Thank you so much Melanie and of course now we'll just introduce the presenters for the next session and the focus for the next session is training, learning and also looking to the future. What next after links after this meeting and the people to host us in the next session is Hana Faw who is the IAPB president and we also have Mr. Josiah Onyango who is the coexter chief executive. So over to you Josiah and Hana. Thank you, thank you very much Robert. It's a pleasure to welcome all of you to this fourth and final session of international partnership events. I am Josiah. Josiah you're just breaking up a little bit. We're having difficulty hearing you. Hana's also on the line as well. A word of welcome from me to everyone and I thank the facilitators and presenters of the third session. This is the fourth and the final session of celebration of international partnerships online event and my co-host is Hana Faw from West Africa. She can say a word as we look at looking at training, leadership and the future of links program. Thank you. Hello everyone. Can you hear me? I'd like to thank everybody for staying on throughout the first three sessions and coming into the last lab which is probably the most interesting lab because it brings together all that has been happening in the previous three sessions. In this session we are going to touch on how does one get the human resource for delivering service? How does one train the human resource for doing that and how does one get the human resource to think research and conduct research? We've got a very good team of speakers and it's in the program but just to quickly go through that we've got Melanie and she's going to take us through the training of trainers which has been a quite a successful program. They've got Chiku who has an extensive life experience on training of cadres and parts of the country in East Africa. We've got Bill Dean who is moving the frontier on simulation and surgery training and a huge lesson that have been learned in East Africa on research and leadership mentoring and we're very very lucky in this session that IAPB is coming as the chief partner in all that we do to give us a few minutes. Peter is a very busy person and he has accepted to have some time with us and I'll try to wrap up at the end with the way forward and Melanie will take us through the last poll sessions and the questions and answers, small group discussions and large group discussions so without much ado because we've lost a bit of time I'd like to invite Melanie to take us through the delivering the training of trainers project. Melanie. Thank you very much Hannah. Training the trainers has been a fabulous journey between the RCOP and Coexa. This has been for eight years. We've been working with over a hundred trainers and many of the friendly faces are here now and I've got to know some of them very well. We've worked to create ethos that's appropriate for training to develop skills to embed processes within units and this has led on to a sustainable process that can then be cascaded throughout the whole Coexa region. So this has been of benefit to the trainers, to the trainees and also to the patients. So it started back in 2013 when we got funding from FET to provide the link and this was part of a five pronged approach with curriculum, exams, training the trainers, guidelines and professional development and this was all trying to produce a skilled and motivated workforce who can develop high quality eye care. So we are really trying to develop this group of trainers with high training skills so as the Royal College faculty we are working with a Coexa faculty and developing them first of all to develop trainers in local areas so that they could then support their trainees, their consultants and their other health care professionals to try and provide high quality care. But of course the trainees become consultants, the consultants get trained up in training so they become the local trainers and then they're all on the training pathway to develop into a Coexa faculty. So this should lead to a highly effective workforce delivering high quality care. So we had three different, we have four different objectives with this. We had the phase one was embedding the ethos, phase two was developing the skills, phase three we then embedded the processes and phase four we were cascading teams. And I've just realized that I've got the wrong version of presentation. Apologies. I think the easiest thing might be just to continue with this presentation. Sorry I've just had so many things open. Sorry Melanie. Sorry do you want to go on to Chiku and I will just sort this out and I'll then come back to you. Terribly sorry. Okay Chiku are you ready to present? Yes I can. Anything for Melanie. Thank you. Sorry. Okay so I will just start sharing my slides. You need to allow me to share my slides. Okay good afternoon everybody. I've been asked to talk about implementing a training program and I'm going to tell you basically the story of how we built a residency program from scratch in Rwanda and I will start with a back story and then reach where we are today. You all know the story of Rwanda and the genocide and all that happened but at the end of all that Rwanda had one of the greatest shortages of human resources for health in the world and it was not a time when eye care could be a priority at all and Rwanda literally spent the first six years just putting the house in order creating department systems, creating a new ministry of health and all that type of thing. In 2000 Rwanda became one of the first countries to sign the what was then called the Vision 2020 Blindness Prevention Plan and out of that plan the decision was made that the best place to start eye care services for the country would be at the secondary level. With that decision the first thing was to train the people to work at that level who didn't exist and Akada known as the TSO of family technicians was employed was a training program started to create a group of young men and women who could be deployed to district hospitals in Rwanda and as we speak every district hospital has one or two of these young people who can diagnose, treat, refract, refer appropriately and also host surgeons. After sorting out the district level the next level handled was a primary level and Rwanda has a primary eye care program which aims to provide an affordable eye test within five kilometers of every household in the country. These nurses can treat minor conditions they refer to district hospitals and they can also do minor refractions using adjustable glasses and also dispense reading glasses. In the first five years over 2,800 nurses had been trained in all the 502 health centers in the country and between them had screened over 2.5 million people. So after sorting out those two levels Rwanda then had to move to the next level. By then the eye health workforce was growing steadily and by 2018 when we started Rio over 100 mid-level workers were there already working in district hospitals and over 4,000 nurses had already been trained. Our wrap done in 2015 when analyzed showed that in order to tackle blindness in Rwanda we needed to do something about cataract surgery and about other things like glaucoma and diabetic retinopathy. This then gave us more momentum to do something about training more ophthalmologists and Rio was started not as a school but actually as a not-for-profit and we had four components. We had clinical services which we started in partnership with Dr. Agarwal's hospital. We did research and managed the two rubs that have been done in Rwanda as well as many other research projects and we also had community services providing services like corneal transplants to the poor people. So the school was actually the final component. Starting a residency program became possible in 2018 because of four reasons. One was the existence of coexa. With the existence of coexa we had a body that could accredit our training. We could have done this through the University of Rwanda where we were both working anyway. But we were ready and the university was not ready because ophthalmology was not their priority subspecialty to start. We were also weary of all the processes that will be out of our hands if we went to the university way. We also felt we could start because of the coexatity program. So those two things were directly from the links program that coexa has with the with the Royal College and I'll talk about those in more detail. But the third reason was a good will that we enjoyed from the Ministry of Health and International Partners and also that there was a changing opinion about how postgraduate education should be done in the region. If I start with the Ministry of Health, the Ministry of Health was motivated to start residency training in Rwanda because in 2018 all the 16 ophthalmologists in Rwanda had been trained outside the country. Among them five did not perform surgery and four were at that time undergoing refresher training in cataract surgery having returned to the country from residency training. Six doctors who'd been sent out previously to trainers ophthalmologists had either abandoned their training or chose not to come back and practice ophthalmology in Rwanda. Despite having benefited from NGO or government scholarships and also the MOH thought that local training would allow the residents to be a resource for Rwanda even while they were in training. Because of that the MOH endorsed Rio as a preferred training site for any doctor who expected government support while in training. In terms of the changing paradigm, the East African East Central Southern Africa College of Health Science was started by the East African community. And as part of their in their momentous you will see that they quote things like the health ministers noted that there was a limited number of specialists and they wanted additional training approaches to training health specialists to complement the university system and they thought that this training could be held in various discipline based professional colleges that would be affiliated to EXA and that EXA would oversee and coordinate the functioning of these semi-autonomous professional colleges. COEXA is one of the strongest colleges under EXA and the COEXA factor meant that we had a robust