office for Europe. It's a great pleasure to provide an overall moderation for today's high-level roundtable on accelerating digital development from multi-stakeholder partnerships held within the framework of the Regional Forum on Sustainable Development for Europe and Central Asia, as well as World Summit on the Information Society Forum. But before we are delving into the topic, I would like to give the floor to our technical moderator, Ms. Alina Gergut, who will provide the house rules of this meeting. Thank you, Mr. Yaroslav. So thank you for dear participants. Thank you for joining. I'll be the technical moderator for this meeting. So before starting the session, I would like you to give some instruction on the Zoom platform. So this meeting is entirely remote and held in a webinar format. You are invited to use the chat for any comments. You may also use the Q&A function to ask any questions you might have. My colleagues will be monitoring and any comment or question may be read out if time allows. The meeting also benefits from left transcription and English-Russian interpretation in a few minutes. So please select the live transcription and your preferred language from the bottom bar of the Zoom interface. For speakers, please ensure that you have chosen the appropriate channel interpretation that corresponds to your spoken language when you would like to intervene. The meeting is recorded and live streamed on YouTube and Twitter, and the recordings will be available on the website around 24 hours after the event. So every effort is being made to facilitate the smooth flow of the meeting. Thank you, and I wish you a successful meeting. Back to you, Mr. Yaroslav. Thank you. Thank you very much for this. And ladies and gentlemen, the United Nations Digital Transformation Group for Europe and Central Asia established under the UN Regional Collaborative Platform for Europe and Central Asia and coordinated by ITU and UNICE is pleased to welcome you today on the first day of the Regional Forum on Sustainable Development. And on this occasion of a special high-level peer learning roundtable which will address the key role of the multi-stakeholder and cross-sectoral collaboration holds on fostering the digital development. This morning, opening remarks of the forum delivered by many distinguished colleagues, but also joined by the Amina Mohammed Deputy Secretary General of the United Nations, all pointed at the need to provide access to the internet connectivity and address the digital divides to advance on the SDG agenda. Speakers also emphasized the critical role that collaboration plays to ensure digital development for all, reinforcing the relevance of today's session which encourages all to partner to connect. So therefore, dear colleagues, welcome to this session and it's my great pleasure and honor to welcome and to hand over the floor to our distinguished colleagues opening this event starting with the Mr. Steven Biro, Deputy to the Director of the Development Bureau of the International Telecommunications Union. Steven, the floor is yours. Thank you. Thank you, Yaroslav, for the introduction and good morning. Good afternoon. Good evening to all the participants joining. Excellencies, ladies and gentlemen, esteemed guests and speakers. Thank you for joining us today and it's my pleasure, my great pleasure, on behalf of the International Telecommunication Union and in my capacity as the Deputy to the Director of the Telecommunication Development Bureau to open this high-level pay learning round table today. We will be discussing how to accelerate digital development through multi-stakeholder partnerships. The UN Secretary General's our common agenda emphasizes that over the next 25 years digital inclusivity is and will be a key component required to ensure that no one is left behind when advancing on the sustainable development agenda. In this age of digital interdependence working in silos is no longer an option. It is only by leveraging the mandates of each agency and the potential and expertise of all stakeholders that we can ensure that the access affordability and use of the connected world is achieved in all countries and regions and for all peoples. This includes women and girls, youth, marginal and vulnerable populations. This vision is embedded in the UN Secretary General's roadmap for digital cooperation which nurtures a concept of a sustainable, robust digital transformation for all through more effective global digital cooperation. This roadmap provides a design that brings together the common goals of ensuring universal and meaningful connectivity, taking a human-centered approach to digital transformation and protecting everyone from online risks and harm. Ladies and gentlemen, this event also contributes to the United Nations World Summit on the Information Society or WISIS for short. That since two phases in 2003 and 2005 fosters multilateral and multidisciplinary engagement and cooperation involving civil societies and public and private entities. It provides a set of actions to fast track the potential of ITTs to enable sustainable development. Since 2015 the WISIS and SDG processes have been more aligned than ever before to complement efforts in helping countries around the world to use digital technology for good. But to achieve this numerous challenges still remain. Recent statistics reveal a connectivity grand canyon separating the digitally empowered from the digitally excluded with 2.9 billion people still offline and 96% of those living in the developing world. ITU continues its strategy to connect the unconnected and bridge the digital divide to encourage the uptake of digital innovation and technologies, goods and services through our whole ecosystem approach to enable social, economic and environmental growth. These objectives are covered by our 10 thematic priorities and are defined in a specific set of targets under our Connect 2030 agenda. Within its capacity as the UN Specialized Agency for ITTs and Digital, ITU is pleased to co-lead with UNECE and manage the UN Digital Transformation Group for Europe and Central Asia. This partnership offers a platform for us to work together with sister agencies of the UN family and to capitalise on the synergies offered by our mandates to widespread digital transformation across the region. 2022 marks an important milestone for digital development. The World Telecommunication Development Conference, which will be held from the 6th to the 16th of June in Kigali, the capital of Rwanda, will set our areas of action for the next four years, reflecting the needs of our member states to advance on the digital agenda. Several milestones have been put in place toward this conference, among which the Generation Connect Youth Summit, which will be held before the conference, will aim to channel the voices and aspirations of the digital natives into key policy decisions and to present their perspectives for the future of our gigabit societies and economies. To capture all the commitments towards advancing digital development, the ITU, in close cooperation with the UN Secretary General Envoy on Technology, have launched the Partner to Connect Digital Coalition, or as we call it, P2C. P2C aims to leverage the power of a multi-stakeholder and transboundary approach to digital. It is built on the principles of inclusion, partnership, and SDG-focused digital development, which aims to answer the who, what, why, and how of achieving inclusive connectivity and digital transformation for all. To do so, P2C focuses on four areas which resonate with the SDG-70, connecting people everywhere, empowering communities, building digital ecosystems, and incentivizing investment. These four focus areas, also being the pillars of today's discussion, provide a global action framework to mobilize and announce new resources, partnerships, and commitments to promote sustainable digital technology uptake and ensure meaningful connectivity for everyone. I take this opportunity today to call upon all stakeholders to join Partner to Connect Digital Coalition and to submit your pledge through its pledging system that will serve as the key place for leaders across government, business, civil society, and academic sectors to declare their firm commitment to close the digital divide and as a marketplace that we hope will catalyse new partnerships and collaboration. By going through each P2C-focused area, we hope that today's session will help to capture pointers of immense value to other countries that are eyeing a similar path on their digital transformation journey. Today, ladies and gentlemen, I sincerely hope that this session will help us to unravel the necessary dimension which will ensure a universal, meaningful, and inclusive connected world and the role that multi-starch stakeholder partnerships can and should play on this effort. I wish you all a fruitful discussion. Thank you and back over to you. Thank you very much, Stephen, and now it's my great pleasure to invite to deliver the opening remarks Miss Olga, Olga Jerova, who is the Executive Secretary of the United Nations Economic Commission for Europe. The floor is yours. Thank you, Jaroslav, also for very professional introduction to this roundtable. So dear Stephen Beror, Deputy Director of ITU Excellencies Distinguished Delegates, ladies and gentlemen, it is with really my great pleasure that I welcome you today to the peer learning roundtable on accelerating digital development through multi-stakeholder partnerships with the UN Economic Commission for Europe. It's co-organizing jointly with the International Telecommunications Union in the framework of the Regional Forum on Sustainable Development for the UNEC region. I am delighted to welcome delegates from across the globe and from a range of organizations. Your engagement in accelerating digital development is a testament to our joint commitment and dedication to advancing this issue. We are all connected remotely today from different time zones and different settings and this in fact forms the very base of our partnership increasingly driven by the demand for digital development in the past years. As we stay connected despite the global challenges such as COVID-19 restrictions, there has been an increasing demand globally for advanced technologies and digital transformation. We have entered a new digital era and it is extremely important that we as international community join forces with policymakers, regulators, communities and most importantly youth to seek collaborative solutions for accessible, affordable and safe connectivity. Digital development has a huge potential for a positive change and it is instrumental