O to XM This is going to be some u of these guys This is what we did at the beginning and what you know is that this sequence is going to converge and the same to the Opposite in the opposite direction, you know, they're in the exam and you know that the angle for them is bounded below by some constant independent of the sequence Because this is this constant here. This is a base. This is a compact set But the angle is just the distance On this point to this flat. So the fact that this The fact that this distance doesn't depend them So you have your uniform amount that doesn't depend on the sequence that you picked It's going to tell you that if you pick some other sequence some other point on the sequence You can pull it back here You can pull it back back here and look at this what this distance is and you're going to have the same distance So this this this argument actually gives you okay You can get much stronger results as a scope of which level 42 So for example, you only need the sequence to be long enough You don't need to have a bi-finance sequence You just need it to be long enough and then you have the same statement and this is just because this is again holes here because Because this convergence here was exponential in some sense so You don't need the whole sequence if you multiply enough matters as this is going to be close to somewhere already and the same here some easy Contradiction argument gives you the some direct some afterwards So let me let me just say one last word on what happens in the general for a general assembly simply group Because there is there is there is some non-trivial statement To be made it doesn't follow exactly exactly like this the idea will be the following So the actual statement that that's missing for semi-simple in group is this statement is what does this mean? Can you do you have a statement like this this distance compare to this two guys? So what you're gonna do you're gonna put your semi you're gonna put your symmetric space into some other symmetric space of some matrices So say you have x she semi-simple group non-compact type etc etc So what you're gonna do you're gonna consider some representation for example into SLD Let me reduce your representation say so so that you get some totally shoddistic embedding of the symmetric spaces So you have some point here So when you have these two flags at infinity in symmetric space of sheet, they're going they're going to go to two flags two flags Sorry partial flags in the boundary of the metric space of SLD So what you want to understand is a distance from your point or to this parallel set of the city to these two partial flags So the problem here is that you know how to do that in SLD in SLD It's just so just the angle from this here from this guy. The problem is that the parallel set It could be much bigger now Parallel set in SLD associated to these two flags is much bigger than this So maybe the distance is attained here and this could be very far away So this distance is going to be compared is comparable to the angle between these two guys But you don't know what happened to this distance. Okay, so there's something to show there that it actually remains bounded from this guy So the actual statement is Consider some orthogonal vector here. It's gonna make some fix it It's gonna it's gonna make some fixed angle with the parallel with the bigger parallel set So this is gonna give you the the problem the bond between these two distances here. I think I'm


What's up everybody, Jason here for jaspyscasebreaks.com 2019-20 panini and mac of the basketball premium first off the line There's a sticker right there Basketball one box break random teams number one just sold out they can 30 spots everybody gets a random team in the NBA Exclusive first off the line one sneaker swatch signature premium edition or sneaker swatches signatures premium edition platinum one patch autograph one premium edition of a patch Autograph tags and one other or two and two memorabilia cards. So this stuff can be loaded guys. Who knows what's in here? Hopefully it's that man right there and some good players But good luck guys. So again, we had a dice roll here. We did a couple fillers So from swim in down to Demetrius got those spots straight up and then from Ryan mosaic sell a 659 We gave away eight spots down to Zach Gwin down to Brenton So congratulations for you guys saving a little bit and getting in through those fillers and then of course Hawks down to the Wizards So that's a roll it and then we got ourselves a three and a one for four times four times guys. Good luck one two three and four Four times three and a one So men down to Danny three and one four times Four times are here one two three and four four times Pacers down to the Lakers No, Siri, I wasn't saying what's the Lakers for from a series All right, so many other Pacers Christopher with the Wizards Deacons and economy you have the T was Demetrius of the Sun so men with the jazz Robert Ronco with the pistons Brett you have the Grizzlies Paul with the Kings Daniel Graham with the Blazers Robert with the Thunder Jeremy port with the Wizards John W with the Heats Brenton you have the Pelicans Demetrius with the Knicks Michael Hughes with the Raptors Brian Cross with the Spurs James with the Nuggets Robert with the Celtics Christopher with the Clippers Ryan with the Nets Demetrius with the Hawks and knock