professional college that could accredited our trainees and Rio's accreditation by COEXA was recognized by the regulatory bodies in Rwanda and some of the surrounding countries which which unblocked one of the big barriers that we were battling with. The COEXA factor also was that COEXA had a lot of good things happening that were exactly what Rio needed in order to run a good program and among them was the the curriculum that was being revised and developed. This revised curriculum is mirrored on the Royal College of Ophthalmology's curriculum but customized to the to the region. This is one of the strongest link activities that have happened under under COEXA and the Royal College and we as Rio were just in time to to embrace this curriculum and start using it and I always say I'm probably the only person in the region who has read every word in this curriculum not once but twice because I needed it for my program but also because I had the opportunity to review it and revise it. The COEXA TTT link was another opportunity that came our way at the right time. I do believe that we do need to teach better in order to create better doctors and I had moved from Kenya to Rwanda as a good clinician with absolutely no knowledge on how to train other doctors and therefore when I had about the TTT program I embraced it not because it was there but because I really felt I needed it and through the links program I learned how to teach adults. I learned how adults learn and how to ensure that this teaching is being translated into learning through doing assessments the right way. So for me the circle was complete. The curriculum gave me what to teach and the TTT program ticked all these other gaps for me and you know that I really embraced this program to the effect that I then became the head of training the trainers in the region. You can read more about our program in this paper which was published some years back and I'm sure Melanie is going to talk about it in a few minutes and you'll understand the program more. So what's the way forward for our training program? We have 10 trainees in session at the moment. If we train four doctors each year we will double the number of ophthalmologists in Rwanda by 2026 and still have 12 more in training. During the course of training the residents are expected to perform a certain number of cataract surgeries as is in the competency-based curriculum and in doing so they will be performing 20 percent of the surgeries done in the country. They're also expected to produce publications before they graduate and we will then increase also the research output out of Rwanda. How are we doing so far? Our first cohort sat for the ICU exams which we used as our progression exams last year and as you will see they passed both exams that they had to sit on the same day the visual sciences as well as the optics and refraction and when we receive the analysis of how their performance you will notice that in every subsection the candidates from Rwanda were aware above the global average not just in visual sciences but also in optics and refraction. Besides this we actually do have another link. We are really grateful for the link that we have with Coexa but we do have another link and this link is with the Wills Eye Hospital. We established this partnership before we started the school so we our partnership with Wills started as a partnership in research and also in community services and when we started the school it was just natural that we would continue with the link. Last year at the AO we were asked to make a presentation about our link and as you'll see we discussed a lot of things but all of the things we talked about was the necessity to relate as peers not as donors not as a donor and a recipient and we have had several activities that have been bilateral. Wills doctors coming to to Rio and Rio doctors going to Wills but not just at the faculty at the trainee level but also at the faculty level and those of you who came for Coexa and Figali noticed that we had a joint booth with Wills. Marcia is part of this link. Even though our link is not run out of ICH like the other links it is Marcia who encouraged us to formalize our link and Marcia is probably the most experienced person in the world on how a good link should work. So using the advice from Marcia we formed we have a formal memorandum of understanding with Wills Eye. That process brought in funding for the link not again from Europe but from America where we have an American organization surgical eye expeditions that funds our link. In summary the setup of Rio has benefited us has benefited in numerous ways from the Coexa Royal College links program. We are very grateful to all those who've been involved and thank you for listening. Excellent thank you Shiku thank you very much. We indeed can see what partnerships can achieve when we relate to as partners as you've said. Over to Melanie if you're ready we'd want to give you the chance to complete the presentation that you are on. Thank you. Apologies has too too much going on at the same time. Right so where I got to was that basically the Training the Trainers program was an eight year program split into sections of two years so phase one was creating the right ethos phase two was developing skills. Phase three was embedding the process which is exactly what Shiku has just described and then phase four is cascading in a sustainable way. So we started by running the supervisor level courses which were three day events addressing teaching and learning supervision and assessment and also program management and training difficulty and this the thing about these courses compared to many others is the very high proportion of practical work and skills work and discussions that go on during the courses so they work in pairs setting aims and objectives or teaching practical skills there's appraisal role play or training difficulty role play and also small group discussions that really help the learners to get to grips with the material. So the first course was run at Nevasha and then for the basically the high level trainers within Coexa and then we also had the second course that was run in Nairobi. So the purpose of these was that training skills can be learnt or improved the ethos that a standardised curriculum with assessments is really important and that trainees should be supported through good supervision. So in the second phase we moved on to the development of skills and the important things here were that they would be able to deliver skills in whatever training setting they were. At this point we didn't actually have any funding so we had to link our events to either the congresses or the exams that were already happening. So by developing skills they learned about interactive teaching and a variety of styles and teaching practical skills feedback and appraisal and also techniques for managing trainees in difficulty. So in the third phase this was really embedding the processes as Jiku's just described so educational supervisors were appointed the we rolled out national institutional training teams and also Jiku developed the portfolio which was then transferred to use in the Coexa region and at this point because there had been several delegates who had been on quite a number of the courses they were progressing through from being delegate to facilitate it to faculty and then with Jiku as the lead and the important thing was that they were now in a position to be able to go back to their own local units and to deliver the training the training programs to their local trainers. So this meant that when we moved on to the next phase we could deliver advanced courses so these are also three days but they have split up of separate modules on course delivery advanced skills and also complex issues and on these courses a lot of the teaching and training is actually done by the delegates themselves either lots of them teaching simultaneously in small groups supervising practical skills or here in a large lecture theater type setting but the important bit about this course is that after every single presentation everyone has detailed peer-to-peer feedback and it's the learning from that peer-to-peer feedback that firstly makes it sustainable and it really makes the individual enable them to get a lot of learning out of the sessions. So this took us into phase four when we delivered one course in Dar es Salaam but actually this year we were running an advanced training the trainers course in London and it did happen to be after Covid so we invited the coexa trainers to come too and so we actually had our first joint training course. So at phase four we want the cascade to be sustainable so delivering advanced level courses for all different levels for the coexa faculty to deliver modules to colleagues and also to widely implement in routine practice. So we've had since the Dar es Salaam course over the last year we've had some very good examples of how TTT has been implemented for example in Mozambique they run introductory TTT sessions for staff from two hospitals in Zambia they've been rolling out an appraisal program in Kenya they taught appraisal skills to their colleagues that then could then go ahead and implement these and the Tanzania and Ophthalmological Society ran a TTT session at their congress. So what have the outcomes been and what are we looking forward to in the future? Well in phase one we did some modelling which suggested that over a million patients a year were touched in some way by someone who had been on TTT or managed to cascade the learning. In phase two we published the outcomes after four years in globalisation and health as Chiku mentioned then in phase three we set up the national teams so that every single country actually had TTT trainers and this is now spreading out to every single institution and we also alongside that started the TTT program in Indonesia using the same model we've now delivered three courses in Indonesia. So by the end of phase four we've now got 108 participants and 23 faculty who are trained to be able to deliver most parts of the program and also the TTT subcommittee is also part of the coexa organisation. This has also been a huge benefit to the UK certainly a personal benefit I can't imagine the amounts of learning and enjoyment and enthusiasm