세 s'u bhei t'amro' gilit'a tarua' di t'avlun'a e s'u' dho' ron'a e' m'y n'pigdo e' kola' i' i' pigdo n'g lesser e' kwa' t'a ron'a e' nai ng'ah e s'a t'amro' gilit'a e' t'abhia e' s'u a l'interno della piazza il gonfalone del comune di Siena la comparsa storica dell'università di Siena con il labaro i direttori di dipartimento e il magnifico lettore una siena a tutti Siena che ho in priviletto bidono il benvenuto stasera oggi noi cerebriamo due eventi molt importanti per la nostra comunità il conferimento della laura magistrale ad onorem in strategie techniche della comunitazione a Piero Angela e il graduation day dei laureati dell'università di Siena nell'anno academico 2017-2018 sono due celebrazioni molto importanti per noi edere il motivo per cui abbiamo siento di tenirle qua in piazza del campo vorrei ringraziare perché poi non ci sarà tempo per farlo dogo vorrei ringraziare tutto lo staff dell'università di Siena che assiena lo staff del comune di Siena arreso possibile dalestimento questo bendissimo alestimento in questa piazza straordinaria e vorrei ringraziare gli studenti tutor dell'università di Siena che si sono doperati per agevolare la vostra sistemazione e con loro l'associazione degli studenti curedio che coprera l'interovento adesso possiamo iniziare con la prima parte della cerimonia cioè il conferimento della laura magistrale ad onorem prende la parola alessandro innocenti direttore del dipartimento di scienze sociali politiche e cognitive per leggere la motivazione con la quale il dipartimento ha proposto il conferimento della laura magistrale onoris causa in strategie e tecniche della comunicazione a piero angela il dipartimento di scienze sociali politiche e cognitive ha approvato all'unanimità il conferimento della laura magistrale ad onorem in strategie e tecniche della comunicazione a piero angela per la sua ampia edattenta actività di comunicazione che è sempre stata rivolta l'educazione scientifica intesa come componente essenziale di una cittadinanza attiva e consapevole questo importante contributo è stato associato ad un lungo edito del metodelevisivo volto al divulgare ad onambia platea non solo il contenuto delle varie discipline scientifiche ma anche a promover il metodo nazionale nelle grandi questioni del dibatito pubblico in netto contrasto con le tendenze e gli attegioletti antiscientici prende la parola il professor Giovanni Manetti professore ordinario di semiotica dell'università di Siena l'università di Siena in it's over 700 years of existence ha sempre portato in front of a line of research and diffusion of knowledge in front of the values of la laicità and the rational scientific method piero angela doesn't need a presentation because it's a character that everyone knows and appreciates for the quality of the communicator and the extraordinary divulgator of scientific themes that masteries with competence and presents in the right way to the great public they can't identify the activities of deep cultural civic values as for example the foundation of 1989 of the Italian committee for the control of the affirmations on the paranormal in which they faced themes that are of great quality in relation to the debate on the fake news and on the possibility in the field of information of the communication in general in all the communicative activities of piero angela they are shown fundamental two qualities the clarity first of all the Greeks will recognize the expression sapeneia and the unique dimension the Geloion that is the attachment of the dendodischere that creates communicative complicity with the right public it constitutes a special example the use of extraordinary animated cartoons elaborated together with Bruno Ozzetto clarity and humor therefore constitute the real the right figure of the communicative proposal of angela which is a strongly innovative result in the panorama in which it was born and which is demonstrated capable of attracting also the generations more young there are now three these generations those of color that have followed and appreciated the programs of piero angela I conclude with this observation piero angela has just continued 90 years but his mind his enthusiasm are those of a young student like you as you have been that of a modern cleric always looking for news the laureate that today has been conferred that has been conferred wanted to highlight also this aspect all his professional career the commitment in scientific education but also the invention of an efficient method to communicate a rational vision of the world and the problems of contemporaneity take piero angela a model to which all those who take fascinating courses science of communication can and must look thank you piero angela his dissentation from the title the role of technology he is very kind he is very kind he is very good he is of course he is a man he is very good he is very good so good he has such extraordinary words he was also said he did the work thank you really I thank the readers for the work for having promoted me as a student for an active and therefore I do not want to keep you in trouble because I am doing the work I am doing the work I am doing the work I am doing the work I am doing the work I am doing the work but I can not say I can not say I am doing the work I am doing the work because all of us as a team and as a team and as a team I want to bring to the public the knowledge of the science of technology which they are discovering because this is a quality brand of knowledge and the community the academic university appreciate the work that we do in the degree of education that is needed in our program which always requires a simplification but the simplification is correct I always say among others for the content and for the public the language the language is really a key that has the power in the knowledge they are very important in many occasions speaking with a simple person but also with a simple person because you talk to a physics lawyer but when do you do it? I do not know I do not know but if you talk to other scientists and all of us we need knowledge especially the science that can not be read in the original texts and all of us can read in the degree of education but also with the article that appears on the scientific view so in this field the scope of education is necessary which in my opinion is a translation from Italian to Italian I want to say two words but also our laureates since I was as I consider also I but I really liked what you said because I will say that I am 90 years old but in short I am always that of many years and to these students I want to say this for you this is a very important day because it is the end of the course of studies after many years but then with the university and also to do well hard studies renounce many things to obtain this area so if you have arrived on top of the hill and look around and look in front of this hill there is a landscape of a very complex and non-decipherable future because the changes are very short and we can not see where it will take us especially the technical development you will live in this century you are your future how will it be in Italy, the world in 2048 in 2061 in 2076 in 2084 then you will live think how how will it be in the world in the last century I think what else think if it will be worked in the vicinity of 1899 and I at home have the photography of the group of the works of the time we all expect photography because at the time we worked in the campaign Italy was a city 70 percent of the Italians worked in the fields today only in 400 in the United States less than 1 percent produce the food not the food for everyone is sport and why it happened because because there are a lot of immigrants at this point there is a not so much that has never been the case what happened is that anyone has won an energy that is sportable that is, an energetic form that can be transported not only to the wheel in the wheel that will turn in the magic then it happens that the robot will turn in the fields in the workshop in the saloon in any of the magic everything changes and suddenly the cost of the projects the productive efficiency allows everyone to access to certain things that were accessible the energy is multiplied everything changes and from the alphabetic of Mars 70 percent of the Italians would do it you go to Mars to the university of Mars the energy changes the condition of the man the liberation because sometimes in a polemic way there is a protocol of the petrogly the sense that the woman is the most possible today the women are more worked they work better I don't know what it is but the statistics say in general about the man and also the democracy because without knowledge without reading and writing without communication without the quality of aggregation with an economic property the resources to create those structures that oppose the power all this depends on the development of science it depends on the technological development I don't want to talk about this but what is the message that comes out in a polemic way is that the future will be the great part determined by the capacity in our country to be competitive in a world that is becoming very competitive especially in the western and so we want to have a great occupation and all the rest we have to be proud of the recent development of the values and education as much as possible in Italy here we are in the center of the world here is the great moment of the new capacity of liberating many things and projecting the future but it is possible because our schools in Italy are the last in Europe and the school results are 15 years based on them so let's say we want a very strong education but we want especially the colors that have the responsibility based on the values to govern our country to invest much more in science, in technology and are the real factors of the change as you have seen in the second course even more you know these new technologies are already creating disoccupations in many sectors they are playing the game so it is difficult to understand the future how it will be and how many steps you don't know how it will be 10-15 steps but you know if you play badly if you don't prepare the pieces well you lose this I want to say your work the university has prepared you for a deep culture a professional formation that is useful in your work but the work will change quickly my work does not exist in the 800 even in the 900 there will be 60 years there will be a new work to be ready to do it you don't finish your studies love with you finish your studies forever and this is the message always try excellence both in your studies but also afterwards don't be happy of the routine the world will be difficult but for you always try thanks a risk cause a strategy and communication technique the director the doctor Mr. Perfect Vice-Sindaco Vice-Minister Authority Doctor Dr. Piero Angela Dr. Rosa Rosella Postorino Directors and directors colleagues teachers of the technical staff of the University of Siena doctors doctors very kind guests welcome to the proclamation of the graduates graduates of the University of Siena of the academic year 2017 2018 for me that I have the honor to represent University of Siena the grandest satisfaction to see you so numerous here in Siena in the most beautiful square in the world called from our invitation to share the satisfaction for the view you have reached I would like to begin this brief message of health thanks to the municipal administration and in particular the Vice-Sindaco lawyer today it is impossible to participate marriage for a progressive commitment to have accepted our request to turn the graduation day here in the square of the field the symbol of our city the place in which the Sienese meet and they are always met in the important occasions as when 126 years ago the priorities of the 17 contracts called to collect the whole city to protest against the paventata suppression of the University of Siena the way the fate of our city so it is read in the manifesto of the priorities that was the suspension the suppression the minister of public instruction of the then government and that fortunately was never realized thanks also to the rise of the Coesa against