to achieving the 2030 agenda for sustainable development particularly its SDG17 partnership for the goals. It is important to ensure that this transformation is inclusive, safe and well governed. The issue of digital cooperation has been very high on the United Nations agenda and I would like to highlight just a few following initiatives on the global scale. The US Secretary General launched a roadmap for digital cooperation which calls for enhancing global digital cooperation among other priority areas. The Secretary General's envoy on technology has been appointed with a mandate to lead implementation of the roadmap, facilitate dialogue and recommendations and serve as an advocate and focal point for digital cooperation. At the regional level in our UNEC region, member states decided that its 70s commission sessions scheduled for April 2023 will focus on digital and green transformations for sustainable development in the UNEC region. Contributions from UNEC's governance architecture are being collected in preparation to the session and in the efforts to showcase activities supporting the digital agenda as well as to foster digital development in the region. Finally, in the context of this session I would like to highlight our long-standing collaboration with the ITU in many areas including connectivity, smart sustainable cities as well as on electronic business. I am pleased to share that since March 2020 UNEC has been co-chairing UN digital transformation group for Europe and Central Asia jointly with the ITU. Together we seek to deliver one UN response to the cross-cutting priority through cooperation between different UN agencies in the field of digital transformation. I'm truly encouraged by momentum that we have gently generated both at global and regional levels and I hope that these efforts will translate into priorities of your national agendas as well. As we embark on the digital transformation journey we must consider potential challenges down the road. We need to ensure that this transformation is inclusive, sustainable and resilient and that we are mindful of potential environmental and privacy risks. Most importantly we must make sure that accelerating digital transformation doesn't contribute to enhancing inequalities and increasing the further digital divide. As you may know as of 2021 only 63% of the world's population had access to internet which means that at least three billion people mostly in developing countries are still lacking access to internet and hence don't participate in the digital progress. In the UNAC region for example in Tajikistan only 36% of population had access to internet in 2019 according to UNCTAD which means that more than 60% of the population don't benefit from digital development and most of them unfortunately are women. We shouldn't contribute to the growing digital divide and to greater inequalities. We should rather collaborate towards closing a digital gap considering a gender aspect and connecting more people together in a safe, inclusive and affordable way. At the UNAC we are working closely with other agencies to address these challenges and I hope that this event today will be an opportunity to reflect on the past, to assess the ongoing efforts and to pave the way forward. As we recover from the pandemic, as we learn our lessons we must look forward with determination to thrive. In closing ladies and gentlemen let me emphasize that your engagement and participation in the meeting today are testament to our joint commitment to advancing digital development and delivering on the 2030 agenda and confident that together we can capitalize on digital development potential and accelerate progress towards achieving safe and sustainable internet for everyone. I look forward to continuing our gender efforts to making this digital transformation a success for everyone and I wish you successful deliberations. Back to you Jaroslav. Thank you very much. Thank you very much miss Algaerova for all these kind words and also for inspiring speech. Thank you very much Stephen also for setting the context and conveying the strategic messages. With this I would like to declare that opening ceremony arrives not to the close because in front of us we have a special guest today and this is his Excellency Admirin Aliti, Minister of the Ministry of the Information Society and Administration of the North Macedonia who will deliver a special guest statement and share his vision in terms of digital agenda for his country and the enabling power of ICTs for development and the importance of the partnership building. So with this I would like to hand over the floor to his Excellency. Thank you Jaroslav, dear Mr. Stephen Baroks, dear Mrs. Algaerova, dear Mr. Ponder, dear participants. It's really an honor to be part of this event organized by the ITU and I think that the topic is very important. There is a great need in all countries both in political level and in other levels that we must work in the direction to connect all the people and to have a digital inclusivity and as we know in Europe and in many countries of the world there are big discrepancies between one country and another. While we have countries that we can admire for digital inclusivity we still have countries where a lot of regions, a lot of people have no connection to the internet let's say or today with the media that we consume and with the trends that we have also we have problem with the speed of our connections. So I think that it's important that countries focus more on this and to accelerate this process I think these events like today are of great help because they just bring together different participants from different countries where they have the possibility to share ideas and to share good experiences used in one country and applicable to the other. One of the topics used in this event I think is very important to emphasize and that is the multi stakeholder approach. This I think depending on the level that we see is important because today let's say connectivity that I see as a main stakeholder is the ITU which is like the bridge to connect other countries but also countries need to help each other to reach connectivity at least by sharing good practices and experiences but also we need to find a way that within the country there is a bigger cooperation between government institutions academia and private sector because there is a sense that in certain countries we have the knowledge but that knowledge is isolated in one of the stakeholders so that's why bringing forces together of all stakeholders is very important to reaching the goal of connecting all the people and you know in my closing remark I just want to congratulate the ITU and all the organizers for today's event because I think that we need these kind of events as often as possible because these are one of those elements that help us to to expedite our road to connecting all the people and to improving digital inclusivity. Thank you very much. Excellent Ciality, thank you very much for inspiring words and for drawing attention to key components which we must integrate while we think further on digital transformation and the achievement of the 2030 agenda. I also want to take this opportunity to thank you for great collaboration with the ITU through the Office for Europe on these topics such as digital skills, children protection and connectivity. Thank you very much. Ladies and gentlemen so welcome one more time to this session. This session also builds upon the pre-event on this topic of the digital transformation beyond the COVID-19 which was held on the 1st of April and this side event has took a look at the different aspects of the digital component contributing and enabling the achievement of the SDGs 4, 5, 14, 15 and 17 as expected by the HLPF and therefore this makes us proud that on the occasion of this event we are able to provide to you already the outcomes of this meeting and to build upon those discussions but this event also is benefiting from different inputs from the other groups including our youth envoys who will be joining us and conveying the voice of the youth but now it's my great pleasure to welcome to the floor is Natalia Mocho, Regional Director of the ITU Regional Office for Commonwealth of Independent States and Ms Elisabeth Turk, Director of the Economic Cooperation and Trade at the UNEC who will be our co-moderators of today's discussion and with this I'm handing over the floor to Natalia. Natalia the floor is yours. Thank you Yaroslav for such a great introduction very cheerful and indeed feels and is a great discussion a great event that we are holding all together in frames of the Regional Sustainable Development Forum and it is my greatest pleasure to co-moderate this event together with you and with Elisabeth and taking into account that we are a multi-language region and the benefiting of the interpretation that we have here today let me turn to Russian language so that our Russian speaking participants also feel fully inclusive into our event. which I hope we will hear a lot of interesting and such breakthrough proposals and ideas from our speakers today as speakers with us, the representative of the Simon Manley, the representative of the UK, Mr. Drashko Milinovich, the representative of Serbia and with us was supposed to take part today, Mr. Ashat Arasbek, the deputy minister of Kazakhstan, but in the last minute he could not connect to us due to objective reasons, so instead of him and his name, our new participant, Mr. Ashat Besemhanov will speak. And let me invite Ashat to speak for the first time and answer the question. Ashat is the director of infocommunicational holding of ZRD in the Republic of Kazakhstan and directly works with the Ministry of Digital Development and Innovation of Aerocosmic Industry of the Republic of Kazakhstan on the projects related to infrastructure and communication in the Republic of Kazakhstan. Ashat, please share with us what problems are in front of the country in the creation of reliable infrastructure, IKT and what examples of successful partners you could bring, which are aimed at providing universal connection in Kazakhstan, in which you, including participate. Ashat, please, you have a word. Thank you very much, Natalia. Dear participants of the forum, dear colleagues, thank you in general for this opportunity to speak on the forum. I would like to note that in the whole world, the pandemic, Covid-19, has increased the problems with the connection of the existing digital explosion between the rural and urban areas, for example, in the field of education, has become even more complicated. The low speed or lack of Internet in the purchase of a sharply increased volume of traffic in some time did not allow to provide high-quality access to educational resources. In general, according to statistics, almost 90 percent of the population of the country use the Internet, but the connection with the protection of universal connection for remote and low-settled regions still remains a problem. Almost all state schools have access to the Internet, which is about 99.7 percent, although the average speed is significantly different in the region, and only 59 percent of schools have access to the wide-banded Internet. 