I've got out of this but also as we've developed the coexa TTT program there's a lot of learning that has actually fed back into the UK program the UK program is definitely better as a result of the coexa experience. So looking to the future I think that the advanced courses will still probably need input from our Royal College although coexas should now be able to deliver the supervisor courses itself. I'm hoping there'll be more joint modules with the UK because at advanced level it's much easier to deliver it over a telelearning platform whereas it's much more difficult with the supervisor level courses and let's talk about whether we can cascade this to adjacent countries and also involve non-medical eye care professionals. So this this has been a brilliant journey an amazing program I think we've achieved a lot and we've certainly enjoyed ourselves and learned a lot out of it so thank you to coexa for the opportunity. Thank you very much Melanie for of the TTT program that indeed has grown much interest even from the nanopharmologist's specialty. Just speaking from a recent stakeholder's workshop we had in Rwanda we had General Sergio New developed quite interest in the short session that was facilitated by Chico and moving forward for coexa we are looking at you know developing a fully run program in-house we see a change in the chemical homology. So looking on next to our presentation we have Dr Runga and leadership mentoring in the coexa region. I would want to welcome Shafi who participated in the lead forward program that we had over these years of collaboration so Shafi if you're in the meeting kindly just feel welcome to share with the audience your experience in terms of what is the take home. Yeah I hope you can all hear me so basically the lead forward workshops it was a program which was meant at quality improvement in low-resourced settings by improving the leadership within the hospital settings and this was mainly done by holding workshops so for example Malawi over a two-year period between 2015 to 2017 we had two leadership trainings which were delivered to workshops and then after that there was a cascading effect where within our unit over 20 workshops happened over that three-year period so everybody was empowered to run some kind of a workshop and also to implement to initiate and implement a quality improvement project so for the second time just to share some key lessons out of that leadership training which we had we had a different perspective towards leadership where we learned that the traditional approach to leadership where the most senior person is regarded as the leader is not always the most effective approach rather we learned that everyone can be regarded as the leader in their own capacity and when the eye care team is looked at in this approach you find that all the members of the eye care team become very motivated to give their best and everyone it's easy to share your vision with everyone because everyone is valued that they have a role to play and another thing we learned is the importance importance of humility where if you're in a leadership position you need to be willing to learn from everyone basically at any time in your leadership setting and this is the way where you you grow as your leader and you also help to move your team forward and another important thing we learned about leadership is that a good leader really needs to be visionary you need to to assess where you are for example as it's a hospital setting and where you want to take the hospital forward and you also need to be able to share this vision with all the members of the eye care team and having a vision is really what separates a leader from a manager because the manager is simply there to get the job done so the lead forward projects in Malawi they really had a huge impact we had a lot of quality improvement projects happening in the hospital and they were sustainable because they were initiated by ourselves within the hospital and people are motivated to to to sustain this in the long run and the lessons we got out of that they are quite applicable to a lot of context not just a an eye health setting they can be applicable to a lot of settings in life so maybe I should stop there thank you Dr Shafi for for your talk I want to invite Dr Runga Simon from Barara Uganda to give us this bit of perspective his engagement with the research mentorship program thank you over to you Dr Runga thank you very much Josiah good afternoon everyone um so just like she could touched on it earlier on the challenge we had was that the many faculty who support residents in training did not have any formal experience or training in how to do that and so the question was can we take the lessons from the lead forward model and apply that to research so what we did was in partnership with the ICH we had the faculty from three universities that is Barra University of Science and Technology the University of Nairobi in Kenya and Kilimanjaro Christian Medical College in Tanzania so we had a three-day workshop where these the faculty from the ICH provided training to us on how to supervise a master's residence research and that was a very useful training because it was an eye opener many participants had never received this training before and leaving that meeting we each had specific assignments and tasks to do in our universities including cascading this training to our fellow faculty but also being able to support our residents better we met again after one year to reflect on the changes that had happened in the institutions and the general feeling was that research supporting residents do research was now a much more enjoyable experience for both the faculty and also the students and following this we were able to include that in now in the coexa congresses a program where we have research mentorship support as part of the program that runs alongside the coexa so that's that's a reflection from our side we're happy to note that actually what we feel is one of the spin-offs of this is that some of our residents like Maureen and Denise went on to actually do well and and get an MSc scholarship at the London School which they just finished last year so we feel that was part of a direct spin-off from this because we're able to enjoy research and do better thank you very much thanks a lot Dr Roonga from Mariana Uganda maybe just also to add on is that we've been able to develop out of disengagement the research repository for residents this is in the whole region so currently we have four participating universities and all the postgraduate you know studies are available on our repository as coexa with quite impressive reach across the whole world we have access to these papers as we trace them over 8 000 downloads in 2019 and we we are just glad this is improving our capacity in terms of being able to avail this research work online through our next presentation we have Dr Melanie who will be talking about telelearning in the future welcome Melanie thank you well telelearning is hopefully something that is going to help all these different areas that we've been talking about this afternoon so the aims of telelearning are really to deliver education in a way that's flexible accessible and sustainable we also want to make sure that we can make that we are time efficient cost efficient and try and reduce transport so the idea is to try and provide ophthalmic education for learners when they want it where they want it and in the format that is most effective but whilst doing that we need to recognize that different modalities suit different learners that with different materials and content and different degrees of interactivity so we have to be very selective about what modality of telelearning we use in what which situation the main advantage of telelearning particularly in this setting is the whining of participation so as a college we can now reach out much more easily to our non-members we can provide education for all grades for all professions even reaching out to public and the students and certainly the international reach it can achieve is fabulous so this slide I made for the Commonwealth Eye Health Consortium meeting over a year ago now and it really encompassed my vision for training the trainers as to where I hoped it would be going in the future and really this is something that could apply to any sort of education so within education you have a central event so you can see here that we might be running a session in London but simultaneously we might be having sessions in Africa so the faculty in London will be delivering some of the lecture type work and some of the large group discussions which the Africans could take part in but as I said we have a lot of small group work practical skills and small group discussions involved so it'd be important that these could actually be delivered in the African setting delivered by a faculty member that had been trained up previously on the training the trainers course but with any learning it's important that the event is supported on either side firstly by some preparation beforehand which can be done offline as it were and then also some consolidation afterwards but it means that the materials that are produced actually during the sessions can be used in terms of audio video sharing of slides afterwards but these can then be fed in to being the preparatory work for future events so what sort of modalities and resources have we got if we think first of all about sort of self-directed learning or advised learning mandated learning it includes the books some sort of interactive tasks like reflection and dynamic online work with quizzes and tests it can be mapped map to curricula or used for cpd any of these recordings whether surgery or events like this or especially prepared events can be used and shared later but also we've now got the remit of live events certainly with platforms like this and they can include either observer only or interaction the way we have at the moment but ideally i want to move towards this idea of a multi-site facilitated event and certainly with covid we've got some conferences which are now providing online packages for learning so but there are quite a few considerations we just need to think about when we're moving education into a telelearning environment