the health of the cause are still the original words of the manifesto called to collect which was evidently necessary to defend I remain symbolic to celebrate the proclamation of the laurels here in the square of the field the place Solenne the theater of daily life temple and house at the same time civically sacred but never instantly is always familiar and especially the place of welcoming, inclusion of sharing favored in this its function by a form that embraces its guests and makes them feel part of their story I like to think that the senesis that in the years have participated to the architectural evolution of the square had truly this precise objective make a living center of meeting and dialogue make that the symbol of a sena that as it does for over 778 years with its own students since when the community financed its studio to the alboros of its foundation with the approval of the tasses of the school facilities and with these tried to keep high the level of teaching calling to sena good teachers here laurels and laurels being written to sena 2, 3, 5, 6 years ago according to the course that you have taken has also meant to write to this story that here we keep and of which now you are part of a story but that does not end with the achievement of your title but that has become part of you cemented from the sense of belonging of an institution to a community to a city the same sense of belonging a few years ago a group of ex students of the university of sena to build the association in the last 5 years the association has grown in the numbers and especially in the quantity and quality of the initiatives supported by the enthusiasm and the passion of those in any part of the world has not forgotten its love and diversity and its prestige through participation to the great network of trans-national contacts that is called sena alumni and that here in this city in this university the testimony of this enthusiasm and of this passion and the president of the association cinza angeli the laureate in economic sciences and banking in the academic year 1993-94 with which we will close this ceremony after the council of the parliament now you too have become students of the university of sena and if you want you can start to participate in the initiative of sena alumni even those organized by the association to participate in the initiative of sena alumni you have become part of a network that connects this experience to the already done network of which as a tradition for our graduation day we try to give a direct testimony in this day dedicated to you among these Lorenzo Fioramonti researcher of research compared to the european of the university of sena in 2005 now ordinary of the political economy of the university of Pretoria also vice-minister of the description of the university and of the research to him I will ask a short greeting both in the region of its prestigious ministerial work and also maybe to remind you of the experience of Dr. Andrew Asiena and the impact he had on his academic career after him we will have the pleasure to listen to our testimony Dr. Rosella Postorino writer laureate in our faculty of philosophy in the academic year 2001-2002 Rosella, who I thank for the availability recently for the appreciation of the prestigious champion prize to his master Roman a vibrant story of the experience of a group of German women during the Second World War Rosella is the best testimony of a student who has faced the university experience with the passion and tenacity of those who pursue a dream and can do it I am curious to listen to the words of Rosella and the story of her story in the conviction that it can be the inspiration for all of you for very few minutes has become part of this network and also of Piero Angela who enriches and appreciate our community with his prestige, her story of journalist and publisher for the boys of my generation and for those of many successive generations animated by a gap of interest for science and knowledge Piero Angela represented a kind of Virgilio the metaphor seems to me opportuna having just arrived next to the university the celebrations for the 7th 100th anniversary of the death of Dante Algheri a kind of Virgilio, I said who accompanied us in a journey between the secrets of science with words, images, stories simple but never banal a giant of journalism and of divulgation on which shoulders we all went up to observe better the world from the infinitesimally small to the infinitely great Piero Angela has helped us to give us the knowledge unique well as Socrates said and as he reached the slogan of our series of divulgative seminars called Studium and to value the support the supreme value of social emancipation Piero Angela has been the enlightened precursor of scientific divulgation and on this he has carried out the formidable future career which for incision is still active and constitutes a fleeting point of reference and he has been a pioneer of that activity of which the university has spent only a short time to get out of the mountains and to talk more with the people to learn to use a simple and understandable language without banalizing what is complex to make the knowledge accessible so that everyone can enjoy and so that the diffuse knowledge serves to make humanity progress as it has always done we also feel invested in this role of this mission and to confer the laureate Piero Angela to honor and to make the homage for all that he has done for the divulgation is the most significant way to manifest our commitment an commitment that every year is enriched with new initiatives starting from the formidable experience of Bright, the night of researchers in September with the collaboration of the commune of Siena and many other partners will return to animate the way of the city to divulgate the science is not enough to be good scientists is also necessary to be good communicators here because the association is not alumni and has decided to dedicate the traditional connection appointment that precede the graduation day to that reflection we wanted to give so many different because communication is one of the most polyhedral human activities and precisely in this polyhedrality the right instruments are found to vacate any form of knowledge also the most complex ones from today laureate and laureate also you are ambassadors of the knowledge of the world of the path you have made you have chosen to do and you have succeeded in completing start from a small city province but with an old heart and deep roots to the conquest of the world from today the society will begin to ask you to contribute to the development because remember well you are not to need the society it is the society the country the planet that needs you of your competences of your knowledge to build a world more fair, more eco and more sustainable of this your role doctor and doctors of the university that comes from the title that you have achieved with the efforts made in the last years you have to be proud and aware and you have to be proud of this awareness the energy and the conviction that you will need to face the challenges of the society paraphrasing an american song of the 70s if you have done it now you can do it always and everywhere I greet you with great affection and I wish you a future radius thank you doctor Andrea Corsi doctor I greet you the authority I thank you the director I greet you doctor Piero Angela who has honored us today a great welcome to those who have arrived today in Siena outside of our city a great welcome to the Siena I greet you of the municipal administration telling you a small episode that comes to mind this morning and I think about and I can be proud of the sources for each of the doctors that we celebrate today you know your experience what you have brought deep down in these years in our city was already written was already present in the ideal of the city that our antennas have prefigured because if any of you in mind present the allegory of the good government that are miraculously illustrated in the public palace of Siena probably you will have already there your figure that is present in the good government in the city university this testimony is the fact that you are part of this story you are part of that ideal Siena always more beautiful always richer always more welcoming and attractive even with your help who will understand once you have conquered the world or come back here or conquer it in Siena thank you all take the floor vice minister to the university professor Lorenzo Fioramonti good evening I thank the magnificent director the colleagues department director to have invited me this beautiful ceremony in this beautiful square in a city that gave me a lot because as the director remembered I have been a student in Siena more than 10 years ago I have done here my research doctorate but above all I have learned here to be part of a scientific community I had the privilege to be inside of a structure that allowed me to learn to love research and talk with men of all the world the scientific community of Siena has nothing to envy at the best universities in the world I have learned this here I have learned it day by day even in this square because as you know in the summer it becomes a beautiful beach of culture and of different knowledge I have also learned to have fun studying I know that you have done it in these years the path of research and training must not be a complicated path must not be a lot of challenges but also a beautiful moment of personal growth so I have become a university professor since a year and a half I have been in charge of the university as the minister said with the delegate at the university at the research and what I want to tell you what the new doctor Piero Angela said is that no one knows how the future is nor even I imagined a few years ago to perform the professional function that I perform now I long to imagine that I had a role of institutional character but what makes the difference is the ability to be curious the will to learn to learn I know that I do not have to tell you the day of your conference but I tell you that when you have learned to climb that hill as the metaphor used by Piero Angela said there will be other hills some maybe faster, some less some more beautiful, some less beautiful you have learned how to climb the hills now you can do it with greater capacity with greater efficiency the technologies do not tell us what will be the future of the work it is always more difficult to anticipate where the economy will go even in a country like Italy what you need is a generation of people who will not be afraid a generation of people who want also as the doctor said to conquer the world and this also means to use all your skills in a transversal way today you are not economists engineers, writers, philosophers jurists, you are people who have learned to train in the future you should continue to do it even in a way perhaps unexpected few minutes ago before the beginning of the celebration of the graduation day I visited the college where I graduated near Porta Romana, once we called it the Santa Clara College, today it is called the Santa Clara Lab in that college you do the future you do that type of research that type of training where I saw people working in letters using 3D printers to produce the future crafts softwares experts maybe collaborate with engineers with doctors to guarantee to sick people curators with modern technologies it is a new logic a new way of research and training you will be perhaps the first generation for which this will not be a difficult challenge because it comes from a training model that I have done in Ferigventoio in which we worked in a discipline and only knew that but you are already a generation of people who think it in a very transversal way so the invitation that I make is I do not know what the future will be but the future is in your hands the future is in our hands we do it in a way to make it not only a better future but a more sustainable future a future in which this country can explain the rest of the world as we have done centuries and centuries ago how to live well a future in which you should not find a job abroad to make