74 percent of schools have less than 10 megabits per second, 26 percent of schools from the total number have less than 4 megabits per second, then, as for a fast and reliable access to the Internet, it takes at least 20 megabits per second. It is known that the Volocon optical lines of communication are the best way to connect and transfer data. Given the extensive territory and the small density of the population in the Republic of Kazakhstan, the spread of the Volocon in the whole country in most cases is an inattentive measure of access for operators to connect. Although there is a relatively sufficient level of competition on the market, in spite of all the settlements, everything is still required by the state. Perhaps this is the greatest difficulty in building a strong and reliable infrastructure and KT in the Republic of Kazakhstan. And to solve this problem, the Ministry conducts a targeted work, for example, in the 18th-20th year, two large-scale projects were carried out. The first is the supply of rural, populated areas with a wide range of access to the Internet through the Volocon technology and the supply of mobile, wide-band access to rural, populated areas with a population of more than 250 people. It is also worth noting that one of the solutions to provide the remote rural schools with high-quality Internet is the partnership between the Ministry of Digital Development, the innovation of the Yara Cosmical Industry of Kazakhstan, UNICEF and the International Union of Electricity, along with the joint implementation of the GIGA initiative. The first result of joint work was the provision of a wide-band access to the Internet for 38 schools of the Turkish region last year. This allowed almost 19,976 students, almost 20,000, to improve access to online education and improve quality education. Also, using this opportunity as a member of the Giga Committee in Kazakhstan, I would like to once again express my gratitude to UNICEF and the UNICEF for the implementation of the Giga Initiative in Kazakhstan. Despite the restrictions due to the pandemic last year, certain positive results were achieved. The Turkish region and the Republic of Kazakhstan managed to take the first steps. Thus, 38 schools of this region were connected to the wide-band Internet. We would like to spread this positive experience in other regions of Kazakhstan. In this regard, the representative of the UN Children's Foundation in Kazakhstan, the IMCA was developed and approved at the meeting of the Giga Committee. The plan is to work on providing access to the Internet to all Kazakh children in the next five years. In conclusion, I would like to express my hope that the partnership with the IMCA and UNICEF within the Giga Initiative will reduce the digital explosion and improve quality education for children in our country. Thank you for your attention. Thank you very much for your speech and for the specific example of the partnership that is currently being implemented, in which Kazakhstan participates, together with the IMCA and UNICEF, our Giga Initiative for the implementation of the Giga Initiative. It is a shame to hear the successes that have already been achieved. Yes, there are about 20,000 students who have been connected. These are quite high results. We sincerely hope and wish him success in the implementation of this platform. One more thing that I would like to pay attention to in your speech is the long-term planning for the next five years. It shows that the country and we as part of this partnership are looking seriously at the decision to connect all schools not only at some kind of a short-term perspective, but also with such support and a look at the future. Thank you very much. Once again, ASEAT and the best wishes for the success of Kazakhstan in the complete connection and achievement of much higher speeds than four or ten megabits, which you have also marked. I would like to invite you to our virtual podium of our next speaker, Mr. Simon Manley. Your presence, Mr. Manley, is a ambassador and a permanent representative of the United Kingdom at WTO and other international organizations in Geneva. Mr. Manley, let me ask you the following question. Why, how do you think? Why is it necessary for all of us to act slowly to improve the global digital connection and connection? And how does your country work? Mr. Manley, let me ask you the following question. Why, how do you think? Why is it necessary for all of us to act slowly to improve the global digital connection and connection with other international partners to solve this problem? Mr. Manley, please, give you a word. Natalia, thank you very much. It's a great honour to be here on this kind of virtual podium with such distinguished speakers on such an important issue. And I think as we've all been reflecting, the last few years of the pandemic have provided sort of a curious lesson. So the pandemic has both, as we know, revealed and reinforced the digital divide, both within our societies and between the developed and developing world. But it's also led to this extraordinary leap forward in terms of the digitalization of our economies. So never have the opportunities been so great and never have the divide been so deep. And therefore the necessity to bridge that digital divide, whether it be domestically or internationally, has never been more important. And right now we also see with the effects of Russia's unprovoked aggression in Ukraine and the damage that has been caused by Russian missiles and bombs to the critical infrastructure, critical IT infrastructure in Ukraine, the loss of connectivity, the failure of telecom services at the mobile phone outages, the effects for a modern democratic society being without connectivity. So we very much welcome the ITU Council's Resolution on Assistance to Ukraine in rebuilding their telecom sector. And we also know that we have to work together even harder to bring underserved communities and digitally excluded groups into the digital fold for the benefit of all of us, whether that's about improving the dissemination of information, growing the digital economy for both developed and developing economies, and bringing new voices into our global debates as we try and tackle the great challenges of the global commons in the 2020s. And to do that, I think we all know that we need smart and indeed sustainable investment in digital connectivity by both the public and the private sectors, complemented and need enabled by improvements to policy, regulatory and licensing frameworks. We need accelerated technological innovation and we need business models in the private sector which support affordable last minute connectivity, sorry, last mile connectivity. And we also know that connectivity alone isn't enough, that it's important to build digital literacy, digital skills to promote safe and secure digitalization so that our citizens can and our businesses can take advantage of that connectivity to build successful digitalized businesses and to enjoy the benefits of a more digitalized society. As the Foreign, Commonwealth and Development Office in the UK, we want to see accessible, affordable, safe and sustainable connectivity to reach those who need it most. And we work with partner countries to use telecoms, technologies to drive sustainable growth and widen social development. We have, as you'll know, a digital access program which works with governments, with regulators and with industry in a few key countries, Nigeria, Kenya, South Africa, Indonesia and Brazil to catalyze inclusive, affordable, safe, secure digital connectivity. The program supports digital skills development, pick up my point earlier, and the creation of locally relevant digital content and services. It tries to boost the cybersecurity capacity of governments and businesses. Such an important issue for us right now. And it helps create, we hope, skilled local jobs. For example, by providing technical advice to help community networks make use of low cost, sustainable technologies suited to those that are in remote contexts, or through the advice that we're offering, for example, the Kenyan Communications Authority how to update its own universal services fund, expanding inclusive connectivity nationwide as part of that digital access program. We launched a new partnership with the ITU last year, as you'll know, in which we bring together our expertise, experience and networks to help partners improve telecoms regulatory frameworks, develop scalable business and funding models and strengthen again those digital skills. And we hope that the outcome of that collaboration with the ITU will be the basis for a longer-term digital inclusion partnership. I think that everybody else in the school, we can and must help others close that connectivity gap at home and globally. And we stand ready to work with the ITU and UNICEF and others here, private and public, to achieve that goal and to bridge this digital divide. Thank you very much, Mr. Manly, for your presence, for such a clear and strong position and aspiration to act in overcoming the digital divide in which your country participates in the international cooperation with the ITU and other countries. The world is very happy to hear that the partnership that is now being carried out with the international cooperation has a very joyful perspective, a long-term planning for overcoming the digital divide and providing such a full-fledged digital inclusion. And the areas of work that you noted are very good to invest in the partner-to-connect platform, which was mentioned earlier by my colleagues. I think all the components of our global platform, the initiative of partner-to-connect are captured within the programs that you have talked about and in the part of providing access to communication and in the part of creating services services and in the part of building skills, improving the quality of the skills of the population and attracting investments that are so necessary, especially for developing countries. Mr. Manly, thank you very much again for your active position