we need from the digital point of view we need to think about security confidentiality privacy and the downside of doing a recording versus the live event from from the social point of view there may be less engagement i mean we can still see everybody but it's not quite the same as having those corridor conversations speaking to a computer isn't quite the same people don't come across in quite the same way but i'm sure we're learning more about it but the interaction is is quite controlled and there's also things to do with the length and managing breaks that's a bit different from when you're doing it live and the educational considerations as well you've really got to consider the the suitability and just because you can include everybody should you be including everybody we want to still ensure that the juniors or less experienced people have an opportunity to present and if people say they're going to catch up later will they really catch up later the other thing is that if we they if the managers type people think we can do education in protect in any hour of the day or night are we going to lose our protected time for education and then of course there's a whole load of different funding models that come into play when it's then available very widely so what about the future of tele learning i think the important thing is that we need to we need to write a challenge we need to try new things we're trying a lot of new things today i mean not all of them are working 100 but we're learning as we go along but i think it's important to try and use the full scope of the opportunities because then hopefully we can fit the best opportunity to every type of option that we're trying to deliver it's important that as well as just education in the sort of more formal type sense that tele learning can be included in sharing sort of clinical and other experiences we saw a fabulous mdt this morning we've heard about leadership and so on this afternoon and also training the trainers as to how this kind of learning can happen on a tele learning basis but also there's all the brainstorming the discussions i mean i think from what came out of one of the things this morning is that with this covid that people want much more input from each other for example about restarting services but we can have discussions we actually run one at the royal college already a symposium on how do we get restarted in clinical services after this but that's ideally on an online platform so i think the thing is that there's there's plenty of opportunities coming along we're learning all about them and the answer is that we need to develop this together to really get the most out of it thank you great presentation thank you very much melanie in terms of looking at the future actually with the new normal covid disruption that is making us not be able to meet physically and have live events over to a next presenter is will din who will talk about surgical simulation thank you just i'm africa thank you will thank you just i thank you hannah i will share my screen here good afternoon everyone it is virtually impossible to even attempt to summarize surgical training programs and the importance of partnerships in a week let alone in 10 minutes so in the interest of time i'm going to try and summarize it in two minutes and that is simply to say that their effective surgical training not only benefits from but depends on partnerships and collaborations and although an individual surgeon's journey from novice to expert is uniquely individual no surgeon learns on their own there are some fantastic examples of fellowships from the ico the clinical fellowship program where 141 fellowship of fellows were involved from 19 different countries but looking forwards there could be more south to south surgical fellowships there should be more sharing of resources and that could be subspecialist expertise a slightly closer to home more sharing of educational resources and having open access to online and other educational resources for surgical training and then is there a role for simulation based surgical training for cataract certainly manual small incision cataract surgery and feiko the royal college of ophthalmologists have been doing feiko multiplication training courses for over 10 years for glaucoma for cornea vitro retinal trauma complications as well as team training and have these integrated into current surgical training curricula and develop new modern digital classrooms for surgical training and the question would be fairly binary and and this is the question if as a trainee or as a trainer if you had the chance to take a trainee to to theater for live surgical training which trainee would you prefer to be or which trainee would you prefer to take the one on the left who would be novice to cataract surgery or the one on the right who has undertaken just a four or five day simulation so intense simulation surgical training course in small incision cataract surgery and I assure you this is the same trainee four days later after a simulation surgical training course it's it's an interesting question with hopefully a fairly clear answer we're already developing numerous training simulation surgical training centers throughout sub-Saharan Africa and hope to develop many more in the in the coming couple of years thank you very much thank you will that presentation has been well received I believe and I just wanted to remind everyone in the meeting room that we can type our questions on the on the group chat wall so that we can pick these up and the Q&A and the discussions that will be led by Ana Fal that opens door for the next presentation by Peter Holland who is the chief executive of IAPB on vision 2020 successes and challenges welcome Peter Holland to give us his presentation thank you thank you well thank you very much and thank you very much for giving me the opportunity to join you and I'm sorry I haven't been able to be with you for longer today I've only got a few minutes and we'll only speak for a very short time I also feel frankly slightly fraudulent in talking on this subject because I suspect in the audience of people much better qualified than me particularly to talk about the experience around vision vision 2020 and I think and I'm sure actually you all know really many of the successes I think I'd point to three or four broad high level ones firstly the the impact and and and I think that's critically important the reduction in prevalence in avoidable blindness over over the vision 2020 period and real progress in significant areas like obviously trachoma and oncotocasters and those sorts of things and that that ultimately is the most important success that we see but I think underpinning that are three big areas firstly around global advocacy I think vision 2020 put eye health on the global agenda and kept it there and that's no mean feat over a period of 20 years uh and and continues to do so secondly behind that then mobilized resources both from governments and new resources from governments but also from new sources from the corporate sector through things like the seeing is believing program foundations like the queen queen Elizabeth diamond jubilee trust so really drew resources into the sector and then behind that and and and probably most importantly in many ways are then the new and innovative program services and partnerships and grew from that obviously like uh like this program like the linked program uh and then behind that the infrastructure that was set up at national level the many national eye health committees uh and then the investment in things like human resources in our health so I think all of those are real achievements and real enduring achievements of vision 2020 and at the same time I think we're all familiar with with the challenges that we've now got and I think some of this would probably touched on in the first session and in some respects the world reports on vision set those challenges out really clearly we've still got at least a billion people around the world who have vision impairment whose vision impairment could have been prevented or has yet to be addressed and critically huge inequities and inequalities in that uh and and so that for me is the is the challenge we're all involved in tackling uh and trying to and trying to confront and and the world report on vision sets out the in sense the framework for how you do that but that in itself is a real challenge because really what it's saying is that eye care needs to be a core part of universal health coverage in many ways universal health coverage is not universal if it doesn't include eye care and so you have to make uh eye care a core part of the mainstream health system and it's easy to say but I mean that's what you're all involved in in practice and that that is really it seems to me the critical challenge over the next 10 years how we really make that uh happen and we build on the experience of vision 2020 where a lot of that has been going on already and I wouldn't and I build just picking up what Melanie just said and will just said the that that that is made that much more difficult by the situation we find ourselves in now and you will all be experiencing this directly that the impact on COVID-19 is having directly on eye care services and the challenges that we're facing just right now in terms of beginning to restart them and how we uh how we get how we actually set services up so that they can operate safely in the current environment but then also reassure patients and communities that they can use those services so that's a real practical challenge that we're up against which I think we're going to face for some months and years ahead but I think along alongside that one of the one of the risks we face is that having made that real effort to get eye care up the agenda that there is a risk in which we have to acknowledge that entirely rightly with people's attention on coronavirus on COVID-19 that we lose some of those games and we slip back down the agenda so I think for us at IPB one of the big one of the big things we're looking at is is how as we begin to emerge we can begin to make the case uh for eye care that eye care is critical as part of as part of rebuilding health systems but I think more broadly beginning to make the case that it's also