your dreams but you can try it in Italy because in Italy you start to live well thank you it is a great honor for us to invite to go on stage Rosella Posso-Rino laureate at the University of Siena writer and editor winner of the 2018 Pantiello award thank you good evening congratulations to laureates and laureates of the academic year 2017-2018 imagine if it was exciting for you to conclude a chapter of your existence and for a new one and I hope that this last one will be exciting but you know that I am also excited to talk with you today 17 years after mine in laureate that I have achieved at the University of Siena but who would have ever imagined that I would have found myself here at the square to talk with all these people the great writer Francesco Frati invited me to do an interview I accepted because it seemed to me to close a circle to recite something about what I received in this tenure to have the opportunity to express the sense of gratitude that I have tried studying in this city and studying in general but I do not hide that I have also been asked about the remarkable fear that I always carry behind me what kind of writer and editor the person totally inhabited by the books could tell you of useful but then I remembered that before the usefulness for me the beauty has always come do you remember your first day in Siena when you started the university yes, it was the first and only time I saw my father cry and he cried for me he already brought me here to write me the admission exam then he brought me again the day of the exam he did not do anything and then again and then again to look for a room when we had the news that I had been admitted but every time he brought me back with him and in the car we sang Luccio Dalla with him always the same song that was entitled song song set in a auto-drill yes, there were still the song set in 1996 not for nothing in the last century and then again we had learned it in memory I do not think I have lived with my father a more sweet day than the one in which I supported the admission exam at the university and I do not even think to have ever been grateful to have not left me alone in that my first attempt to become an adult even if I became an adult unexpectedly I had done it I was one of 150 set in the course of law in communication of the Faculty of Philosophy I say unexpectedly because the candidates were more than 1600 and I suspect that in front of that number my father had expected that he would not enter so I would not have had to transfer to go home instead on a Sunday in October I found myself forced to leave I did not win in front of the Cinema Pendula that I would soon have read among my favorite books because Monday I would have had the beginning of the lecture and after having greeted me frantically took courses on the stairs to not show myself with tears in my eyes it seems too intimate maybe this story but I have to leave here to tell you what was for me the university it was a privilege you will think that the study is not a privilege it is a right and you are right the University of Siena gave me the opportunity to study what I liked the most thanks to the study bags even if my father was selling vegetables and what I liked I did not understand in the end but he trusted of course because he did his way but he trusted every individual has right to the instruction he says the Universal Declaration of Human Rights we know that it is not so and that is why we are privileged in the world there are 57 millions of people whose instruction is denied and there are 130 millions of children who attend the schools without any acquisition of basic skills of alphabetization reading, writing, assimilating mathematical calculations 60% of those 130 millions are women who is excluded from the right to the instruction they say the statistics risks a destiny of social and sexual exploitation of minor work and pre-marriage we did not touch it we were free to form and we took the academic studies because we believed that the instruction was the main way for freedom I continue to believe it although today the knowledge is no longer fashionable in fact it is even stigmatized the faith in the reason seems to be excluded following the global financial crisis exploded in 2008 which has progressively eroded our sense of security recently we published in the book ship William Davis' message professor of sociology and economy at the Glossman's College of the University of London called state nervous and reflects on how and why even those politicians seem today determined by the emotions in this book I read that only 30% of the human brain is dedicated to the rational thought while the remaining 70% is occupied by elementary tasks such as physical protection when a danger arises or at least when we perceive it we focus more on the physical response we worry about our survival thus the suspect accuses against the competence of the experts that are spread in the last years and that seem an irrational refute of truth are rather the response to the sense of danger I am the symptom of a refute against the system with which society is governed the experts are retained in a new league the so-called elite with which the impact of the alliance is interrupted if the knowledge of the experts has not prevented the deterioration of the conditions of life we ask the citizens if there is no doubt then what is the use the reaction is that of releasing the experts but releasing the experts would not imply an authentic expression and realization of the objective rights this refute is more similar to a form of dishonor from the community and from the duties it represents almost every individual integrated, alone solitary, self-referential and legitimate to a kind of individual autarchy individualist from the status of the crisis if there are no objective data if no one knows the author if we do not trust the doctors who take care of the teachers of our children if we do not trust science and let us convince that in ignorance there is a kind of innocence of genuine purity then we are really in danger it is not a perception without what we call culture it is not possible some freedom until a few phases it would have been trivial to say it but today unfortunately it is no longer today it is indispensable if the world is not doing well and we want to change it even more we have to know it without knowing it we cannot even imagine changing it knowing it means for me to have the courage to face the complexity and to try to decipher it to manage it in the attempt to understand it it means to face the contradictions the ambivalence the difficulty of the coexistence between people which is always complicated because complicated are the human beings for example they live as if they were dead and because the research of happiness direct inalienable of each is against with the caduce of existence and above all the happiness of others is linked try to put yourself in the pain of others it is the fundamental theme for me I write because writing is a way to put myself in the pain of others only through the others it is possible to understand yourself it is worth for anyone not only for the writers maybe it will seem frustrating to work with the books and for the books considered by TISTA on reading in our country in 2017 only 41% of the subjects over 6 years read at least a book for non-study professional purposes yet I realize that books are central for everyone's life think about it at some point in time it coincides with humanity books have been the way in which our story is built the way in which we have preserved memory the tool through which we have been able to reach the knowledge and transmit it develop a critical spirit learn about civility, distance in time and space reflect on the conflict trust in the knowledge please listen to the path you have made so far cultivate doubts feel the lack of knowledge don't lose the curiosity that usually accompanies youth don't darken the desire to explore to deepen, to understand what seems incomprehensible to you don't be ashamed to want to know don't believe that in not knowing there is a form of innocence in ignorance the risk of becoming victims and the story teaches that often to be victims can transform us into hit the people you have as the last end always the people the more you will make you condition the knowledge of the story the value of memory the more you will renounce the easy answers and you will force you to consider the plurality of visions and to verify the sources and you will suffer the fatigue and the humility of understanding the more you will be interested in the research of happiness respecting the happiness of others the more you will be free and that's why you are here today that you have studied and that you are the laureates to try to be free Auri the director teaches Rosalia the pen of the University of Siena now on the stage the president of the association I am a student of Dr. Cizia Angeli good evening to all of you present in this square today was an extraordinary day very long but undoubtedly so rich of emotions that we will not forget to you laureates to you laureates welcome to the students of our university and also a special welcome to Piero Angela and for us a great honor to be able to honor among our students it is always a joy to see you on this stage to remove the parchment the recognition of the commitment of these years living and studying in one of the oldest Athenians in the world you know that many Italian universities are among the oldest also for this reason you have and we have a great responsibility towards those who have believed before us in the importance of knowledge in the role of knowledge in the foundation of culture today in this square one of the most beautiful squares in the world you are the protagonists you are the ones who will have to make sure that as much as you have taken in the halls and in the laboratories guide your future our future at the beginning of this afternoon we have given you we have given you we have given you a book with a sentence from Seneca we can not direct the wind but we can orient the winds from Velista I can not but underline the strength of these words I wish you with all my heart that your winds are always oriented to reach the pre-select destination and to orient the winds I assure you, you need preparation you can not improvise because the risk that you run is not only to navigate slower but to not arrive in the radius of your dreams I wrote it to Leonardo da Vinci those who fall in love of practice without science are like the knocker who enters the ship without a kiss who is never sure where to go adjust the winds, you know read the wind carefully and you will realize your dreams prepare yourself always put yourself in a discussion in a world in a continuous change how did Rosella Possorino excellent student of ours thank you Rosella for accepting the invitation of our reader thank you for your work for your books for the beauty you give today during your intervention you remembered the privilege of academic studies a privilege even greater for us who had the possibility to study in this university a urban field in the heart of Italy rich history, culture, tradition innovation and passion a period and a city Siena that will remain in your hearts and that will bring you back to try to revive the years just passed the association Siena Lungni was born from this deep bond with the university with the city who pushed so many of us to come back to meet new friends, colleagues, teachers but above all to bring their own contribution as to Lungni to give, to forgive after receiving a lot from this tenet knowledge, knowledge relationships it's already been five years since the association and I can't thank once again the director Francesco Frati and his predecessor Professor Angelo Riccaboni for having firmly wanted his birth to have promoted and supported his development today we are more than 11000 and many are the programs and initiatives launched to make Siena Lungni a positive force for the tenet for society as allow me to remind you the appointment of April to prepare for the birth connections the depth on the transversal moments of sharing and reflection and then the mentoring