and for the opinion of your country in the part of the importance of the partnership over which we work. Colleagues, allow me to invite our next speaker, who is a representative of the Agency for Regulating Connection, Bosnia-Gerzegovina. Mr. Drashko Milinovich is a diploma journalist, has also a rich experience of work in the media, works in the state service. Mr. Milinovich, what are the problems with your point of view, with your perspective? It is strange to face the creation of a reliable infrastructure and a partnership that needs to be built to provide accessibility and security connections. Please, we will be glad to hear your opinion. Mr. Milinovich, your words. Thank you, Natalia. Excellencies, fellow colleagues, ladies and gentlemen. Global partnership across sectorial and multi-stake holders, initiatives made during play a crucial role to accelerate recovery and to getting us where we are striving by 2030. We are all aware that digital transformation can only be fully realized if high-quality access to communication networks and services are available and affordable prices for all people, no matter who they are and where they live. Achieving this goal is not an easy task, especially for developing countries and it requires collaboration between all stakeholders. Communication regulatory agency of Bosnia and Herzegovina CRA is to that and dedicated to its task to implement regulation that provides incentives and opportunities for investment in high-capacity broadband infrastructure to promote competition and to ensure affordable and secure access to high-quality communication networks and services for all. Furthermore, together with the Ministry of Traffic and Communication Agency is actively working on transposing the European electronic communication code into the new law of electronic communications and adapting broadband strategy for Bosnia and Herzegovina since COVID-19 provides that reliable broadband and affordable access is of the vital interest of our societies to be able to adapt informally regulatory decisions to monitor policy implementation and to determine regulatory challenges we at the CRA have identified the need to relay on data analytics as a prerequisite for the comprehensive broadband mapping system is required in order to overcome strategic and institutional shortcomings CRA applied for technical assistance from ITU project was launched in second half of 2021 to the collaboration of ITU and the engagement of experts from Slovenia regulatory body ITU policy paper under the title enabling environment for broadband mapping in Bosnia and Herzegovina was issued main objective of the project was to support efforts in Bosnia and Herzegovina towers strengthening its broadband mapping operation to improve the deployment and uptake of connectivity throughout Bosnia and Herzegovina in particular the aim was to identify and empower key stakeholders to better perform the tasks that under being targeted development project activities encompass the regulatory assessment as well as proposals and recommendation to establish a positive limit that will enable the national regulatory regulatory authority to obtain exchange and use data on telecommunications infrastructure infrastructure and services for needs of the digital digital platforms and developments a number of meetings with different stakeholders have been organized to increase awareness that the institutionalization of geomapping in the country is necessary in case proposals and recommendation for enabling environment to receive institutional support clear project design and all technical specifications can be easily undertaken a good practice and experience from Slovenia where of huge importance for the project the exercise of assessing Bosnia and Herzegovina's broadband landscape in order to landscape needed to already exist experience which Slovenia could leverage. ITU's decision to leverage Slovenian experience not only from collaboration established between ITU and Slovenia national regulatory agency but also from the geographical these that exist between Slovenia and Bosnia Herzegovina the project may serve as an example of multi stakeholders cooperation that is as important for mobilizing and sharing knowledge and expertise to support the achievement of the connectivity for all as a part of sustainable development agenda. ITU and UN DCE dedication to develop and implement partnership is therefore highly applicated finally I really assure you that the partnership agency remains open for dialogue and cooperation and I'm very much look forward to meeting you in person in future helps of technical priorities. Thank you for your support technical infrastructure connection Dear colleagues, dear gentlemen today's speaker let you thank you that you presented and the information of the perspective of your countries told and shared with us with examples of existing partners directed at creating a stable with other countries or organizations we have heard examples of such initiatives as Giga we have heard examples of work directed at a large-scale access in Bosnia Herzegovina we have heard examples of large programs for the right access which is realized Great Britain and those partnerships that already exist with the international ties with UNICEF and we hope that these partnerships will expand understanding realizing that communication infrastructure is not the only component that allows to use all the advantages digital technology our digital era another important component is to give full power to the community people, citizens to use these technologies and this question will be addressed to the second segment of our today's event about expanding the rights and opportunities of the community, community citizens and the whole population and today with us as part of the second segment will be the presentation of the representative of Armenia and Yanis Vardakanastis if I'm correct which as far as I know will not be able to access to us but we will be able to listen to his video answer to my question so colleagues continuing our discussion I would like to note that one of such projects which is aimed to expand the rights and opportunities of the community to build such public networks and Mr. Manlik also noted this direction of work such approach when the community has the opportunity to create and develop such public networks access to the Internet helps to connect the most remote rural areas but at the same time due to the complexity of such networks their development does not always have broad distribution in some countries this experience is quite successful for example in Georgia but nevertheless changes where other technologies are not possible in this regard I would like to invite Christina Guindjan who is the head of the Armenian Union and under her leadership the organization brings a very significant contribution in the development of the telecommunication sector of Armenia and works in partnership with the government, the civil society with international organizations in part in the implementation of projects on the development of digital skills security in the Internet and so on and so forth I would like to invite Christina to share your opinion, your experience how to expand the rights and opportunities of the community so that they can fully provide digital society how to provide digital inclusion the most vulnerable areas of the population people with limited health today you have already participated in the other side event within our forum which was directly tasks digital inclusion for people with limited health and thank you very much for your active participation within this forum Mrs. Guindjan please answer share your opinion and experience Thank you, Natalia Thanks, dear colleagues Thanks for inviting me to this high level event and thanks for the chance to share my insights and experience about the communities empowerment Empowering communities means also empowering vulnerable groups and as Natalia mentioned this morning I had the pleasure to participate in the side event dedicated to digital inclusion for people with disabilities and I find it very important as the digital inclusion can present an important opportunity for people with disabilities since they are increasingly enabling to get access to education skills development and employment electronic communication sector and digital inclusion is priority for the Armenian government last year the government of Armenia adopted the digital transformation strategy of Armenia and currently the broadband development strategy is on the table and under discussion two strategies should be interconnected and work collaboratively and it's important that government and public sector collaborate to reach better results the digital inclusion and broadband internet development is also priority for the union of operators and to support it last year we have started the pilot community network project initiative partnering with the ministry of high tech industry regulatory ISOC ITU World Bank Network operators and other local partners partnerships with different entities help us to cover all the aspects of the project some of them support us support the project financially some with advice some provide their infrastructure and some support with the digital skills development programs when I have started thinking about the project bringing the broadband internet to a rural underserved areas my main concern was okay what would they do with this internet how the community can benefit from it and what actions should be taken and whom to empower the community to benefit from the opportunity of having high speed internet one of the doubts was how to involve everybody in the community not leave anyone behind it's easier to involve young people they are always interested in new things and technology but labor force and pensioners are also an important target group in the agenda of the digital development taking into account that there is a need to ensure continuity of the employment process and the possibility to use the digitalized public services to support the digital inclusion in a few weeks a robotics labs will be opened at the school of this rural area only safety trainings will be provided to children and their parents and teachers as well as digital development trainings are planned for all age groups according to their needs we are actively working with ITU on digital skills development telecom sector and child online safety issues and on many other different initiatives and I am very thankful to my colleagues in ITU for supporting us in this we want to cover all the aspects of the digital development and be sure that the result everybody