you have the Rockets Demetrius with the Bucks Christopher with the Magic James with the Mavericks town with the 76ers Brenton with the Cavs Deacons you have the Hornets G1 you have the Bulls and Danny with the Lakers So again if anybody wants to trade I'll give you guys a quick minute if not we are print and ripping Jack is saying Kings up for trade Is it does it feel like to me that Devon to Smith can actually still grow into his body? Or is he just gonna be like that tall lengthy receiver like that? Because I just feel like the dude can just get more bulkier for the Sacramento Kings. Yes 1920 we call guy a Lot of people are kind of high on him too as well Zags you insane Hawks Hawks for Bulls So Demetrius, I don't know if you're watching would you like to trade the Hawks for Bulls? Give me guys another 30 seconds if not, I'm gonna close it Jared, I'm not sure man. If you're talking about a Macklin football would love to We did do two of those yesterday fresh case today looks like But it's up to you guys Let's do it So you took the Falcons, right? Very nice We're getting close enough.  So we want to try to Get a Macklin down maybe to like five or something so we can try to R&B because if not it's gonna get a really really expensive So let's try to take on though. There's still a lot of 30 $40 teams guys Yeah, I mean I would like to do black football. I mean if we're gonna do a football break today, too I mean we're gonna do the collegiate black football that's six. So I think I'm gonna start trying to get that R&B All right guys, I'm closing the trade window. I don't think customers here. So Yeah, black football mean like I said, I wanted to try to get a little closer But if I have to all round on normal block the rest of these 16s, but might be a little bit more pressure than I wanted But someone wants to grab the Ravens for 50 bucks colts for 60 Um, then we can R&B the last 14s, which would be the bangles chargers dolphins and eagles All right guys, stick with what you got. Don't know what's gonna pop out of here. I hope it's greatness and Very exciting stuff So first off the line premium edition Yeah, it was right Jack Definitely fun when you get a herber, right? fun fun fun Oh, this box does feel a little thick I always say we got a blockchain at the bottom and we got RJ Barrett. That's a rookie patch autographs tags So this is all blockchain edition, but some of these blockchains guys actually sell pretty well And to start us off right there that is not too shabby That is uh, Demetra's last Bob Mojo with the Knicks and just wondering what is tags out of I mean I'd assume it had to be one of one or out of three or something Some of these blockchain cards actually sell for some good money and Anthony what's going on, bro Yeah, let's we can do 10 box mosaic already Like I said, I know there's a lot of options guys, but there's a break. So there's a couple breaks that are super close All right, so we're looking for rookie patch autograph tags And that's card number 104 So yeah, that's a one of one actually that is a one of one RJ Barrett rookie autograph patch tags For the Knicks So that'll add a little extra value right there for you Demetra's just because you know, like I said, even though it's digital Uh, some people will pay some good money. So that is a one of one RJ Barrett rookie patch autograph tags very nice So we'll go New York Knicks That is a one of one Uh, once that once it's sold out Nick, there's no time slot I'm gonna probably create a random number block soon to help sell it a little filler But there is no time slot. It's whenever it fills it breaks All right, first one we got is deandre hunter. That's 12 out of 99 and guess what guys I believe that is a jersey number match 12 out of 99 little eva one of one for the atlanta hawks and Demetra's We have a carl anthony towns That is a little jersey 49 49 for the teawolves That is Danny tonal. All right, the next one we have is wow. Look at this One of one sneak peek Tongue logo for the seattle supersonics, which is ricky pierce Very nice Seattle supersonics will be going to the okloma city thunder and robert ronkel.  Very nice Did I pull ricky pierce already? I thought I pulled the the other legend for the sonics tongue I if I remember correctly, I thought I thought that's the one I pulled before it. What is it? Um Forget his name Nikola joke it just patch autograph premium edition Very nice and premium edition Would be either 20 or less or 14 or less There you go So nicole joke it's just denver nuggets going to james Oh, did I really? Oh, maybe it was ricky pierce. I thought it was the other guy Why is it blanking in my head? You know what i'm talking about? Oliver, um It's blanking in my head again Sean camp. I thought it was a shan camp. This is what I thought it was but maybe not All right a couple more guys Little lorry mark in the patch and autograph Oh, so did I pull the heel now the tongue? Oh nice. I don't remember that good good memory I just know I pulled something similar of uh Of that tongue, but Chicago Bulls tried to trade couldn't trade mojo. It's actually when they got man And we have a sneaker swatch patch auto premium edition of jerry culver I don't think i'm gonna put this in a toplers.  That was the break So very nice stuff. I mean much more loaded than the regular box We've got some nice names little one-on-one tongue And then of course the blockchain was pretty strong to one-on-one rj barrett tags rookie patch autograph So there you go guys. That was immaculate premium edition first off the line random teams number one Uh, appreciate you guys. Jasper's case breaks.com