crucially part of the the broader development agenda that in a sense it's part of that it's essentially part of the gold of thread that runs through the sustainable development goals and and you know while like while um while that I do think that's challenging I think I think this won't this won't be easy for us to do that there I'm quite optimistic as well and just one example of that we had a meeting at the beginning of this week at the UN Friends of Vision in New York which was done via this mechanism and we had over 40 member states attending 40 countries most of them represented at ambassador level which is is pretty unusual in the foreign like that normally they send some junior desk obviously wrong we had no we had over 20 ambassadors there and and really they were basically saying that what they really wanted to do was to make eye health really part of their discussions on sustainable development goals and put eye health as part of the development agenda as well as part of the health agenda so so I think that's you know that's one small positive sign beyond that I think what that means is we've got to look to work in partnership both within the sector and and outside the sector and look at new partners who are in education and employment in the economic development as well to to bring them on board too but I think that's also where this program is a real exemplar because of course you know you've shown what partnerships do across internationally and that's something that of course is very dear to IPB's heart because that's what we are so so I think those lessons are really crucial and should give us some hope that even though the challenge there are some tough challenges ahead that that we can we can face them so thanks very much. Thank you very much Peter for your great talk and just looking at recalling to mind about the discussion at the health minister's conference meeting in Nusaka Zambia this year was a big debate about positioning IKF to be part of the national health debate and then then closer home it is said we we need we don't need to take the eye out of the body we need to be part of the discussions about national health agenda so without much talk I want to welcome Hana Fal who's going to lead the the session on the way forward Hana Fal. Thank you very much Josiah and I am just overwhelmed at the progress that has been made the diversity of it the multifaceted nature it has taken and and all in a very very short time congratulations to all the countries all the speakers and everyone who has worked so hard to get this going in all countries there's so much to say about the way forward so it's it's what I tried to do was to extract what I thought were the golden nuggets from what I have listened to in this session and then share some of my thoughts on what I think the way forward is I think the very first one really impressed with was the the training of traders and the fact that they had built in a monitoring and evaluation so that they can collect the evidence to see what how successful it has been and that's something I would want us to encourage and the telelearning for me is is for much of sub-saharan Africa is the proof of the of the pudding it's in the eating it they have shown that yes telelearning can be done what are the pitfalls what are the problems and and and so people who have a mental block to telelearning can say well no it's not that difficult we can get it done on the on Chico's presentation and what struck me there is that there she is she was doing it absolutely from scratch and taking advantage of anything that was going on that would help her in that journey so the word that came to my mind was fast tracking Chico fast tracks human resource developments and much of the links with coexa and the royal common royal college of ophthalmologist is the adoption of a stepwise approach I mean Chico had shared that earlier with us the first stage was that the the mentors from the royal college came down to East Africa and walked the walk got themselves familiar with the terrain of their trainees the second time they let their trainees take the button and they walked beside them and the third stage is they let them go they ran with it and they provided the support so I think that stepwise approach as was adopted was very wise and I would say that even in the surgical training programs the simulation is something very similar it's fast tracking but it's also a stepwise approach so in terms of concepts we've learned a lot from them the research supervision for me pointed out two things the word research for clinical practitioners is always something that belongs to another world it's too difficult to do and the lesson that has come out of this is that yes it can be done it can be done properly it can be done to the highest standard and finally the fact that it all got embedded the coexa maybe policy institutionalized all that has been happening so it has been tremendous really what has happened to summarize I cannot say everything but to summarize from my perspective what's the way forward and I feel that number one partnership as defined in this program being relationship between human beings should continue we should continue it and it should not be in the realm of feelings it should be in the realm of science we should try to get the evidence to show that partnerships and relationships is a good way to go number two is the concept of a ripple where the stone is thrown into a pool the ripple's form and I can see the ripple widening and widening it's widening to the coexa countries but I have no doubt that it will widen to the rest of sub-saharan Africa I want us to adopt the successful strategies that have come out of this partnership not just celebrate it but adopt the successful strategies and we cannot do that if we do not document so I would implore all those who have done this work to document it so that it goes it has a life and is read and studied by others the institutionalization is extremely important many governments are very bureaucratic so like coexa has done it's made it policy and it's made it a process of their annual meetings to hold these meetings so that it's done in a way that is affordable the audience is all the ophthalmologists who attend so again we are fast-tracking a process now preparation for innovation because we have a new normal a new normal of telelearning it's multifaceted telelearning has come to summer I'm passionate about climate change so there is there is an impact a very positive impact of telelearning on climate change and just like the COVID-19 virus is exponential in its spread I think telelearning is exponential in its spread of knowledge and skills so we can learn a bit from COVID-19 virus that my last two things are a bit controversial the royal college is one college limited resources and limited faculty and so on but I think we can explore the explore partnerships in other regions of sub Saharan Africa seeing it as a north south but also seeing it as an intra-african we don't leave it all to the royal college but even within Africa we can do partnerships we within south south we can do partnerships there's so much to learn of good practice that has come out of this celebration and my last point is on technology technology is important even for the training we need to look at the technology that we need to invest in to for the training primarily but also for the service delivery so that to ensure a high economic rate of return on the training there's nothing I find as painful and as wasteful as training someone for service delivery and when they get home they haven't got the technology to implement what they have learned so again the way forward can we cannot go without looking at technology for training and technology for service delivery and we're very lucky with the explosion of long distance thinking and work that the medical profession is keen into that investment in distance teleconsultation tele-surgery and ophthalmology cannot be left behind so that's that's my summary it's a very short one I've got many other things in my mind but it's just to say how excited I am at this age to see all these young people you know I wish I were 30 years younger so thank you so much thank you so much Hannah Fowle for the wonderful summary we're not wasting much time I will I think we might go straight into the participants poll thank you very much Josiah so we've done one poll already to find out about who you are we're now going to find out some more about your thoughts so Graham if you could please put up the first poll so we've mentioned a little bit about lockdown I think we have to have a few thoughts on that so but what should our priority be until lockdown lifts so regular remote meetings unit to unit or regular remote meetings that are specialty based should they be remote webinars of large groups for example restarting services new ways of working or should we just wait until the flights reopen okay so if you just choose one of those buttons to to click and I'll just wait until the length of the bars has stopped growing in front of me where over 50 percent of you have voted there so let's end that poll um Josiah do you want to make a comment about how we might deal with addressing new ways of working I'm not sure Josiah you're on mute actually or whether your connections dropped off sorry Melanie I my my connection was unstable thank you I don't know whether you just want to pass a comment quickly on that or before we move on to the next one I think out of the poll we can see 60 62 percent would prefer remote webinars with the covid scenario persisting which is actually the way to go currently we know online events perhaps replace the need for live you know experiences but it provides a very viable alternative looking into the way forward with one percent actually waiting for flights to reopen so that says a lot that we we have an available alternative in having in hosting virtual events perhaps we all just went to get out of lockdown okay let's go on to the second poll right so this one is really forward looking beyond the end of of covid so how would you like to be involved in partnerships in the future so giving remote support to an existing links partnership becoming actively involved in the existing links partnership including going on visits help set