can benefit from the high speed internet access community network project came to create a real model which can be applicable for other communities as well this model with support of partners can be spread to other communities as well and cover the digital divide when affordable access digital skills and trust for technologies technologies are in place government, private and public sector collaborate I think it will be easier to reach the digital inclusion for all Natalia you are applying to bring the results and capture not only a separate category of people but as you noted all people, all communities and especially attention as we see is given to remote regions in which significantly less opportunities to realize their potential without such a mutual help and partnership between all interested participants as well on the side of the government private sector civil society but also international community which can be and should be in effect to achieve the purpose of the development of the digital divide and especially pleasant the support you are doing inclusion in part of people with limited opportunities as we noted on the side of the government this topic is very lively and we see that the countries make great efforts to try to realize their digital transformation with full inclusion of all people of the society Thank you very much Kristina and on this colleague let's continue as I already noted our next speaker is Mr. Yanis Vardacantasis is an active fighter for the right of people with limited health in 2021 he was elected as the president of the International Alliance of People with Invalidity and we congratulate him unfortunately as I understand personally Yanis can't connect in the form of unpredictable circumstances but he recorded our question which I will repeat once again how can we expand the rights and opportunities of the society in particular people with limited opportunities with Invalidity so that they can fully use the fruits of the digital society and I would like to ask our technical moderator to show the video response Yanis to the European Sebelty Forum and the International Sebelty Alliance I would like to thank you for inviting us to this very important event today many of you would already know the International Sebelty Alliance but for those who may not IDA is an alliance of alliances we represent over 1,000 organizations of persons with disabilities and their families in 182 countries around the world the United Nations Convention on the Rights of Persons with Disabilities has been our milestone we work with organizations of persons with disabilities to use international human rights and development processes to create change in our own countries and we advocate at the UN for a more inclusive and accessible global environment for everyone as highlighted by STG17 digital development can only be achieved with a partnership based approach inclusive digital development processes must be participatory and accessible this was one of the most important outcomes of the second Global Disability Summit had a few weeks ago in February digitalization is not a silver bullet that would solve all of our problems but it could allow others to understand individuals with disabilities communications it could augment children with disabilities access to education it should connect voters with disabilities to accessible information such as sign language interpretation easy to read formats to take part in political processes the pandemic has brought us to an inflation point where ICT advancements are racing ahead for some and threatening to leave others just with these inequalities we know that many persons with disabilities have already been left behind we see the promise in partnerships for a digital society not to be fulfilled to make this a reality these partnerships must include partnerships with persons with disabilities and their representative organizations we have the mechanisms through the united nations sustainable development through consultations with our governments and through the wither 15 campaign for the private sector together these things will improve access and inclusion and information for persons with disabilities in election cycles in the workplace and in this new digital world I would like to thank you all for your attention let's make change a reality let's bring the respect of human rights and inclusion in this very important sector of our life that you could not personally participate it seems to me very strong inspiring words in general everything is said and we all have what to take and what to continue our joint work thank you very much all for the first and second of our segment and bringing the results I would like to note the intermediate I would like to note that the predetermination of the right to break and provide equal rights and opportunities for the entire population and for the most vulnerable category of the population is of course for all the purposes of the region of sustainable development for the purposes of strengthening poverty, poverty, health well-being, education decent occupation all these aspects were touched today by our panelists digital technologies provide people great opportunities including people with limited opportunities helping to overcome barriers education, access to information communication and thanks to digital skills and the possibility of remote virtual communication and work as we have seen in the last two years of the pandemic we understand that all communities from remote regions people with limited health get valuable opportunities to acquire new skills in the field of IT to find new opportunities for work and self-realization however, of course together with new opportunities it is not easy new barriers appear but we look at them not as a problem but as a challenge a task we need to solve together and create multi-sided partnerships with unconditional involvement of representatives of all interested parties of the society civil society academic academic circles private sector of course will allow us to achieve so that no one is left behind of the entire society I would like to finish the first of our two segments and I will return the microphone Yaroslav, Yaroslav, please Thank you very much, Natalia and I think that now we would move to the next session which is going to be moderated by Elizabeth Many thanks, Yaroslav but Elizabeth, I was just informed that in fact before we are starting the next session in moderation we would like to welcome the youth representative to join us and convey the message on behalf of the youth So, over to you. Thank you very much, I'm Paulina Lalfa and thank you for giving me the opportunity to speak to you about the voice of the youth being heard as youth of the I.T.U. Generation Connect we aim to ensure meaningful youth engagement and participation to create, advocate and contribute to the policymaking process shaping the digital future this Monday we organized the second digital youth and preparation of the Generation Connect Global Youth Summit during this event a series of inspiring messages and discussion took place on meaningful youth participation in the digital transformation policymaking quality education for future digital societies and actions undertaken by youth to empower young women and girls in STEM these three points resonate well with the focus of today's discussion the youth leaders and identified three priority steps to ensure meaningful youth engagement first there's a need to take into consideration the diverse backgrounds of young people and as such there's a need to tackle inequalities to access and navigate in the digital world globally therefore we must provide the necessary I.C.T. hard and soft infrastructures to all communities including vulnerable populations girls and women or persons with disabilities to take quality education available for everybody secondly in line with the first step we need to give young people the chance to learn and grow this can be achieved by providing a flexible education that adapts to the fast changing digital world digital literacy technical and soft skills open doors to a brighter future youth all over the world and especially girls who have access to I.C.T. in sectors empowered by the knowledge that it provides to them a great impact to foster digital development at the community level and become role models for future generations third we as youth ask you digital and I.C.T. stakeholders and policymakers to bring young people to the table the involvement of youth into collaboration between stakeholders and decision makers should not take places the end of the process but already at the very beginning and in every of the building blocks we the I.C. Europe group are already engaged in active role in policy making towards the digital future and we are working to mediate our fellow youth to get involved and become part of the change but we will also continue to point out inequalities and decision making processes and in situations when the voices of important stakeholders like the youth women or minorities are missing or underrepresented we have an opinion and we are not scared of change so we will happily play an active role providing ideas and solutions make sure that the voice of the youth is not only heard but listened to thank you very much for your attention thank you very much for this intervention and all points are quite well noted but of course it's not only to note the points now we have to together think how to transpose them into the real actions and this is exciting part of making the meaningful engagement of the youth in this work and we are looking forward also to work with the group for Europe but also youth group for CIS to be engaged in the implementation and design process on the daily basis so thank you very much for this and now it's great pleasure to hand over and the floor to Elizabeth for the moderation of the third segment of this discussion Elizabeth, the floor is yours many thanks Jaroslav and great pleasure now to follow suit on the youth statement and I couldn't agree more with the fact of the great importance but also value added of bringing youth to the table some excellencies distinguished delegates, ladies and gentlemen distinguished speakers