This is your host Satil Bharti and today we have with us once again Clyde C. Prasad, SVP and general manager of training and certification at the Linux Foundation. So first of all, tell us about this open source jobs portal. As you know, this is a multi-year effort on our part. And so we've been doing this for seven or eight years now. And it's really important for us to be able to have hard data when we talk about this to complement the anecdotes, right? It's quite easy to get carried away with the anecdotal things that we hear. And what this report allows us to do is sort of plant off refirmly in terms of what is the market actually telling us at scale, right? From hundreds of people from across different geographies. And so what this report allows us to do really three primary things. One, it informs us as an organization, where should we be putting our focus on training and certification? Where are the gaps in the market today? Where are the gaps likely to be? And so it helps us shape our decision making about where to put our focus. Because a big part, the strategic reason behind the training and certification group at the Linux Foundation is to ensure that we're not just putting great code out, but that we're creating the right talent pool, especially at that entry level. So that code can then get deployed, used in production, and able to help people on their career journey. So the first group, we use it internally to create focus in the right areas. Secondly, for individuals, right? Individuals who are looking to start or to grow their IT career, they're looking for some signals. And again, to get away from the anecdote, they're looking to try to figure out where should I go next, right? So we're in an era now of continuous learning, where the things that served you well two years ago won't necessarily serve you well for the next year to come. So people are constantly asking themselves the question, where do I need to go next? And this helps in that regard. And lastly, the employers want to know where are the skills coming from? Where are the gaps going to be? And what are the strategies they need to use to fill those skill gaps in their organizations? This is particularly important post pandemic, right? And so I think a lot of people have now realized that hiring talent based on searching on LinkedIn is not a sustainable strategy for the long term. You've got to find other ways of finding talent. Some of it could be developing talent in-house, some of it could be reaching out to non-traditional markets. But it does serve that market as well, right? It helps them get their heads around what are some of the challenges, what are some of the pinch points, and what are some of the strategies to try to create new on-ramps for talent as these different open-source projects take their place center stage. What I find challenging when it comes to open-source job reports is and it could also be the scope of the report. And I can partially be a Linux foundation for that because if you look at CNC and other organizations, you folks are creating, not you folks, but the communities are creating so many new technologies that just to end, then new paradigms are also coming up. We talk about DevOps and DevSecOps, so the rules, what kind of skill sets needed is also changing very fast. So it's a big challenge. It's a big daunting task for you folks. So tell me about your methodology internally and how do you track all these changes so that people do get at least the actual situation that is going on in the market? So it is a little challenging, right? Because it is a longitudinal survey, we do it year after year. And one of the questions we have to ask ourselves every year is think about the phrasing of the question, think about the topics that we're covering and are we grouping things correctly? Are we articulating correctly? Three years ago, there wouldn't have been as much granularity when you think about DevOps and DevSecOps. So every year, we take a look at it and say, are we helping people understand the framework of what's out there in terms of open source with language that is going to be easy for them to recognize where it fits? And then that helps us when we interpret data, to be able to say, when people thought about cloud, this is what we know exactly what they were thinking about. When they think about DevOps, this is what they have in their mind because of course that's one of the challenges in survey methodology. Are they answering the question you thought you were asking? If you look at this report, I just said, pandemic also played a very big role in the industry. What are the technologies that are in most demand? And does it also, do you see because you have been doing this for so long that this is the natural organic trajectory of these technologies are coming out in demand or COVID changed something there too? You know, that was one of our big questions, right? Is what happened as a result of COVID, how big was the change and is the change permanent? So the piece that we've been trying to work through is looking exactly at that to say, what do we know now a year and a half into the pandemic? And I think there are two main things