program the first in a public university and the encounter for the development of useful skills for the world of work activity, encounters resi possible thanks to many of you present in this square students, teachers and students who have shared their knowledge, their experiences their network and who have invested in their time in English this concept is expressed very well by the words give back restitue give back part of how it was received and we as students can really restitue a lot and if as written by Albert Einstein the value of a person resides in what he is capable to give and not in what he is capable to take in these five years I met people of great value thanks to all of you who have allowed the association to live and to grow also in this time I tried to give to share what I took during my training and perfected with my professional experience it had to be a circle that closed but for sure that is not so and that is not so the circle is not closed the circle has become a spiral that moves towards the outside that finds new energy and that continues to its movement because in our Athenaeo we are never allowed to receive I continue to receive a lot even from the Moon I receive the smiles of the students that are on their way the enthusiasm from the new projects of the association with solid bonds I create new friendships and I learn a lot perhaps just as Gaten said you want to live happy travel with two bags one to give the other to receive and about the two bags some months ago we launched the first crowdfunding the first received funds for a good cause a campaign to offer a prize of study in the memory of Mark the student was born prematurely a year ago and he was recognized an aposthoma laureate during the last graduation day a campaign was born to give to all of us the history of Mark the great participation and the involvement of the academic community the many messages and the divisions represent much more than what we have given another project of how the students can be a connection between generations between university and society I conclude by inviting you all to become active part of our network we need everyone to continue the virtual spiral and to build together a future rich of opportunities and beauty as Rosella reminded us thanks to the great reader Piero Angela, Rosella Posterino the board of directors and the group of communications of the association the society UBS and USOPS the university of Siena with the people who can contribute to strengthen our network in particular Marta Moschini and all the students positive strength of our team see you in the evening to celebrate this extraordinary day and from the 22.30 there will be the graduation day bon vento and a great future thanks send to the Pergamena the study title to Marka Fionbontosu the director to give the reading of the Pergamena for the public proclamation which will follow the traditional launch of the touch we Franciscus Frati Sinarum University Studiorum Magnificus Rector we declare post moda commemoravimus at gradum doctoris es edmisus ano septingen tesimo septuagesimo sceptimo a studio generali senensi instituto viva all university grazie a tutti Participato al graduation day di university


Life has many surprises and sometimes the only way to pull through is by learning ahead and understanding some basic principles. Why people try to learn from others? According to Lada's blog, life is a continuous learning experience. Throughout our lives, we keep rising and falling, picking up important lessons along the way. Some of these lessons come from experience, yet there are others that will learn watching others or reading in books for example. No matter how much we learn from the books, there is a significant difference between practical and theoretical experience. In today's video, I am going to share with you 12 lessons in life you need to learn. They can guide you on your journey towards success. If you are new here, consider subscribing to our channel for more awesome videos such as this one. 1. Time is life One of the major things you will learn as you grow older is that time is life. People underestimate how much they can attain over time and they often end up without a lot of achievements. Start a business today. Start that trip you have always wanted and it will all sort itself out in time. The courage to do what needs to be done on time is perhaps your single most valuable pass a young person. What are you waiting for? Time is very valuable and should not be wasted pursuing things that don't matter.  The only way you can get your dream job is by resigning from your current one. Indeed, you may not be certain but what you can be certain of is that you will never do better unless you take the chance. 2. You can't please everyone The world cannot be satisfied with anything because it is comprised of many people and people do not often agree on things or hold similar views at the same time. Trying to please them is simply impossible. Even God doesn't please everyone. Always trying to do this is not a good thing. According to Psych Central, people please us yearn for outside validation. Their personal feelings of security and often confidence is based on getting the approval of others. If you always try to please others, you will likely lose yourself. People can be greedy. They will take and take from you until there is nothing left. The only way to survive and be happy is to put yourself first. This may not sound like it is a good thing but trust me, it is. Imagine getting depressed over other people's issues when you have a life, dreams and aspirations you are not working on. No one owes you anything. Even if you help them, it doesn't place them under a legal obligation to help you in time when you are in need. Look out for yourself and you will end up happier. 3. Value people who appreciate you and quit hero worshipping. It is cruel work and will need as many people as we can get. If you have friends, hold on to them. If you don't, try and make some. Stop following people who treat you like trash because you think they are important people. Someone who gives you their homework to do over the weekend while they go to have fun is not your friend. Someone who only calls you to ask for a favor and never calls back when you call him is not your friend. You need to value your time more. Spend them studying and becoming better at your areas of interest or just imagining your future. It is far more profitable. 4. Define your principles early. What type of person do you want to be? The type that will listen to everyone or the type that is sure of everything and where they are going, every serious person will have a set of principles that will guide them. These principles can span across several areas of their lives. They may have principles relating to their health. They may have principles. They may for example not eat after 6pm every day. When it relates to their career, they may for example publish one paper a month on an area of interest. Every year, they are sure of at least one publication. People who are this principle seldom miss out on their targets. Let your principles guide you. It helps you to stay on track. 5. Identify your priorities. What do you want from life? Setting your priorities requires asking yourself deep questions that give you clarity. You don't have an infinite amount of time. You must therefore focus on the things that truly matter. According to Chinese Hong Kong American actor Bruce Lee, it is not a daily increase but a daily decrease. Huck away are the in essentials. If you have figured out you want to become a judge, you will start working towards getting a law degree. This applies to any career part at all you might be considering. Don't allow friends to distract you from your goals. If you are a highly sensitive person, always ask your friends this, do you value your career more than you value making your friends happy? If your answer is yes, you have to prioritize it. If your answer is no, perhaps you need lessons in saying no. If you never say no, people will always try to exploit you. One of the surest parts of freedom from stress is learning how to say no. The more you can say no to things that benefit you in no way, the better you can prioritize the things that truly matter. 6. Leave to leave a legacy. What do you want to be remembered for? Do you desire to be remembered as someone unable to leave out his dreams or someone who excelled in your area of interest? Many of the times young people live their lives recklessly without thinking of the future. If you want to be president, you have to be willing to make sacrifices now to achieve your goals. Your conduct should reflect your intentions even from a young age. You should maybe volunteer while your mates play video games and maybe join the military or become a lawyer. Don't joke with your legacy. It is all you will leave behind when you are no more. 7. Your network is your net worth. What kind of company do you keep? Do you think it matters? According to Forbes, networking is not only about trading information but also serves as an avenue to create long-term relationships with mutual benefits. Your network is not about how many friends or acquaintances one has. Some of us have hundreds. It is more about people you develop strategic process relationships with. The greater the process relationships, you are not the better your career prospects. 8. To be financially free, build a business or have multiple investments or streams of income. To be financially free, build a business or have multiple investments or streams of income. Although people have a lot of regrets, a common one is the fact that they wish they had a business. They had businesses they built in their youth. When you are young, it is the time you can afford mistakes. You can afford to start all over, to go for the things you want with everything you have got. This is not the case when you are older. Everyone wants to be rich or at least wishes it. Start on time to plan your finances. It is a lesson you don't want to learn the hard way. 9. Leave a little and make beautiful memories. Make our time to admire the world. Walking all the time will not let you leave. Travel to those countries you have always wanted to visit. Watch the sunset. Share memories with loved ones and smile. The world is such a beautiful place when you make time to see it. We are ultimately all we have. Make time to be with yourself. You can seat in a garden and just smell roses or take a walk. Enjoy the warm breeze on your skin and stretch out your palm when it rains. If you don't do it now, you may never do it. 10. It's okay not to have it all figured out, just take action. The lesson of action is one that a whole lot of people still haven't learned. The more action they take, the closer they get to accomplish their objective. Have you ever spent an entire week wondering what will happen if you did something? Well, here's a solution. Just do it. The more you think about the problem, the less likely you become to take action. Most problems are solved by taking action. This is after all how ideas are refined from working on them. Take action always. 11. Happiness lies within, not with others. No one can make you happy, not even if they love you and are with you. You alone can make you happy by choosing to be happy. When you hinge your happiness on people, if they leave you, they take your happiness with them. Happiness is not and should not be the function of the happening or absence of something or someone. It makes happiness fragile. You need to choose to be free. Look inwards. What are your greatest desires? Once you identify them, put them aside and admire yourself. Learn to enjoy your own company and smile when no one is there. It makes it easier to deal with the world. 12. Artigate is everything. This is perhaps the most important lesson of all. How you perceive something changes everything about it. If you see yourself as a failure, for not passing a test, you will feel bad. On the other hand, if you see tests as events, you will recognize that you did not pass the test, but you will likely not feel bad about it. Embrace as much of these lessons as you can. They will help you as you progress in life.