up a new link remote only or help set up a new link partnership including visits so we've got remote support to an existing link active involvement in the existing link or set up a new remote only link or set up a new link including visits okay we're over 50 cents so we'll end at that so Hannah I don't know if you've got any thoughts on this on this I'm excited the actively involved in existing years and for me I'm taking that as a given but I'm excited about people want to set up a new link partnership including visits and I would say add to that the long-distance partnership as well so yes those two stand out so it's partnerships partnerships partnerships good and a few flights along the way might be helpful yes good okay so at this point we're going to go into some small group discussions so this is your opportunity to talk with people you probably haven't met before you can talk about what interests you most but we will give you some questions also to guide your thinking you'll be randomly allocated to those rooms just as you were this morning we're going to give you a bit longer in which to chat so it'd be useful if if somebody happens to take the lead and try and encourage everyone in your group to talk if you unmute yourselves and put your videos on it'll just help you to get engaged and if you could also appoint a scribe to the room as well who could then feed back to a point to scribe who can feedback to either marcia robert or education at the royal college because we're very interested to hear your views and also the lead might well want to think of one key point that will be able to come out in the discussions later so the the two questions that i want you to think about is where should partnerships be going next and how would you like to be involved so where are we going next and how would you like to be involved so you'll disappear into your rooms now and then you'll get a warning before you then automatically come back then we're going to large group discussion so that didn't quite work quite as planned right do you want to have another go at graham so when we go into our groups we're going to be looking at where should partnerships go next and how would you like to be involved in the partnership so we'll just see if graham can manage to get the the breakout rooms to work so graham i think if you could take off the slide at this point i just want to see how many people we've got left in the main room if you're in the main room still that there is probably a notification on your screen getting you to agree to going into your small group breakout so if you can just press okay to accept going into your small breakout group that would be fine oh that's good we haven't got too many people left in the main room um if you can hear me if you can just um take off your videos or and take off your microphones and we'll run this group as a as a as another small group if you haven't to be left in the room here so if you can just unmute yourselves maybe i've got the people who aren't really there let's see if any of you are there i've got somebody there that's good on a on a video excellent we can unmute you so are you able to unmute yourselves yeah you can now yeah there we go good right so if anyone's still here let's see oh we've got we've got um john and alan and various people if you're able to unmute yourself then that would be useful um but anyway the two of us could have a discussion so where where where do you see the partnerships going next are you talking to me talking to you because i'm not sure where the only ones here i'm not sure how many other people are listening so well the i've been the my link has been oh i think everyone's is everyone coming everyone's coming back again right uh okay don't don't worry i think okay everyone's rejoins the main room well that was a very short one again um i think what we'll do at this point is we will go um straight into the um the question answer discussion for the large group discussion so i'll hand over so can we start the questions yeah yeah uh there are a few questions sent to the charts is mike there i am yes there is one position for marcia and the question says after 16 years of excellent work with the links what does she see as the next steps marcia what are the next steps for the links well again i have to say that it's really not about what exactly what i think but i i i can hear from what we've listened to today that um it is a good way forward to do what even what has happened today to have opportunity to share learning um together and also um particularly what chiku was talking about and looking at um that whole training aspect um but doing it collegially so collegiately so it's not for example the uk going overseas to give their input it's shared learning together so their faculty on both sides and i think that that is a brilliant example of a way forward good another question was addressed to shikov and the question was how difficult was it to convince those bodies to give you accreditation as a non-university institution you are new okay uh good evening um i have to say that it was not easy in terms of the medical board in rwanda i think that like i said the fact that the regional bodies were beginning politically to encourage college-based education helped us a lot uh we had a track record as trainers and clinicians in rwanda as the founding founders of rio so that helped also i think the inclusion of some mandatory international benchmarks like the ic exams helped our case also and when we presented our training model it was more structured than a lot of the existing specialty programs i think all those together helped the registration bodies to endorse the program and recently there's been similar sentiments from the bodies in kenya tanzania um zambia i think when we did a similar presentation in terms of accreditation from coexa that is one of the hardest exercises that have ever had to go through the accreditation team was led by the heads of departments of all the existing programs um and at that time there was a bit of uneasiness about training going outside universities i think there was some sympathy because after all i was their student and they knew that they train good people and dr ilaco and professor kagame were quite uh sympathetic and supportive of what we were trying to do having a good curriculum having the tools for both summative and formative assessments and for supervision which i had just adapted from what i learned in ttt we were lucky to have good space as well as a modern training hospital and access to large numbers of faculty not just in-house which were not so many but also through our partners uh agarwal as well as wills i think accreditation is by coexa is uh to add on to what you asked marcia should be part of the way forward because a lot of institutions are beginning to want to do what rio has done and the accreditation processes through coexa need to be robust and this is somewhere else where links can be forged to show what standards should be for accrediting new institutions so i'm grateful we got through all this but it was not easy thank you yes another question was open question to anybody who can answer they say those who benefited from the links trainings how many have started training others and how many are ready to start training others and if not what are the challenges why why does it not why does it not happen so that is open to those who benefited from the links training programs so feel free anybody to unmute yourself and make a comment a bit quiet at the moment while they're thinking john i think you need to explain how you could look to your left and uh say to chico uh you're still muted i think if i can read john's mind he's trying to ask whether why those who benefited from links do they feel that in future they will also be able to create links from their institutions to other institutions within their countries maybe and i think it's a valid question i think as rio when we are mature and more experienced in this we'll be quite happy to mentor maybe the mid-level training program within rwanda and we are we we should propagate what we've learned i i have really been shadowing and uh trying to suck all the juice out of melanie in order to become as good as her entity and i hope that i will somehow be able to encourage others the way she has encouraged me thank you i think melanie wanted to say something well thank you very much chico i mean i've just been so thrilled the way that you have actually taken what we have built up over many years in our royal college and compressed it into literally a very short amount of time and delivered to such a high level so incredibly impressed with that the other comment i did want to make was relating to the tele learning and basically interaction because we've had a lot of experience of this in the last two months and one of the things i think we found is that if people have had previous face-to-face interactions they've had live links live partnerships then transferring onto a remote platform is relatively easy because you've actually got all that background you know what people are like you know how they respond you know what expression on their face means and things like that whereas when you're setting up new engagements on a remote platform for the first time then that becomes a bit more difficult so i see that tele learning is not going to replace completely all the things we've got there's a really really important place for that that feeling of cohesiveness that you actually get through working with somebody in the same space on the same project so i think this is where it comes down to being very selective about what we use things for and i'm was glad to see that all of you felt that you still wanted to do an active partnership rather than purely a remote partnership so Melanie can i can i just say something that we also learned is that a lot of us and in many countries they they also started doing a lot of video consultations with patients as well and that that's technique and the way how you talk on the phone and how you behave and where you sit and everything is extremely important so in adding to the training as to how to behave on camera it's also important to appreciate that that the once if you want to do it with the patients is why there is another