Oh, yeah, thank you. Well, thank you for organizing this. This is such like a gem and a hard time. This is a very, very awesome idea. So can you guys see my screen and everything? Okay, so the only problem I have is that sometimes I will scroll my screen and it won't start scrolling on the main one. So if I'm talking and then it doesn't make sense, just let me know and I'll try to. Yeah. Okay, so yeah, this is called vertex distortion of lattice knots. And I guess I should provide a little background because hopefully this doesn't make sense at all. So I went to a liberal arts school, which I loved, but it was low on resources for glad grad classes. So the topology I had, you know, didn't have any algebra or any analysis to help me along. So I tried to come up with an idea or something fun that you can do that didn't require much machinery. And this is that. So my name is Nicholas. And I worked with a professor at San Jose State, Mary and can PZ. Okay. And I assume most everyone here knows what a knot is and all that but I because this is recorded. I'd like to just start from the beginning and make sure that everyone. You know, if you haven't seen a symbol or something that you know we're all on the same page. So the technical definition is that I'm not as an embedding of S1 and S3 typically think of these as being smooth. Now I think being such a vast field it's kind of a it's kind of a quaint little definition so few words but really what you're looking at is a closed curve in in our three. It doesn't intersect itself and I get to play around and move things. And I liked the big question is, you know, when are these equals so these three are in equal if I have these in my hand and I get to push things around.  So clearly that's not a knot but it'll it'll just be like a line like this and it has two ends. Well, if I think of this as being closed in a ball. And then once I touch the edge of it I'm going to consider those to be the same point so really this S3 definition is probably the one that you think of. And if you haven't seen this before because once I hit the edge here and the edge here I close it up.  So I guess just to save time if I were to give you this piece of string and in the real world, the laws of physics, you're allowed to push things around you can't cut it. And that's essentially what the ambient isotope is going to keep track of.  It's kind of weird but you can you can create a knot and you can shrink it down and technically shrinking a tangle down to a point is okay if it's isotope, but the ambience means that I'm, I'm actually adjusting the space around it. And that translates to not violating any laws of physics if I had these things in real space. And that kind of speaks to why, why study these things. Okay, if you haven't seen a righto meister move. If, if I'm allowed these three moves this is all I need to do if I give a planar diagram. Okay, I see a lot of shaking heads people know what this is. I'm mainly, if someone would like to come watch this video later it's for them. So take a look at these I only need to do these three moves to, to somehow describe this complicated ambient isotope which is a very fundamental idea. But the reason why to study these and giving you all these terms is this this the problem that I'm going to talk about actually has an application to has an application to biology, because certain DNA forms a loop. So if you've seen if you took, think I took AP bio and bacterial DNA is exactly this it forms a loop. And you like to know where does it cut itself and so forth so these these things are are studied there. So the problem I was told is that it's not nice like this diagram it's more like you get a plate of spaghetti, and it's just all full. And you say what not is this. And it's very hard to tell what's not it is so we have to come up with some type of an invariant that is going to be this so low, low crossing knots are not as bad so those rules I showed you above, that's what's happening here. So each one of these will call a diagram, or I guess I had been calling him confirmations but roll sin and some very famous. Not theorists call it a diagram. So if you decide to Google these this is a better term. So I diagram is a specific embedding. Okay, and then I have a an equivalence class which means anything that I can get to with an ambient isotope or those three rules. So each, each eight of these is a diagram, but they all belong to one class. And I just need to determine the class of one of these because they're all it's an equivalence relation so this one is called the not in the first slide. So therefore these all belong to the bracket of the sometimes you use a you. Okay, okay, so now here's some more technical things you may not have seen before so there's something called the distortion of a not and notice that this doesn't have a bracket right now so this is a diagram so it's a specific embedding so you're dealing with a closed curve like a picture on a piece of paper and I the distortion, it looks complicated I take the distance in the space. So this one we know. I'm in the numerator I have this new metric that I'm, I have the distance along it's an embedded type of metric that I have I to I choose two points on the not and then the length of the of the arc that is the shorter of the two. So if I do two points on a closed curve, there's going to be sort of two paths that I can take from one to the other, and I take the shorter of the two. And I take now the supremum so I'm trying to find what's the worst ratio of this, and that is called the distortion so I have a nice picture for that.  And that's actually what is trying to measure. So both of these embed a, an unnoted circle, and the one on the right seems to be more distorted. It looks like an ellipse. So the distortion of the one on the right is larger than the one on the left, is it for diagrams. Now this isn't a quick question if you don't mind. Yeah. So is the metric on the not the same. It's even.  Yeah, yeah, yeah. The integral was headed to six hours a week so I can.  Okay, so you can turn this into invariant. Can I also jump in really, I don't know if you saw in the chat, but people are saying that if you do full screen mode and use the arrow keys, then you might not have to scroll. I don't know if that makes it easier or not, but. Oh, I actually that's a setting on my iPad that I can do here. I think this is going to be better now. Okay, cool. Is that good. Yeah. Okay, let me have, I'll also my okay yeah my chat has gone away. So I will not be able to see a chat. Yeah, what will monitor the chat for you. Okay, great. Okay, so you can turn this into an invariant for the class. And by, and how to do this is that you take the infimum over all diagrams that represent that class. So hopefully, sink in for a second you do a supremum and then you do an infimum and hopefully you think about it for a few seconds and you're like wow that's like impossible. I don't want to think about that, because any, any little adjustment counts as a new thing that you have to run this, this argument for. For example, here I select the P in the queue and then okay great I have to do it for every pair of points. So obviously infinitely many, but if I make any slightest adjustment to that curve k one or k two, I have to then do it all over again. And then that's what's called the distortion of not so because this is fairly nasty. I wasn't studied too much, other than it's when it was initiated so Gromov was setting this and say oh what a cool idea and I think that we're going to have to be greater than pi over to. So yeah, so he showed actually it's greater than pi over to and it's pi over to when it's exactly this geometric circle, so something that looks like the unit circle this k one. Okay, and then someone showed a pair of people showed that if it's not it you have to be greater than five pi over three. And in fact this is kind of the extent of the. So there's one more very famous one, but this was kind of the extent of what was shown for this for a long time. In fact, the only not class that has his distortion calculated is this is the and not was just Gromov result. So it turns it turned out to be a, you know, it still is but it's a very hard problem. So there's approximations that show the tray foil is probably five power three. Okay, and so he asked, is there any upper bound to this so as not to get more complicated let's say crossing as they get more crossings. Perhaps, do I bellow out like can I not distort a diagram so far, I think they said like can you get above 100 and pardon show that there, there is none so if I take. So if you do know not theory this is probably like a very obvious place to start these are called torus not but for now let's just say they're not and they depend on integers p and q. And as p and q get big the distortion gets big. So this was, this was a very well received sort of annals of mathematics results. And it doesn't seem to be that deep and it's, I would say it's deep for respect of how difficult this problem is. But there's just there's not a lot you can hold on to is my point so what what I decided to do was well I probably don't have a good chance at solving something like that so let's look at a simpler case so these polygonal knots are something that's made up of sticks. And it's, it's hard to, in this time to give a formal definition but hopefully you can just see this picture. So they're piecewise linear straight lines. And they form a knot. So the more specific type is a stick lattice knot. So you're allowed to go if I'd like to give these an orientation you're allowed to go up and down left and right. But that's it, you must be confined to this, this lattice. So the formal. It's R cross C cross C business but really go up down left right and you want to end on the, the lattice integers so she did the three questions on this and breaks for a question. Maybe just a quick question. So, yeah. I was just going to ask why, why do you need the factor of R in there as opposed to just having it on Z three or something. So I'd like to be able to be a not so like a continuous curve and that's what allows that so if, if I choose and let's say the origin and I'd like to stick that goes just straight up. So people at some point have you know 00 pi. So that's okay I like I need I need two of them as I'm moving two of them have to be fixed integers. And then I end on another triple of integers. And my screen is doing that thing I talked about where it's not moving the next one so let me try to fix this. So these are studied. The big question in this field is, is how few sticks do I need. So it's a pretty cool question to ask if I'm constrained to this piecewise linear I'm not allowed to curve. If I'm a lot if I want to do just sticks not stuck to the lattice that's something else but for us, how few sticks do I need in the lattice to create a certain type of die. Okay, and the step length is the length of this, this arc so that'll be an integer as well. And the vertex set is going to be just the, just the Z three points that are traversed. Okay, so