Well, I've got this far, okay, all right, it's a little peak at this now I'm sort of a little bit worried. I've got those two wires in there. I've not actually I don't think connected to this end yet. I'm gonna connect these wires in and I've just had to fix that bloody thing because the Nothing in there somehow bent over and so it wouldn't shut down And right, so I'm gonna go figure out what I'm gonna plug this in and we can see what happens I'm just gonna see we can get some sort of buzz or something off it Don't bring my light down That's gonna be to the camera And then I was putting these together, I forgot that I was gonna need to put the These wires in It's a little bit I know you haven't got the best view or anything, but So you're not really missing much Put this in the ground So what we want is we want some buzzing noise Both speakers, but one speaker or the other speaker. That's not so hot enough this side Once it could be the kitchen's here Let's try it again. I've only got one side even though Saying that I say there's only one side, but that makes a buzz and that goes pop when I disconnect the power. Okay That one buzzes and that one over there. There's a little pop when I take Disconnect the power So we have got a connection, but it might be One of these not so good. There's a possibility this wants to do with these Connectors because they're not the greatest pushed in on these boards But I'll tell you what I'm gonna do. I'm gonna plug my laptop into it. Let's see what happens I don't think this through though. I'll do like this here is there. I have to do this on a laptop space in a way And then wonder if it can actually Put it in here. There could be a problem with one of these on here as well Let's see if I can Do this like this Move everything up a little bit. I wonder if it will go. I suppose it's not gonna go very far with something like this I should have probably prepared a bit better shouldn't I? There you go. This is all part and parcel of it. Just put that way there Something with the front up.  Let's plug it in If anything else we should get one channel. Probably that's a bridge rectifier Easy bridge work. Probably want to keep that out of the way, don't we? So here we go. We've got my trusty laptops kicked in And all we're gonna do now is just put a little bit of music out and we'll see what happens I know it's not the greatest viewpoint, but let's just see if it works I just gotta find some music out here Just give me a second. I've got something easy to get to No, that's about right, isn't it? Oh, hold on a second. Where's that? Where's that chip? I'm pretty sure there's a chip or some music in it Right, I'm just gonna stomp the power onto this Here we go.  Very quiet on the channel Okay, I can't hear it out the other one, but it's very, very quiet So I'm just gonna disconnect that You know, disconnect it And I'll pull this out of here And I'll... Yeah, to plug into it, but I'm gonna see which channel's working and which channel's not If I plug it in here, so if we get nothing now And I know that on the side, but I can't hear anything But then this only plays in one channel anyway Because it's broken, that's why it's no good for doing this Um, no idea, but one... So it's probably just a bad connection because it was quiet It was really quiet, I've got the power off, haven't I? Yeah, there's not a lot of... I thought I had an okay resistor over I couldn't figure out where it would go Well, I've obviously got power to it, and that doesn't seem to be bad I wonder if I just play around with that a little bit It's all there, but what I don't want to happen is for metal to touch metal any of these connections Because that will be catastrophe And they're both new chips, so I'm expecting both to work as they should And I'm definitely plugged into the right holes I definitely have power as that output It's so difficult to tell whether these are actually in When trying to do that I should have done a bit further Not that it seems like it's moving at all, but down a bit further That one's in for the output I'll give it a go again like that, but now I might have to... Definitely seems like it's pushed in quite well I'll give you a bit of a better connection in there if that's possible These tweezers are rubbish It's no good if you can't put any pressure on, you know, to get into place Get your wires to go into place That's got a nice connection in there, so Maybe fingers crossed that might help Well, I know it should help them Maybe fingers crossed that might sort it out Let's give it a go There's a power on, and we can hear it making noise through the other Through the other channel That'd be good I've still only got one side I've only got this left-hand side See, but it makes a pop on that side, then I disconnect it It pops when I disconnect the power Yeah, I don't know, I'm gonna have to come back and Maybe take another peek at... Not the power side, should be okay, being powered by that I'll tell It's nearly there, it's nearly there I should be back in a bit, and hopefully it'll all be sorted


So I put up on the board over there a reference. I think, essentially, everything I covered in the first part is also covered in a nice survey paper by Ettinges, called Groups Acting on the Circle. It's a lovely little expository paper. It starts very gently and ends up very complicatedly. But in particular, it starts very gently. In L'Encinema Mathematique, and there are lots of beautiful mathematics contained in there. So I highly recommend. This second half is going to be somewhat disjoint. I will use some of what I talked about before, mostly the definition and properties of rotation number. But if you got lost, you can sort of start over right now. And because for the first half, I was talking about general properties. What can we prove about theorems generally about groups that act on the circle, or about particular homeomorphisms? Here I want to prove not a theorem about all the groups that act, and what do they have, but about a particular action of a particular group. So this is the advertised theorem about surface group automorphism acting on their boundary. And let me start by just describing this. So this is where we are. I want to just draw a different picture of what this action looks like. So some of you might know that if I take my surface and forget that it's fundamental group for the moment, I want to look at the mapping class group of the surface. But I also want to sort of see what happens to the fundamental group. So I'm going to fix a base point. I want things not just up to conjugation, but I want to fix a base point. So this star will be with a marked point. There's a map from mapping classes of homeomorphisms up to Ipsotopy to automorphisms of the fundamental group, where my fundamental group is now with this base point. This is, in fact, an isomorphism onto an index 2 subgroup. And the only reason it's index 2 is we look at mapping classes that preserve orientation. So this is an isomorphism, what do you do to the fundamental group, onto an index 2 subgroup, which I'll write as a plus. Sitting inside of here, I have inner automorphisms. That's isomorphic to the surface group itself, and that inclusion has quotient out. What is this surface group sitting inside the mapping class group? This is what's often called the point pushing subgroup. What do I mean by point push? Here's a piece of my surface, and I have a marked point. And one thing I could do is I could just take my finger. Here's something that's isotopically trivial if you didn't require me to fix that point at all times.  Or in other words, in this annulus, I'm going to do something that looks like a sort of a dain twist here and then a dain twist on the other side in the opposite direction. That will move this transverse curve before to the picture after where it goes like this. And that's my marked point. So I know maybe this was a closed curve you drew. So that was pushing around the curve gamma in pi 1, where gamma was this thing that I pushed my marked point around. It's a based curve. Yeah? Can you go as an example with an isotopically simple? Yep.  But I can tell you what the thing is, you do an isotope of your surface by pretending your surface is made of a very stretchy material and dragging your point along until it crosses over. So here, how would I point, push around?  But yeah, this is not what you want. So let's see if I, what would it look like to point, push around? I mean, so the point is that if you let's do a curve that maybe goes like this and then crosses itself and goes down there. I'll try and point, push around that. OK, so in my color scheme from before, I'm supposed to sort of point, push around like this in this neighborhood. OK, so I have my, now my base points over here. It's a new picture. And I had a transverse thing like this. OK. And oh, sorry, that's, if I'm going to go this way, I should be on this side of it. Sorry, I'll be, yeah, I'll be pushing it along. So I'm going to follow this loop, which will make this curve look like that. OK. And then I'm going to hit here, and I'll see this other piece that I was crossing. Right, so this will now get sort of moved along for the ride. I'll have to have nudged this over. And then maybe I'm crossing this image of a white thing again, and it will continue. OK, and then this whole tube of things will end up, this will get nudged up, and it'll end up sort of capping off over here with my point. OK, that will be the image of a transverse thing if I loop over myself. I'll do another picture, I'll do another picture slowly. We'll actually mostly care about the picture of what happens on simple closed curves. But the point is that if you do this point push, OK, so there's that white curve. And then I do another one, say, in this curve, in this direction. What will it do? It'll now pick up these two little white strands and move them around, both of them at the same time, and come back. And you'll see a doubled up picture of this one. So that's what I was trying to draw here. If you cross yourself, you see the two strands moved again. OK, so this is a famous inclusion here. And there's another easy to define map where you just forget that this point existed. OK, so any homeomorphism up to isotope of a surface where isotopies and the homeomorphism have to fix that point defines a homeomorphism up to isotope not fixing the point called forget that you had to fix