that we've seen. First, the shift to cloud has accelerated, which is perhaps not surprising, right? When people found themselves physically unable to go to their data center, it changed something in their mindset of, how do I operate in this new world where I'm going to be able to need to administer and run my systems without necessarily physically being able to go touch them in the way that I would have in a bare metal past. The second, which reinforces that, is this idea of remote work. So of course, we all became virtual organizations over the course of 2020, and there's some dialogue about what point people go back to offices. What we're seeing, I think pretty consistently, is you can't put that genie back in the bottle. Now that people have gotten used to working remotely and working productively remotely, that's going to continue to be part of the way that work happens going forward. And what that also does is intersect with the first trend about the shift to the cloud. And so we've got more people working remotely on more systems, and that plays to the strengths of where the cloud native ecosystem has gone, which is remotely hosted systems, running Linux as the OS with Kubernetes as the orchestration layer, and a suite of DevOps software practices and software for coordinating the deployment of these. And so I think the old model with bare metal servers with twice annual deployments, that's never coming back. So the real challenge in our view is, how do we take a huge install base of legacy apps and move them to cloud native? And that's going to be a question of time, that's going to be a question of budget. But just as importantly, it's going to be a question of talent and the availability of the staff to take those apps and move them into a cloud native architecture so they can be deployed on this next generation infrastructure. How easy or hard it is to find enough open source talent in today's world? So you've seen this in the report, right? Upwards of 90% of people saying that hiring open source talent is going to be a priority for them. And the increased investments that people are making in training, the increased investments they're making in certification, those are all signals that there is a shortage in the marketplace and that companies are starting to try to find more creative ways to develop that talent. And of course, it's not surprising in a sense, right? So the traditional college degree program isn't really geared towards creating software developers who are natively open source, who are cloud native in their orientation. And so this idea that the talent pool to be able to create, deploy, and maintain cloud native apps was never going to be something that fell out in the sky. It was always going to have to be a journey. It was always going to have to be an investment. And in many cases, an investment in your existing talent, right? So the same folks who've been running your legacy apps are going to be the same folks you're going to have to rely on to convert those into a cloud native format and get those up and running in a Kubernetes powered cloud hosting environment. Because you're not going to be able to hire your way out of this challenge, right? You're going to have to do an all of the above strategy where hire when you can cross train and upscale the people that you have and then reach out to some of these non-traditional communities as sources of talent. Because otherwise we're all going to end up trying to fight over the same few people, which is great if you're an experienced cloud engineer, kudos, right? You're probably getting multiple LinkedIn invitations every day. But that's not a sustainable path to the future. We've got to find other ways of bringing people in because the market and the data is telling us that there isn't sufficient supply out there for this huge new wave of demand. I mean, we have been seeing that, there is a lot of folks because they have experienced remote working. They don't have to relocate to a particular region to find that specific job. And they also are becoming more picky who they work with, which can also create a lot of challenges for employers to not in terms of recruiting new talent, but also keep the folks that they have. So what advice do you have? Because I feel that they also need a cultural shift in the way they deal with their employees. Just the way we have to drop the legacy model of building infrastructure. We have to adopt the cloud native model for building infrastructure. We also have to embrace new ways how we interact with our employees. So what tips do you have for employers so that they can more efficiently retain and attain talent? One of the old jokes you used to hear was people saying, well, I'm worried about training my employees because what if I train and upskill them and they leave? And of course, they were taught, well, what if you don't train them and they stay? But that's actually increasingly true. If you have people at an organization and they see this opportunity from the shift to cloud native, and you support that with their skill set and involving their skill set and the expectations of them to be able to be competent in this transitional phase, that's probably the biggest single thing that you can do to create loyalty and to create engagement and to create this idea that people can see a career path into the future. Because if you send a signal that