here's a, here's the picture of the trade foil. The reason why I need that are is because while I'm traveling I'm going to travel over some like not so nice rational irrational point but that's okay, as long as my end points are. This Z three. So this is actually how few sticks you need. So the stick invariant, the lattice stick number variant of the triple is 12. You can't make it with fewer than 12. You can't make the half length with fewer than 16. So it's what you think, like I have a square here, and then a square year. So this is like 2222 horrible picture but hopefully you see that, you know, kind of like how you normally would do a hotline. But now there's great. Yeah, pretty close 12 figure eight is 14. You're going to need more than 15 sticks in general. Cool problems. It's a fun thing to think about. Okay, but what I want from this is now to adapt that distortion to this field. So I'm going to call the vertex distortion the lattice. It's a very similar thing except I'm not going to check all points. I'm going to just check the vertex points. So I'm going to just check these bold ones. So that goes from checking an infinite amount to a finite amount. So I can replace the supremum with the max and turns out still very hard, but it's at least like obtainable opposed to the previous one. So I can turn this into an invariant. If I just now take the infimum over all of them. So I'm going to try to find the worst case for a diagram and then the best case for all diagrams. That means I'm going to change the metric now to a, a little l one to the taxi cab or Manhattan metric. So this is the metric of, if I'm only allowed to go down the streets left and right. I think I have a picture of that coming up. So for example, if I have two points here, I'm not going to measure this length. I'm going to measure just the, I guess, to be more technical kind of like the, the length of segments. I'm going to sum up the coefficients of the basis, or if I have like one zero zero one. And you know to get to this point I need three of these and two of these so that the five is going to be my metric. Okay. This is what we showed. So for any confirmation of the not in the cubic lattice, if you find out that the diagram you have has a distortion of one then then you know you're the not sounds obvious but it's, it wasn't. But this is good. This means like the result and the idea that we're coming up with, you know, mirrors the, the smooth case. And then also, we have like the foundation to, to that to pardon's result that there's, there's no upper bound distortion. So we don't have it for a class of what we'll see as tourist nuts, but we have specific ones that are very special. They're like this, they're minimum, or they're reduced and they have the fewest amount of sticks or we're thinking that that probably means that the class itself should follow suit. So these are the main, main theorems if you guys have questions on these. These pictures came from a Cohen Adams paper. They put these in here and they said, Hey, these are, these are tourist knots, but they didn't show how or why. So we did that and we showed, you know, the actually when it comes up, it'll make more sense. Questions. Okay, so like I said before, so these are the, these are the, okay, I think technically they're called staircase blocks. If you're a common tourist, I called them, we called them taxi cab paths for a long time, but I think staircase walk is the thing. So this is, this is going to be a key idea. So I want to show that if I, if I say I run the distortion and I figure out it's one, then the thing I have is the, and I do want to go through the proof of this just because I think it shows kind of how fun this problem is. So from 00 to one, one, there are two paths. And then we can kind of iterate these and these are all the possible paths. And I will note the staircase walk staircase path is the most efficient way if I'm restrained to this metric. And I like to go from one point to the other. I have many options, unlike, you know, the, the geodesic of a, the Euclidean metric kind of like the straight line is going to give me the best way. There is more than one best way to get there. And I'll explain in the next one, but the, that's how you can check.  And you are the most efficient way to get from one to the other. Okay, so this is going to be the slide to talk about. So let's see. So if I have a distortion of one, that means that the largest thing that I can get is, is one. And if I choose any other points, I'm going to be less than this because the distortion is going to be the supremum. But I can't, I can never be less than one, like I can't be closer along the knot that I am in the space. So this is also constrained below by one. So this tells me if I take any pair of points, the ratio I have is going to be one with the length, the shortest length along the curve and the distance in space. Hopefully that makes sense. So I'm going to pick a point here. I guess I'll just call this one P. The nice thing to, it's like a good little homework problem for discrete math classes that these are all, all, all of these stick lattice knots are going to be even length. That has to do that if I, if I want to be a closed loop and I, I go five meters out, and I have to end where I started I got to come five back at some point. It's going to be even. So what I can do is I can always choose its antipodal point. Okay, so this is the antipodal point of this. Okay, but kind of like I talked about before, so the shorter of the two path lengths, divided by the distance, the L one distance is going to have to be one. So that says that this, the green one is a, I'm going to not call it a taxi. This green one has to be a staircase. So it's like the most efficient way to do it. But this also says, now since this is an antipodal point, the other path is of equal length. So it actually says that this one must be a staircase as well. Okay, and then I want this idea is let's say I had this note. I've gotten pretty well that's a horrible drawing that I've gotten pretty good at remembering how to draw these. So I want this idea of a minimum bounding box. So I have my shrink a dink and I put in the oven and I so I have my shrink a team. I'm going to put it in the oven. It's going to shrink around my not. So it's going to, I'm going to end up getting, you know, a box that kind of just rest and it's going to, it's going to hit on the on some corners here. So this is another idea. It's an idea of the bounding box by a corner. So a corner is a corner if it's it's somehow a extrema point, meaning that for the X, the Y and the Z it's somehow either the smallest X value you can get the largest X value can get the smallest Y. So everything lives to one side of a corner. Everything lives to one side is not the right point, but one oxen. Okay, so, in fact, is so if I look at this P point. Everything lives a bug into the right. Everything lives above into the right because we verified that both of these are staircase paths. And that's kind of like the idea staircase path is that I never buckle over. So in fact, the point I picked, which was arbitrary is a corner. So therefore every point must be a corner.  So this was hard because the pictures we kept drawing were not these two. So it's just a bunch of counter examples not knowing it. But this we spent a while we so it does if someone finds this interesting, you know, we, and we were looking for a way to talk about this. So we originally tried to do write a Meister move so that like you can do it. And what you do is you can you get something that you can always unravel that's the big idea here. But to avoid so right a Meister moves are defined for the smooth case so we didn't really have it for the this stick case and they do some people just assume that you can do it but in just to avoid that we had this different this different method. But if I run this thing and I get a one out then I have to be one of these two so I am the end not any questions on this one. So I'm going to move to the next theorem. Okay, so the next idea, I think is a lot more beautiful but not as much generalization. So I'm going to show that there's something there is some collection of diagrams that get more and more distorted with our version of distortion. So I'm going to spend a lot of time just kind of talking about what those knots are and how you construct them. I actually, I would hope that someone who's interested in coming a torques takes this because you can kind of get the idea now distortion this vertex distortion tells how efficient your pads are. So if you have distortion one you're like the most efficient to get from one to the other. You're going to go as quickly as possible but if your distortion is 100. That means there's going to be a pair of points that you're going to be close in space so you know you live right next door your neighbor, but you have to go all the way around. So, I think for a graph theorist this could be an interesting idea. Anyway, so we do want to construct knots they're called torus knots. I don't have enough time to just say so I torus not means that so torus is a donor.   So those are both. So longitude is like the long way around the donut and then you go through the whole that would be meridian. And that's what the P and Q represent.  So we call an Adams show that the amount of sticks you need is going to be greater than equal to six times the P for P P plus one that actually has to do with the bridge index. So you have to be six more than the amount of bridges. If you do know the idea of bridges this kind of makes sense for sticks because you would expect you do at some point you go up at some point you go left. At some point you need to go right then and forward so you need to do all six up down left right forward back. Okay, so I had this idea of how to tabulate these if I was better at computer science I think this would be a great method to just compute these instantly so I'm going to say I'm going to orient these. And I assume you guys probably understand this but I'm going to so a way means that I have a close curve and I have some arrows on it. So there's a path I'm going to follow away I'm going to go around. So if I start somewhere I'm going to start the origin. If I go up, I'm going to say that this is z plus, and you know if I go x plus direction and so forth.  