the point. So that's a mapping class group. And this sequence is called the Berman exact sequence studied by Joan Berman. And the Dey-Nielsen-Barr theorem is what's telling you that these are isomorphisms. So this whole story is just to tell you that if you like mapping classes better than automorphisms of groups, there's a way to see this. And there's a way to see this boundary action on d plus pi 1 sigma g. And that says follows I could fix a hyperbolic structure on my surface. So now it's universal cover is the hyperbolic plane. And I can take the, say, the Poincare disk model for the hyperbolic plane as a universal cover. And I'm going to fix also I have my base point for pi 1, my marked point on the surface. I'm going to fix a particular lift of that. That star maybe I'll call this guy lift of star. If I have a homeomorphism of this surface, there is a unique lift of it to a homeomorphism of the universal cover that fixes if my homeomorphism fixes this point, there is a unique lift of it that fixes my chosen lift of the point. So if f of star equals star, there exists a unique lift to a homeomorphism of the hyperbolic plane fixing the lift of star. And this homeomorphism of the hyperbolic plane induces a homeomorphism of the boundary. And that map on the boundary depends only on this guy up to isotope fixing the point. So only on what f represents in the mapping class group. If I took some other thing that was isotopic to this, I could just lift that isotope. My isotope, because it came from downstairs on a compact surface, it's only going to move points of most distance 25 or something. It moves points of bounded distance. So up here, lifting the isotope, well, it'll move points around, but each point will move distance at most d, whatever the bound was. In this model, the metric makes distance d look smaller and smaller and smaller as you go to the boundary. So I will have moved no points on the boundary by performing this isotope. So that's why it depends only on the isotope class of this map. So what does this say? This gives you a way to lift mapping classes to homeomorphisms of the boundary of the hyperbolic plane. So this gives a map from the mapping class group your surface with a marked point to homeomorphisms. Here, if I preserve orientation, I'll preserve the orientation of the boundary of the hyperbolic plane, which is the circle. And under these usual identification, this is the same thing. This is the boundary of your group. If you want to think of your group as the translates of this point under deck transformations, it's a good way to sort of see that these two are the same action. So you may, as you prefer, think of this in either way. You want to put them both out there. This also sort of gives you a nice way to see what's happening with the push subgroup of pi 1. So you can see this directly from the group perspective. Or if you see what happens if I push this point around. OK, well, one way to do that is I could lift this push.  And it'll move this base point over to the next one. OK, well, that wasn't very good. That broke my rule. I was supposed to choose a lift that fixed the lift of my base point. OK, so that was the wrong one. I should now post-compose with a deck transformation that takes this back to there. What's that deck transformation? It's exactly, you know, this was the axis of that curve. That deck transformation is exactly, though its boundary action is the boundary action of that isometry coming from this deck transformation. So that's gamma. And here is its lift. The boundary action of the push subgroup is just the usual action by deck transformations. So I will record that for posterity here. OK, so you can think of that as the PSL, if you want. If you put your hyperbolic structure on your surface, you can think of that as coming from the usual subgroup, discrete subgroup of PSL to our defining your surface subgroup acting on the boundary of hyperbolic space. So here gamma is acting by translating along this axis. So on the boundary, it's got two fixed points and it's moving points. So in other words, the automorphism of the mapping class group, it's a much bigger group in which I see this surface subgroup acting on the boundary of hyperbolic space. And I want to talk about a question and its answer. So here is a question that was in a problems list called Problems on Mapping Class Groups written by Benson and Farb in I think 2006. So he asked, here is a group and a very natural sort of coming from geometry action of this group on a space. It's the boundary of the group. Is this the only way this group acts on its space? So here's the question. Suppose you have an embedding, a faithful action of this group on the circle. So I'll call this homomorphism, if you will, from this group to the group of homeomorphisms of the circle. Now, yeah, if you wanted this to be injective, so a faithful action, the question is, is this the only one there is? So is rho necessarily conjugate to this thing I described here? Let's call it the standard boundary action. So that is the statement of the question. Maybe this group has a remarkable property that it only acts on the circle in one way. So this statement needs an edit that I think is just a typo. You can do something silly to any group acting on the circle. And this is not just conjugacy, but something called semi-conjugacy. Jair Minsky's picture of replacing an irrational rotation with this thing where you thicken some points and whatever and you get something that's no longer an irrational rotation, there's an invariant canter set, is an example of a semi-conjugacy. In general, you can imagine a picture where if you have a countable group acting on the circle and you look at the orbit of a point and just enumerate this orbit, OK? I don't know, x1, x2, x3, whatever. You replace point xi in your circle with a little interval of length, I know, 1 over 2 to the i. That'll give you a bigger circle, diameter 1 bigger, OK? And it tells you how your group is still supposed to act. You permute these intervals, just as you were moving the point. Move 1 to the x by the unique affine map. That'll give you an action that's not necessarily conjugate to the original one. If the original one had dense orbits, now this one is in case 3 where there's no longer all orbits dense, I have this interval that goes along forming the complement of something that will look like a canter set. So there's a trick that you could do called semi-conjugating that I don't want to worry about too much, but it's how you move between the canter set picture and the non-canter set picture. You can go back and forth. But if you don't like that picture, you can sort of think conjugate without moving too much of the spirit. And the reason I want to gloss over that part is I want to spend this lecture telling you the answer to the question, because it's a good way to showcase some different tools. The answer is a theorem that I proved with Maxime Wolff last year. Yes, and in fact, even better than this. Any action of this group on the circle is semi-conjugate, the best you can hope for, to the picture we just saw, the boundary action. It looks as best as you can like the group acting on its boundary, or is trivial, where trivial means literally trivial if genus is at least 3. And there is another silly way you could be trivial in genus 2, when g equals 2, the abelianization of this group is a finite cyclic group. It's a Z mod 10 Z. It happens to be, I think that's a theorem of Bermann. So you could map to the abelianization, and then you're like a cyclic group of order 10. You could act by a rotation. So for g equals 2 can factor a non-trivial to show that the abelianization is that. So yeah, so this theorem says that it's either injective or it's badly, badly non-injective. It's trivial, or factors through a finite group. And I want to just spend this whole time sort of outlining all the steps in the proof, because it shows you how to use a bunch of the basic techniques that we used before. This is one of those things where you prove a theorem and you find a very complicated way to do it. And you're like, yes, we answered a hard question with a hard proof. And then you're like, well, that step could be easier.   And then you're like, well, what about step two? Oh, actually, that wasn't so bad either. And at the end, it's something that is, I think, appropriate for this mini-course and a good way to teach people about how to understand groups that act on the circle. OK, so let's prove it. I mean, the point is you don't need them to know a lot to get started. What do we have? I have a mystery action of a group on the circle. And I want to show that it's not so mysterious. It's either extremely boring, or it's one that we can understand as much as we want. It's group acting on its boundary. So that's my setup. Suppose, and I'm going to assume the genus is at least three, so I don't have to worry about two different cases. I'll point my finger at the one place at the very end where we're going to actually use that assumption. So I'll assume genus at least three, but I don't need to use that until the end. And I have some mystery action of this automorphism group on the circle. And the goal of the first two parts here, the first part, is OK, well, this group is big and complicated, but there's something I know that sits inside it. There's that inner automorphism group. There's the surface subgroups. And I know very well what I'm aiming to show that action looks like. I want to prove this theorem. I want to prove that it's either the usual deck transformation action, it's looking like that, or it's totally trivial. So let's study the surface subgroup first. So the restriction of rho to my surface group, that's the inner automorphism subgroup. And what I need to prove some facts about this that show it looks either like it's trivial or it's like the usual one. Well, one property shared both by the completely trivial everyone's the identity action and the usual boundary action is that these push or deck transformation, they all have fixed points. In PSL2R, they're all hyperbolic transformations. And in the trivial action, they're trivial. So our first lemma is to say that, hey, that's true even under the mystery one. And how do I say something has a fixed point? Well, it's a fact that you have fixed point if and only if the rotation number is 0. So that rotation number we defined before picks