you're going to try to hire that next generation of talent in, what you're implicitly saying to your existing base is we expect you to become less and less relevant over time. So structurally, if your intent is to engage with folks and keep them engaged over the medium to long term, you've got to signal to them that you expect them to be contributors over the medium to long term. And the only way to get from here to there is to have structured ways of ensuring that folks have the opportunity to use these new tools, to train on these new tools, to certify on these new tools so that they keep their skills sharp and that change is just somewhat subtle change in mindset I think is really profound and it's something that employer after employer is telling us that they're doing, is they're doubling down on the investment and the fear and concern that if I train my people up and positioning them to go take that next job somewhere else is being superseded by the realization that the best shot you have of getting the talent that you need is to create that talent based on the folks that are there today. One of the beauties of open source is that you can just go check out the code, download it locally and start pay, put something on the cloud and start running it. You don't have to kind of go through any official training but when you are working in the production environment, you do need to know what you're doing. I feel that training and certification, they do play a role. First of all, from the perspective of the employee that, hey, I do know what I'm doing and employer that, hey, you know what? This person knows the job. Plus, as you also mentioned, the way talent pool is getting a right person is becoming challenging. It does play. So if I ask you, first of all, if you did ask any questions in this survey to understand how important is training and certification when people hire an engineer? And second is that why people should care about it? Yeah, it's a good question. Thanks, Shlopnam. It's a bit of, it had become a bit of a truism in IT for people to look down their nose at certification exams. And I think it was a large part because the legacy type exams which were largely multiple choice had become very compromised by the growth of the internet and the speed with which exam questions got exposed. And so people won't really be interested on their skills because they were coming into the exam knowing the answers. What we've seen more recently, and this shows up in the report with a much bigger appetite. The percentage of employers interested in certifications has gone up significantly, as you can see in the report. And we attribute that to the fact that the push has been on performance-based certifications. So not picking answers out of lineups but having live systems where you have tasks to complete. So my confidence level that you have the skills that I'm looking for goes way up if your certification was a live system performance-based because what I see is even if you had some pre-knowledge of what was in the exam, the fact that you could do those tasks under the time pressure of a clock running down under the observation pressure of a proctor watching you tells me that you actually have the skills. So even in the most restrictive sense, if you assume that the person had a pretty good idea of which skills were being tested, the fact that you have those skills and you can demonstrate them on a live system under time and observation pressure is actually still telling me something meaningful about the investment you've made in your skill set. And so we see this increased acceptance of certifications as a valid marker to get somebody even in the door for an interview and being able to have confidence that there are a certain baseline level of skills both from an efficiency of recruiting perspective and importantly, because most companies are dealing with a shortage of skills, if you think about Kubernetes as a classic example, they don't have enough Kubernetes engineers on staff to run their system. So having those people have to spend multiple hours on every candidate trying to see if they know the skills or not is a double whammy. They've taken the few people that they have and they've taken them out of circulation to try to check on the new people coming in. And so these performance based certs are addressing a bit of a gap in the market where it gives the employers more confidence to bring that person in for an interview simultaneously reducing the overhead on the technical people who are trying to do the interviewing. And that's important, right? Because we're in a talent shortage environment right now and so the contribution that a certification can make if it's performance based to increasing that confidence to reach out and find those candidates, especially if they're from a non-traditional diversity type background, it's making a meaningful impact in people's ability to find and hire talent from more than just the usual sources. Thank you so much for taking time out today and talk about the latest report. Share your insights on what companies are doing and also what they should be doing to not only retain the talent pool but also attract more. So thanks for those insights. And as usual, I would love to have you back on the show but we should not wait till the next report. We should talk before that. Thank you. Thanks for having me. Stop now.