level of complexity and i completely agree with you it is much easier to do for example follow-up conversations with patients you've seen before then court calling and unfortunately we all experienced that in the last two months you have so many extra emails and links to click on it's the management and the human behavior of it and what we have learned we can propagate to us as well thank you can i just ask is bernie chang available bernie are you yeah i'm here excellent so just to introduce you bernie for those you don't know i demitted from my post as president of the college raw college of ophthalmologists in may and i'm pleased to say that bernie took over so bernie the question i have for you is okay a can you introduce yourself and b can you give us some pointers as to where you think the links program between the two colleges is going in the next few years hi everyone thanks mike for introducing me and giving me the opportunity just to say a few words actually just in case i don't get the chance congratulations to the organizers for organizing this successful and very informative webinar i also want to congratulate everyone who has presented today sharing their experience it's it's clear that patients have benefited and will continue to benefit from all your hard work and and personally i'm both impressed and very heartened to know that there are such good links out there between international partners i think we've got to acknowledge your role mike in cementing our college's link with coexa and also acknowledge will dean who's our college's chair of the international subcommittee for his efforts and melanie for sharing your immense experience and knowledge on educating trainers i think it's always true that people who give get more back in return so as as the new president i would certainly love to build on the close relationship we have with john through coexa with the i ceh and the vision 2020 links program and you know with cove it we don't know what's happening but i would look forward to meeting with with you and working with with you be it virtually or or in person and i would certainly like to see an increased collaboration between the rc ops and and and all the the the partners out there and i think in that small group session there's clearly the opportunity to increase the number of countries and places that we form these links so i look forward to hopefully playing a small part in that thanks mike thanks very much bernie i know you will take the program forward and i was just going to ask whether john could give some comments as the coexa president thank you mike i think it has been a very good day we've learned a lot in terms of what is happening between different partners as coexa we look forward to continuing our partnership with the royal college to take forward what we've achieved so far as we add more countries on our region we are going to need more support to keep going together this i think has been a good experience and i look forward to the next 10 years to see how far we'll be when we're celebrating again in the 2030 i think there's still probably some people who wanted to comment i don't know if we have time for that otherwise i give back to mike to conclude no i i who if you've got people do do shout them out john i can't see who they are but feel free to invite people bevelly right has got a hand up okay good morning good morning from jamaica um we have benefited from the links program here in many ways and um we are hoping to continue to to roll the program across the island we have about three million persons in jamaica and so far the links program has benefited about two million so that's that's quite a a lot of of um all to each given so far but we were thinking of some training program locally for the nurses for the optometrists and for the screener graders currently screener graders are trained at the university of the west indies so collaboration directly with the um links program in long john but i don't know there's a possibility that we could do something as chico chico did you know in her country but we could discuss that going forward and i just want to reiterate that the links program has been extremely helpful to us in jamaica thank you thank you very much in my experience um the best person to ask in these circumstances is marcia when marcia has asked a question she she takes it forward in a way that i don't see anybody else achieving um so marcia that's over to you um is anybody else anybody's identified that wanted to make a comment if not i thought it was probably nearly time to to wrap up melanie mic if you can allow i'd like to ask uh brent finch here or john anode from wheels if you can say give a comment about what she could talk about about the links between wheels i and rio they can make a short comment brent are you there or john anode yeah maybe they are muted i think you can go ahead mic okay well um i would like to thank uh melanie graham and hue for bringing this program together i would very much like to thank all the participants both the people who presented on those who listened it's been a long but very interesting day i'd also like to thank all the organizations represented here i think at the beginning of the day we reflected on the fact that we were celebrating the vision 2020 initiative launched in 1999 by the world health organization and the iapb with the aim of eliminating avoidable blindness by the year 2020 i think we all recognize that we haven't finished that work um but one of the big things that have come out of it is the links across nations and i think the best thing for me has been been working as a party a community of ophthalmologists determined to drive forward the vision 2020 goals the work is unfinished um we do have unfinished business and i think as we go forward i think maybe we should remember the words of the united nation's general assembly 2030 agenda for sustainable development which i'll quote for you as we embark on this great collective journey we pledge that no one will be left behind recognizing that the dignity of the human person is fundamental we wish to see the goals and targets met for all nations and peoples and for all segments of society and we will endeavor to reach the furthest behind first so that's our job team that's what we're going to deliver over the next 10 years and hopefully as john says we'll meet again uh to discuss how far we've got uh i'm going to say goodbye now and hand over to melanie as the organizer great thank you very much everyone it's been great to have you all on today what we would love you to do is we're going to be sending out the evaluation forms so please ensure that you return your evaluation forms because that's how we can develop this kind of event the links um partnerships um and we do want to have your ideas you know people have been putting things on the chat about how do i get involved um on your evaluation form if you want to put your email address on there then we can pick up on that and contact you directly so that information is really important to us so please just fill out your evaluation form as soon as it arrives so thank you very much in celebration can we clap and dance celebrate thank you thank you bye bye everyone thank you for your time thank you bye bye bye everyone thank you bye bye


This lecture is part of an online algebraic geometry course about schemes and in it we'll be discussing a sort of generalization of the construction of projective space where we do this construction simultaneously over every point of a variety. So first of all, let's recall the construction of a projective variety from a graded algebra s which is sum over n greater than or equal to nought of an algebra s n, sorry a module s n. So, we remember we constructed a scheme called prodge of s, projective scheme of s or something, and as an underlying set, it consists of prime ideals, not containing sum for n greater than zero of s n. And the topology was given as follows, first of all the base was given by the open sets of the form df, which was the set of prime ideals, such that f is not in the prime ideal, you can think of this as being the points where f doesn't vanish slightly informally. And we defined a sheaf on each of these open sets by saying the sheaf on the open set d of f, you get by taking the ring s you and then invert the element f, and then you take the degree zero elements of this. So we gave several examples of this showing that if s was a graded algebra, then this was, so if this was a graded algebra over a field s nought, then this was often a projective variety over the field k. And so in particular we get a map from prodge of s to the scheme spec of s zero. You also remember that this space comes with a line bundle. So roughly speaking for every graded module over this graded algebra, we get a line bundle in this, so we get a sheaf. And for the special case where we take the algebra itself and just shift the grading to get a new module, we get a special line bundle 01. Now the idea is to generalize this, instead of working over a ring s zero or an affine scheme spec of s zero, what we want to do is to work over any scheme x. So the idea is roughly, let's describe it in formal version, what we do is we pick a graded algebra for each point of x. And then this goes from each graded algebra we might be able to get some sort of projective variety for each point. And we kind of join these together somehow to get a map from some space y to x such the fibers are maybe projective varieties or schemes or something. So that's the sort of informal way of doing it, which doesn't really make too much sense if you look at it too closely. So let's be a bit more precise. What do we mean by picking a gradient algebra for each point of x? Well, a better way of describing that is we pick a sheaf of graded algebras over x. What this means is the sheaf is going to be s, which is going to be sum over n greater than or equal to zero of s i. And the sheaf is going to be an algebra so we've got a map from s, hence s to s, giving us a commutative multiplication and this preserves the grading and so on. And so the stalk of this sheaf at every point will be roughly a graded algebra over the local ring at that point. So this is that you can think of this as being something like a graded algebra for each