out whether points move at all or not. So lemma 1 is that if, let's do it for nice curves, if gamma in pi 1 sigma g represents non-separating. So I don't want it to cut my surface in half. Simple closed curve. Gamma's supposed to act on the circle in some way. That's some homeomorphism of the circle. Well, lemma says its rotation number is 0. That's certainly true for things that do nothing and for hyperbolic, for the usual boundary action. OK, prove the lemma by looking at what happens in the mapping class group. So this is where I need to use this picture. In the mapping class group, gamma, my push around gamma. Oh, good, this was the nice picture where it's a non-separating simple closed curve. OK, I'll draw another version of it here. So there's my gamma. And the thing that's supported on this annulus and takes this white curve here, the one that just goes around, the one I drew, is equal to the composition of two drain twists, a usual drain twist in this curve on this side of my mark point, and then a drain twist in the opposite direction in this curve. A usual drain twist in this curve takes this arc to something that looks like up, right? And then one going the opposite way will take the other half of this arc to one that looks like the mirror image of this, so like this around and then here. And that's exactly the picture I had drawn there. OK, so the point is that I can write gamma in the mapping class group, which is the automorphism group of my surface group, as the composition of two drain twists, let's call it twist one, and twist two, where the direction of twist two is the opposite. OK, so I'll pretend twist two is going the usual way, but I'll write it with an inverse. And in the mapping class group, these drain twists around simple non-separating simple closed curves are conjugate. Where T1 conjugate to tau two. OK, so now here's where I just want to use facts about rotation numbers. So these are conjugate. Oh, and there's, I guess, another fact I want to use. These are supported on disjoint little annuali, right? My two blue curves didn't cross. So from what we know about mapping class groups is that T1 and tau two commute. OK, so now let's try and study what this looks like for rotation numbers. So that means rho of gamma is rho of T1, T2 inverse, which is rho of T1, rho of T2 is a group action composed with rho of T2 inverse. Great. And so the rotation number of this circle homeomorphism is equal to the rotation number of these because they're the same thing. Oh, but they commute. And rotation number is a homeomorphism on a billion subgroups exercise. So this is the sum of these two. Well, I don't know why I switched to a color. And this is a group action. So this is a homeomorphism or representation so I can put the inverse out there. Oh, and homogeneity of rotation number means the rotation number of the inverse of something is the minus of its rotation number. So I can take this minus and move it over here. So that was homogeneity. And now what else do I have? Oh, I have conjugacy invariance that was also on my list of properties that follows easily from the definition. So this number and this number are equal because these two elements are conjugate. They're conjugated groups, so in particular, they're conjugated as homeomorphisms of the circle. So this is 0. They just completely cancel by conjugacy and variance. And that's the proof of the level. So just by using things I know about rotation number and mapping class groups, we already have a good step along the way to this looks like how it should. This argument doesn't work because your Dane twist won't be conjugate. And I don't need to know that yet. So I mean, the answer is yes, because the theorem is true. But I don't have a three-line argument that does it. OK, great. Next, Lama. So I'm sneaking this in because I wanted to define a very important tool in studying groups acting on the circle. And this is the bounded Euler class. And I'm going to give you a very hands-on definition of what this is. So let me state step number 2, or Lama 2, which is another statement that's going to say in a fancy way that this has some property either in common with the trivial action or the usual boundary one. So I'll use a word we haven't defined yet. The Euler number, this action of a surface group, is either 0. This is what the trivial action would give you, or up to sign the Euler characteristic of your surface, 2g minus 2. This is what the usual boundary action would have. And now I'll tell you what this Euler number means. So postpone proof for a definition. And I'm going to give you not the usual definition. Even if you've heard this word before, you may have not heard it. But what I particularly like, and actually I learned it out of this way of thinking of it, out of a paper of Anna Wienhardt on the higher-tech Euler theory of all things, where they study actions of surface groups. So I'm sure other people have shared this perspective. But that's where I happen to learn it. OK. So this definition is for an arbitrary action of a surface group on the circle. Suppose I forget I was this row from before. I just sum up row action of a surface group on the circle. All right. I'm going to take a pants decomposition of my surface. Just pick anyone you want for now. And I'm going to say, what does each pant contribute?  So for a pant, here's my pants. So there's my pair of pants. Its boundary curves represent elements of the fundamental group. And if my base point was in here going around this, shoot, I should orient this this way. So it's the induced orientation from my surface from the pants. So this is like a curve that goes like this and comes back. And this boundary is like a curve that goes like this and comes back. Let's call this guy A, this guy B. And then my induced orientation here is this way, right? Yes. And so this last boundary component, I'm just trying to write its boundary as elements of the fundamental group if my base point were here. This boundary component is now going to be what I should do, B inverse followed by A inverse. I'll write it like function composition. OK. So those are its boundary components. And the Euler number for the pant is going to measure how badly rotation number fails to be a homomorphism on this pant. OK. Sorry, I don't understand your picture. So you're right here. Yes. So I have my pants on the surface. And I just want to, here's my pants. I just want to say, forget I drew a base point. I want to say, what are the boundaries of my pant in the fundamental group? OK, so if this is A and that's B, that's A inverse times B inverse.  I'm slow, and I always get orientation wrong. So I was just drawing it very carefully. But the information to record is that this is what I've written down. OK. So I'll steal some space over here. Actually, I guess I can go over to this board, lots of space. I want to measure how much rotation number is not a homomorphism on the pant. So the Euler number, the pant part, P of rho, I define to be the rotation number of the action of A plus the rotation number of the action of B minus, sorry, I'm just going to sum over all the boundaries, plus the rotation number of rho B composed with rho. So I want literally that boundary on A inverse, rho B inverse. And if you like, if it's nicer to you to understand it this way, this is the inverse of B composed with A. So this you could think of as minus rotation number of rho B composed with rho A, if you liked. What is this independent of the choice of pants? Well, I haven't even told you that you have to sum them up yet. But yes, OK, that's one of your exercises, is to show by elementary pants moves that my definition is going to be independent of choice of pants. All right, but there's another problem I have to fix here. These are all things mod Z, and I actually want to get a real number. So I'm going to just lift these like we did to the line and take their lifted rotation numbers. And so then I'll take the lift of this. I'll take its inverse. I'll take the lift I chose. I'll take the inverse of that. And I'll look at this composition. And here it's easy to check on this level that the number you get here is independent of choice of lifts. If I move this by an integer translation, I change its inverse by an integer translation in the opposite direction. So I would add one and I'd minus one. So this thing I've got is well-defined. And this, up to mod Z, is measuring the failure of this guy to be a homomorphism. So this is no longer part of the definition. OK, and so then here's the part that you're like, why is this not depending on pants? I define the Euler number of rho to be sum over all P in my pants decomposition of the contribution from the pant. And exercise doable by changing pants one at a time is this is independent of the pants decomposition. And if you don't like that, there's another exercise which has proved that this is the same as this other number. And the other number, it has no reference to pants whatsoever. It was something you could just sort of produce out of nowhere. OK, but here is a very concrete thing that I like this version because it's very concrete. You can choose whichever pants decomposition you like. And you're just looking at rotation numbers of some nice simple closed curves. And a fact that comes out of the quasi-morphism property I said, OK, so this was actually basically on our list of properties before, so that this number is bounded in absolute value by one. This is a property I called before, called quasi-morphism. And if you prevent me a second of digression, this actually, this statement, what I called fact, is really part of a famous theorem in mathematics. This is the Milner-Wood inequality.  And it boils down to this observation once you frame everything in the right way. That is just to say that there's some kind of interesting math hidden in here. OK, so let's see what I can extract. Let's go back. So I gave you all the definitions. It was just a statement about rotation numbers that added up. And the claim is that this is either zero or this Euler characteristic looking thing. So let's prove the lemma. And at least to sketch it.  