You can create a chart of this and you read this. So the first stick is a z plus the first z length is a 2p minus one that says I do z plus is a 2p minus one. Now I do an x plus. So I look for the first x that's a two, I go through here and so forth, six p sticks, and I get something that looks like all my screen. So I look at the type of stick I want so the first one says that I do a z plus in the sequence, and then I look at the first z, which is the 2p minus one and that tells me then the length, how far I do it. So you got to check is this a loop even do I get back to the point it started with, do I self intersect, and do I get the not that I want to actually get a torus not. So if I do this, these took a long time, but I get this very cool. Not here. I actually gave this talk at an LGBT conference. So the rainbow fit in perfectly. I actually had this thing 3d printed.  In fact, now that we're looking at this one I might say a few things about it. So if you look at any of these sticks. And if I tried to contract any of them, you. So you can't really tell because there's obviously space here but in terms of the cubic lattice I can't move any inward at all. There's something it's like as tight as it can be. And that's the idea. We didn't show the same result as part in but these look to be very special like these are as tight as you can be as few sticks as possible. Very cool to play around with. So to show that these are the torus not I made the torus that they live on. This took a long time learning how to do this in Mathematica. So you can count the P and the P plus one. So the long way around as I come around here. I pop out up here and here here are the sticks that I wind up hitting to get the. Actually, so I hit P of them right here. See if I can't do a finer. And then I come up at the top. And then so that corresponds to coming here here and then I get the P plus one by hitting this one, and then to count the meridian so the whole. This is the reduction I was talking about so same idea. Here's a different picture of it. I think it was easier to describe on that 3D print. This is kind of lame. You know it's it's going to increase your distortion without really changing the geometry of the tangle. It's kind of like a cheap trick. That's what I coined it at first. So these are as tightly packed reduced this way. I'm going to bring up point in. It's going to drag these in and create a plane I just don't want it to intersect as I go. I'm not going to talk about the proof of too much of this because I think it's it's just kind of boring unlike the other one, but this is the big idea I'm going to think of these as all being pointed line segments that have some type of orientation. I'm going to describe all of these so I'm going to do a lot of summing of arithmetic sequences and do a lot of arguments of this this coordinate never intersects with this coordinate. This is a picture from one of the proofs of them so this maybe this gives you the idea of how you wanted to, you know, talk about these things. This is the path that so this is the path that it has a very high distortion so these these two red points are very close but to get to them I have to travel far far around the knot. So these are the points that I selected each time. And they are exactly the distortion of these diagrams for small knots and then once we I got up to like 2020 plus one. It took like five hours to parameterize and right around 10 it flips like the points start being right here instead. So instead of, you know, trying to calculate this for all of them I say well here's going to infinity because so the distortion is the greatest of them. And so it's got to be greater than if I choose these each time, and these each time go to infinity. So the distortion which is going to be worse has to go to infinity as well. So I selected these two because it's right in the middle so if you count these. And the ones in the middle of course there's some times where there's an even amount and you choose. I think I chose the larger one. Yeah so here's the 2223 so hopefully you can appreciate that this may get a little cool picture though. 2728 I had to leave my computer on overnight. Cool. Oh is someone talking. I see lips moving but muted. Maybe. I was talking to someone else. Sorry. Okay, so these are the conjecture so this is the next step. So this paper is getting pretty hefty so we cut it short. This one is a little different than what we showed so these are the brackets. So we want to show the same grommet result kind of that if you are the if you get a one for the whole class then that whole class is the I'm not so we have one direction from the proof. Same thing for the other one so those the stronger result is show that the class of TPP plus one goes to infinity as well. Both. So this one we're very close in fact I think if we were just more clever it's right there this one. So this is the same method. I might need a little more machinery to do that. Both are fun. Both do not require a very hefty. Analytical topological to an undergrad to do it. That's I hope an undergrad decides to watch this one day. This is where I started with the smooth distortion. So I created these plots so this this maybe can show you why the the other way is a little more interesting. So I half of this is redundant, but I choose so I parameterize the I have my I start here and I parameterize so you know length one is right here and I don't need to be integer so maybe pies right here to parameterize the length of this and that that corresponds to choosing one of these so maybe I choose the point that's, let's do 60 along it, and then I choose the point that's 20 along it, and then I find where these intersect, and that gives me the distortion of the point at 20 along and 60 along. And this is where we started turned out to be a little too much that the computer can handle to calculate all the time. But very interesting, you always get something that looks like there's these peaks and valleys it kind of looks like an egg crate. You have these peaks and those valleys and these little dead zones, which means that you are very efficient in your path here, and you're very inefficient when you choose these pairs. So there's like a very natural question is like, can I use this easier stick distortion to then describe the smooth distortion. I think yes I think you know you could smooth the corners here and you could talk about it. You can, there's probably something to be said I wonder if you compare the points that I picked maybe they always line up in a certain area here and there's way to describe them. So this was, there was a master student that decided to do a project very similar to this. The original idea that I wanted to do is like, and one of those plateau problems so if you've seen that where if I have a closed curve like a knot. And it's fixed it's rigid it's not in topology anymore. What's the minimal area surface that that's the boundary of.  Clearly this wouldn't be the minimal area. So I wanted something to do with knots and you know how can you describe a minimal surface so that's why I first said well why don't we make it rigid and make it a stick and then talk about it. And then we saw this distortion got distracted but this is the same. This is similar to that this is saying how instead of how few sticks. I need to create the knot, how few tiles do I need to create a surface that the not can live on. So how few squares do I need to make a tourist. You know, the natural thing is I remove the one here and I have the ones similar game to play. So she came up with some very nice things that do. And that's the last slide I have. But there's any questions I'd be more than happy to talk about something. I'm going to leave it on one of the nice pictures. Yeah, those are some beautiful pictures. But yeah, let's let's clap. So, so it's distortion related to the bridge number of the knot. I'm not directly I the distortion is the bridge index I mentioned here. It doesn't it more has to do with the stick number, which kind of makes sense because if you think of like a bridge position. It seems like an, I guess, when I way that I've, I'm trying to find a blank spot here the way that I've seen bridge. So some people define it kind of like a Morse function. So I have. So I'd like to, you know, as much as I can I stick to this plane. And then, you know, oh no right here I must come up in the plane to go here and then I need to get in the bridge. And then I get to stick on this plane. So that kind of makes sense that I have.  So that, you know, necessitates. Oh, I must have at least, you know, three sticks additional now. But nothing I know relates it to the distortion, there could be. Okay, thanks. I'm kind of curious what goes into the computer calculations and like you're saying at some point. You know, and I think that ceiling might be my fault. I think I, I don't, I don't know if I know how to use Mathematica efficiently enough to where it doesn't time out because I'm so clumsy with it all. What I did with these, once again may not be the best way is I parameterized these so I parameterized each segment by its arc length. So here, you know, so for example here like from here to here, you know, I have this big piecewise and I say I give it a function, and I, and I give it a parameter for that. And then, you know, I do, you know, potentially 200 of these, and then it makes them all, it gives me a whole set of points that I get to, you know, you can run through a calculator. So around 22, it starts taking a very long time. And the smooth way, I think I would hope I mean maybe someone is, I know people are better at Mathematica than I am but maybe someone is better enough to say, Oh, this is an efficient way to describe the distortion because you for small ones like for the I actually ran the smooth one through just a formula like oh take all pairs of points and divide by their distance and it actually it was okay I could do that. But anything bigger than that. I wasn't clever enough to program efficiently. So somehow in this computation you really are having to do like all of these pairwise comparisons. Yeah. So I did have Mathematica to, you know, make sure I did it correctly but in a sense it was all kind of by hand, checking all pairs to make sure. And then once I got big enough. I just said you know I'm going to just check the ones where I think are going to get bigger. So like this pair right here. And then I just checked those. And then what I did is is actually way easier by hand than by computer. But what you do is you pick this point. So you have this table, and you say, Oh, that point is always to P minus six, say, and the other point is always, you know, seven.   So you can actually find a closed form for those pairs of points that I picked. Not a groundbreaking result, but a very cool one. And I think it leads the way to say that hey this is a useful thing to study. It follows what your intuition says so it's worth your time.