point of x. Well, it should have various nice properties. So s should have following properties. First of all, it should be quasi-coherent if it isn't, it's a real mess. So this just says it sort of looks locally like a module over a ring. So this is the really important property. There are some other sort of optional extra properties we can have which make life a bit easier but aren't really absolutely vital. First of all, we could assume that s naught is the sheaf of regular functions on x. So this is, if we're working over a field, this would be like saying s naught is the field k. Thirdly, we can assume that s i is quite is not quite so coherent, coherent for i greater than or equal to zero. So this would be kind of saying it's sort of like a bit like a finite dimensional vector space over a field in some sense. And fourthly, we could say that s one locally generates s. So this is for a graded algebra, this would be the equivalent of saying that the degree one elements generate the whole space. In practice, these conditions are often satisfied and make things easier, but they're not really vital. So now what we do is we define a scheme proge s as follows. What we do is we pick an open affine u in x. And then if we restrict s to u, it becomes essentially a sheaf of graded algebras over the ring of u. So let's say u is a spectrum of some ring a. So it becomes a graded algebra over a. And on this, we can form the projective scheme of this graded algebra. Let's call this algebra something that's called an s a. So what's happening is x is covered by these open affine sets. And on each of these open affine sets, we're defining a sort of projective scheme mapping to the sets. And then we just glue these together. So gluing them together takes a page or two of calculations, just checking that they're compatible on these intersections and so on. But I'm simply going to omit it because it's fairly straightforward and not very interesting. Moreover, each of these has an invertible sheaf o of one that we constructed before. And we can also glue together these invertible sheaves o of one and we get an invertible sheaf over proge of s. So what we get is we get a map from proge of s to x and proge of s has an invertible sheaf denoted by o of one. So it's kind of like the constructing a projective variety from a graded algebra over a field, except that we're doing it simultaneously for all points of a scheme x. And there are several applications of this. So let's list some special cases that we will discuss in more detail. First of all, we can just construct projective varieties. Secondly, we can construct projective bundles over scheme x. And thirdly, we can blow up a subscheme or equivalently a sheaf of ideals on x. Fourthly, we can make ideals locally principal, which I will explain later. Fifthly, we can resolve singularities. And sixthly, we can make rational maps defined everywhere. Actually, these two are really both variations of the same idea. And all these four things are really variations of blowing up a subscheme. So blowing up a subscheme can make ideals locally principal. It can resolve singularities and it can make rational maps well defined everywhere. So this lecture, I'm going to just discuss examples one and two. And next lecture, we'll be just giving examples of the remaining four applications of this. So example one is really kind of trivial. All we're doing is we're taking x to be the spectrum of fields. And we're taking s to be a graded algebra over k. And then you can think of a graded algebra over k as being a graded sheaf of ideals over the spectrum of k if you want. And then the construction we've given for taking proge of the sheaf of ideals s is really the same as the construction we gave earlier for constructing a projective variety from x. So application one, we've sort of already done. Slightly more interesting variation of this is taking projective bundles over a scheme x. And we do this as follows. Let's take s1 to be some locally free sheaf. So this looks locally like o of u to the n for u and open affine subset of x. And then we can put s to be the symmetric algebra of s1 over s0. So for vector spaces, we can define the symmetric algebra, which is just the sum of the nth symmetric power of s1. And you can do exactly the same thing for sheaves just by doing it locally. So this gives us a symmetric algebra and we can then form proge of this symmetric algebra sum over s to the ns1. And locally, this looks just like constructing projective space over open sets u. So locally, this just maps some projective space over u to some open set u. But globally, it might be a sort of twisted version of this. So the point is the projective spaces at different points can't necessarily be identified with each other. So we can probably easiest to see the simplest example of this. See what's going on. Let's just take x to be one dimensional projective space. So s1 is going to be some locally free sheaf. Well, we classified the locally free sheaves over p1. This is growth index theorem or maybe Burkov's theorem. And they're all sums of line bundles o of ni. And let's just take the dimension of s1 to be two. So we're going to take o of m plus o of n. And we're going to form the sheaf that is the sum of the symmetric powers of o of m plus o of n. And we're going to take proge of s and see what it looks like. So what we're getting is over each point. This will look roughly like a two dimensional vector space. So the corresponding projective space will just be one dimensional projective space. So we get a map from proge of s to p1. And the fibres are just copies of p1. So we say it's a p1 bundle over p1. Obviously it could be p1 times p1 mapping to p1, but it can also be some other things as well. So these things are called Hitzebrook surfaces. Hitzebrook studied them in his first ever paper published in the early 1950s. And first of all, let's see how many we get. So obviously if we start with o m plus o n, this is going to give us the same as if we did o n plus o n. So we can just switch m and n without making any difference.  And the point is that this thing here is just o m plus o n. It's twisted by a line bundle. Now if you've got a vector space v, and we tensor it with some one-dimensional vector space l, then there's a canonical identification from the projective space of v tensor with l. I mean, these are obviously isomorphic projective spaces, because they're the same dimension. But the point is this isomorphism here is canonical and doesn't depend on choosing a basis for l or whatever. And because it's canonical, this means if we've got a locally free sheaf s1 and a locally free sheaf s1 tensor l, where this is an invertible sheaf, then the projective space bundle we get from s1 is isomorphic to projective space bundle we get from s1 times l. Because since all these isomorphisms over open sets are canonical, they're compatible whenever you take intersections of open sets. So the projective space bundles of these two are actually isomorphic. So the hits of Brooks surface of this two-dimensional bundle is isomorphic to the hits of Brooks surface of this two-dimensional bundle because you're just twisting by a line bundle. Incidentally, there is one difference between the hits of Brooks surfaces you get from these because the construction gives us not only a surface, but also a line bundle over the surface. And we do, in fact, get different line bundles over the hits of Brooks surface from these two different line bundles over p1. And so let's look at a few hits of Brooks surfaces and see what they look like. So every hits of Brooks surface is isomorphic to a hits of Brooks surface sigma n, which comes from taking the line bundle O nought plus O n over some integer n greater than or equal to zero because if we're allowed to switch these and add a constant to them we can make one of the entries zero and the other entries some non-negative integer. So sigma nought is easy. This is just p1 times p1 because what we're doing is taking the trivial line bundle O of zero plus O of zero over p1 the corresponding projective bundle and obviously we're just getting something canonically isomorphic to p1 because the fiber of this at each point is just canonically a two-dimensional space. So sigma nought is just a copy of p1 times p1. Sigma one turns out to be a little bit more complicated. It's actually isomorphic to p2 blown up at a point. And this is a little bit confusing to see. It's not difficult, but it's confusing. So let me try and get it right. So first of all, we take the copy of p1. So you can think of this as having coordinates x colon y. And now we're looking at the line bundle O of zero plus O of one. And let's think about what this line bundle looks like. Well, this line bundle means we're assigning a two-dimensional vector space for each point of p1. And we want to take an element to this two-dimensional vector space for each point of p1. So how do we do this? Well, O of zero is easy because that just means we take a complex number. On the other hand, if we want to take an element of the one-dimensional vector space corresponding to p1 it doesn't mean we take a complex number. It means we take an element of the line corresponding to p1. So really we have to take points B and C such that xc equals yb. So if we take a non-zero element of this, what we're really doing is taking a point of form A colon B colon C with, again, xc equals yb. So in other words, the elements of the projective bundle over p1 corresponding to this can be thought of as follows. They consist of pairs xy, A colon B colon C, such that yb equals xc. So we're taking a subset of p1 times p2 satisfying this condition here. And this is just equal to the blow-up of p2 at the point 1, 0, 0. So sigma1 is isomorphic to p2 blown up at a point. So here's a book showed that, in fact, all the surfaces, sigma n for n greater than or equal to nought, are distinct and not isomorphic to each other. However, sigma n is homeomorphic to sigma m, if and only if m is congruent to n mod 2. So the surfaces sigma nought and sigma 2 give examples of two surfaces that are birational and homeomorphic, but not actually isomorphic as algebraic surfaces. OK, next lecture we'll give some examples of using this construction to blow up ideals and some of the things you can do with that.