And I'm going to choose one that looks like this, like a really nice looking one. This is my surface. I'll draw it in kind of a round way. And I'll put pants curves like this. So then all my pants look the same. There's like a rotation or like a reflection that moves one to the other. In fact, you can prove that even in the based mapping class group, there is something that takes the triple of curves bounding one of these pants to any other one of these pants triples. So my mapping class group moves these around. And you see I also cooked it up so that all of the boundaries are non-separating simple closed curves. So we're going to pick this pants decomposition. Pick these peas. Now what do I know if I try and understand the Euler number of one of these pants? OK, it's a sum of rotation numbers. I knew something about rotation numbers. That was from lemma 1. If I have non-separating simple closed curves, then they get the number 0. So their lifts are, I don't know, they're some integers. Everything is just like 0 mod z. All right, so that's great. This is something that's 0 mod z. So that's 0 mod z by lemma 1. And our fact, or what I said with some famous theorem called the Milnerwood inequality, says that this number that's 0 mod z, there's only three options. It's 1 or minus 1 or 0. So it's actually equal to 1 or plus or minus 1 or 0 by the clausomorphism fact. So that's something that's true for individual pants. And there's a little work to do, but the fact that I chose these all so that there was some element of some homeomorphism of your surface that I can think of as a mapping class or as an automorphism of pi 1 that took any one of these pants to any one of the other ones, like if I want to go through there, I should just rotate the whole thing around like this. Tells me that these are the same. I get the same number on each pair of pants. Conjugating by that homeomorphism tells me that I should conjugate rotation numbers and they don't change. So every pant here can be taken to every other by an automorphism or a mapping class. And rotation number is conjugacy invariant. So you get the same value. All right, so I'm just summing up the same number how many times, how many pants in a pants decomposition? 2g minus 2 many. So I get 0 times 2g minus 2 or plus minus 1 times 2g minus 2 for the total. These boards a little bit. Great. OK, so we sort of accomplished our first goal here, which was studying what happens with the surface group. That was still a setup for my proof. OK, so the reason this Euler number, I just told you some recipe that you don't even believe me is well-defined because it depends on the pants composition, except I swore to you that you didn't. This number that takes an action of a group on the circle, the surface group, mind you, and spits out a number, is an amazingly rich invariant. And here's one theorem that I'm going to quote that tells you how much it just knows. OK. So if we're in the case where the surface group, the Euler number of your action of the surface group, the one I was thinking of, one we had, but this is true for any action of a surface group, if it agrees with the Euler characteristic of your surface, it turns out that's as big as it can possibly be, then there is a theorem. So maybe I should state this is the theorem, and this is due to Matsumoto, Shiginori Matsumoto from about 1990, I want to say. He proved that this number tells you what the action looks like in the case where it is the Euler characteristic. Then this action is, you guessed it, the standard boundary action. So it is semi-conjugate to the usual.  And he uses kind of ping-pong-ish arguments to say that when I had elements of my fundamental group that corresponded to curves in your surface that crossed and played ping-pong, then the fact that this number is really big means that they'd have to play ping-pong on the surface. And so it's like they had crossed axes. And he sort of rebuilds the surface out of this. It's a beautiful theorem. But I'm just going to quote it and be like, look, in half the cases were basically already done. So it's not super hard to go from this. This is the surface group. This is the inner automorphisms. It's a normal subgroup using the fact is a normal subgroup in my automorphism group. It's easy to show that if this guy's acting in the usual way, then actually the whole group has to come along for the ride and be acting in the usual way too. All of row, not just the restriction to this normal subgroup, but the whole thing is the usual boundary action. And for a minute that it was actually genuinely conjugate, not semi-conjugate, then this means that everyone in pi1 sigma g is acting with sourcing dynamics with an attracting fixed point and a repelling fixed point. Automorphisms of the group have to, an automorphism will send some element of a fundamental group to another one. So I know where this point, where it's attracting point went. It went to the attracting point of its image under that automorphism. That's enough to determine what you do, I guess, on a dense set, all of the attracting points. So that determines what your whole action is. And that's the kind of argument you use here. OK, so we just won. OK, so we only have one more thing to do, and then we proved the whole theorem. We want to know that if I get zero, then my action is trivial. We have the Euler number. And for this, I'm just going to enlarge my surface group a little bit. My surface subgroup, the inner automorphisms, sits in a finite index subgroup of some slightly bigger group of automorphisms, which I can realize as the fundamental group of a hyperbolic orbifold, if you like. And specifically for this, I'm going to study instead, a subgroup that I'll call delta. Claim there's one that has the following presentation. It's going to look like the fundamental group of something that's a sphere with four cone points. So I'm going to get all geometric topology on you for a second, so hang on for the ride. Order 2, 2, 2, and 2g. If that doesn't mean anything to you, I'm going to write down a presentation for it. So this is generated by four things, where a squared equals b squared equals c squared equals d to the 2g equals the product of all of them. And these are all just trivial. Those are your relations. So this, you can show, sits in this automorphism group. You can think of it as coming from special finite order symmetries of your surface if you write your surface in a particularly nice geometric way. And it really is a finite extension of the surface group. It contains the surface group with finite index. You can write a surjection of this group to the dihedral group with 4g elements that has as kernel a surface subgroup. So this is one way to show that you can realize this group is a group of automorphisms. I can write down exactly what this surjection is, but I don't know if it's super enlightening. I need to send a to some element of order 2. So if my dihedral groups generated by an s and an r, this is going to s. This order 2g1 is going to r.  So you can press me to write down exactly this before. But trust me, we've worked out the details. This contains a surface subgroup with finite index. And the point is that groups of this form also get Euler numbers. And the Euler number is multiplicative under covers. If you're good at Orbefolds and Orbefold fundamental groups, this is a sphere with four special points. So its fundamental group has a and b and c and d are corresponding to loops around these points. I can make a pants decomposition of this sky by slicing it like here and use the same kind of recipe to get an Euler number. So if you don't like that explanation, you can just accept this fact that Euler number applies with the same kind of formula to actions of these kind of groups too. And we'll take a value here is a multiple given by the index of the Euler number on the surface group. Now rotation number definition just tells you that it is, if I think of these as my pants and loops around these as my generators, then it's going to be of the form rotation number of row A plus rotation number of row B. That's for like two of the pants. And then here's where they match up. So I'll get a rotation number of row of C and a rotation number of row of D. And I didn't take any lifts or anything. So this is just like plus some integer is the best I can say. But it's always of this kind of form. It is of the form from the same kind of definition. Great. OK, so let's see. I know some things about these guys. Namely, this is order 2, and that's order 2, and that's order 2. And so these all have to look like literally rotations of order 2. So this, let's circle with the color, this, and this, and this are all elements. They're all half integers. OK, or maybe they're 0 or whatever, but they're all in half z. And I guess this one is 2. It's an integer, it's also in half z. So the only way that this guy is supposed to be a multiple of this, what I mean in the remaining case, with this guy, this is supposed to be 0. I know that 0 is equal to some half integer plus, I guess, the rotation number of row of D, whatever that's doing. Well, this implies that the rotation number of row of D must also be a half integer. And since D was finite order, it's acting by some finite order homeomorphism of the circle. Those are all rotations. So if it looks like a rotation with rotation number, some multiple of a half, it's either an order 2 rotation or it's trivial. But in particular, if I do it twice, I'll have done nothing. So using the fact that I know I'm finite order, this improves me to I'm actually an order 2. And now we're done by the finaling fun exercise. Basically every finite order mapping class, like D squared, for example, here or finite order automorphism of a service group, here D squared is finite order, it's order g. It normally generates the whole mapping class group or automorphism group. Here's your end of the proof exercise. D squared, it's normal closure or it normally generates odd or you can write mapping class. Maybe I'll write mapping class because it's more suggestive for how I think about proving it. So what did I find? I found something that normally generates the whole guy in the kernel of my action row. So the whole thing must just be trivial. And that is how you end the proof, modulo exercise. All right, so that was a lot. But I wanted to sort of outline how one goes about proving a whole theorem using some of these techniques, like rotation number. And this particular exercise is not on your sheet because it's about mapping classes, not about circle homeomorphisms. But if you like mapping classes better than that, I won't be offended if you decide to prove this one. Thank you.