 Good evening everyone. So I'm Emmanuel Ulmo, the director of IHS and so I would like to first welcome you and it's a pleasure to host you tonight. So we are very pleased to organize this conference in association with the Foundation Mathématiques Jacques Adamard. In fact, organizing a conference together at this time of a year to celebrate women in mathematics has become our beautiful tradition, and I hope we will do this for over editions. We are doing it today just a few days away from May 12th, which has been chosen by the Committee for Women in Mathematics to celebrate women's mathematicians. This date was chosen because May 12th is the anniversary day of Myahia Mirzakani, who was the first woman to receive a fifth medal in 2014 and who passed away in 2017, sadly. So celebrating women in mathematics is a way to show younger generations that being women in mathematics is not only possible but can also be great fun. Today, we are happy to host some great examples of mathematicians who are passionate about what they do and who are very successful in their endeavors. So the wish to celebrate women in mathematics is one of our actions undertaken to face a major common problem. Women are still much underrepresented in mathematics, and that is true as well as IHS. During the past years, IHS has been monitoring the statistic of its visitors and members. There is considerable scope for improvements. Only 10% of researchers at IHS are women, a very low percentage, compared to the 20% that we currently see in permanent positions in France, both among CNRS researchers and university professors. The Institute has been working on improving these numbers and raising awareness on this issue, and there is still a long way to go to make mathematics and theoretical physics really inclusive and not just in regards to women. We are not alone in this process. These values are shared by our colleagues at University of Paris-Saclay, as well as the Foundation Mathématiques Jacques Adamard, who have already taken part in similar events promoting women in mathematics together with the Institute. So I would like to thank Pascal Massard, the director of FMJH, for his presence today, and for helping us making these events possible. Our organization has been supporting IHS in its goals to make the Institute a more diverse and inclusive place. IHS benefits from the support of several companies to fund the stay of women researchers. So I would like to thank Agilent Technologies and NG, several representatives from NG are present with us today. I believe. So on behalf of IHS, I'm delighted to greet you and to thank you for your support and for sharing our values. I would like also to greet Lord Arcos, senator of the ISN department. We are very honored to have you with us, among us, tonight. And now, before I leave a stage to Dmitri, I also want to thank our speakers, Natali Ayi and Natina Nikoka, for taking the time, along with their research, to advocate diversity in science. Thank you also to our master of ceremony, Veronica Fontini and Dmitri Ventrop, who are both postdocs at IHS. And they will be now coming. Dmitri, up to you. Thank you, Emmanuel, and good evening. My name is Dmitri Ventrop, and I'm a postdoctoral researcher at IHS, specializing in algebraic geometry and representation theory. I'm excited to be with you this evening to celebrate women in mathematics, and I'm very much looking forward to tonight's presentation. Events like this are very important and inspiring to me, as well as to my colleagues and collaborators. All of us involved in this presentation have different origins and different native languages. And as a result, and this is one of the many kinds of diversity that make mathematics research better. As a result, this event will take place partly in English and partly in French. We'll start with the English section and switch to French later on. Without further ado, I'm delighted to open this conference by introducing Nathalie Aïe, associate professor at Sorbonne University and the Jacques-Louis-Lion Laboratory. Nathalie Aïe is also the author of the popular podcast, Tête à Tête Charcheuse, which you'll learn more about later on. Her scientific interests are focused on partial differential equations, as well as stochastic partial differential equations, kinetic theory, and asymptotic preserving schemes, among other things. Nathalie Aïe holds a master's and a PhD degree in mathematics from Université de Nice. Nathalie Aïe is also one of 20 participants in the photo exhibition Mathématique Informatique avec elle that you may have already seen in the hall and that we invite you to discover after the conference. Thank you very much for the introduction and thank you very much for this invitation to this nice event that I'm very pleased and honored to be part of. Tonight I'm going to talk to you about some consideration about social dynamic models. Let me first start by introducing myself and then we will switch to science. First, I did a scientific baccalaureate in Orléans, where I'm from. Then I decided to go to class préparatoire, where my specialty were mathematics and physics. And then I get into the École Normale Supérieure of Lyon, so not by the competitive exam, but by applying, by sending a file. And once I was there, I got an opportunity to obtain a scholarship, so to do my first year in Lyon and my master in Nice. So this is how I arrived at Nice. I obtained the opportunity to do a PhD. And so when I did, I fell in love with research and I decided that that's what I want to try to do. So I tried to obtain a position. So first I obtained a temporary position at Inria-Rennes. I stayed there one year and then I did the competitive exam to obtain a permanent position. And I obtained one at Sorbonne University and I'm there since 2017. Okay, so let's move to science. Okay, so there is the idea. So okay, I'm going to talk to you about interacting particle systems. So first let me start in the context of gas dynamics, because actually this is my original background. When I started, the equation I was studying was in the context of statistical physics. For instance, in that room where there is a gas and the atmosphere is made of a huge amount of particles. And so one way of mobilizing it is to say that, well, the particle of the gas is sphere and they have a position and a velocity. And basically, as you can see on this video, well, they move in the direction of their velocity until they collide and when they do, they bounce. Okay, so this is one way of representing it. And the thing is, okay, so this is the video that I've shown you. This is words. So how do you do math on that? Well, you have to write an equation in that case and the type of equation that you will be interested are what we call differential equation. So basically you need the notion of derivative of a time. So actually all of you are familiar with this notion. For instance, if you're interested into the position of a time, the derivative of a time, it's nothing else than the velocity. So basically, if you know your position, your velocity, in one hour, you know where you will be. Okay, so this is a notion that we will be using in the following. Okay, so when I started, I was in the context of gas dynamics. But actually what might surprise you is what I've been showing you, the fact that you have particles who move and once they interact, it changes their behavior. It can also be, you can use the same approach to describe humans and humans interaction. And this is what I'm going to describe precisely today. So in the context that I'm going to talk about, and it's no longer the particles of your gas, but now it's the number of agents, the number of persons. And the quantity you will be interested in, it's the opinion of a person. So what we write as xi, it's nothing else than the opinion of agent i. So you are interested into how the opinion of a person evolves over the time. And so one quantity which will be important is what we call the interaction coefficient. So what is it? Basically what we denote aij, it's how the interaction, when j will interact with i, how it will impact the change of the opinion of i. Okay, so basically, now if you want to put that into an equation, well here is the derivative I was talking about which lets you know how your opinion will evolve over time. And now the equation that you are able to write here, well it's saying that basically when agent 1 will interact with agent i, it will make the opinion of agent i evolve. So, and this is through this interaction coefficient which is right here. So you are interested into binary interaction and so basically you do the same for all the agents. So agent 1 will impact the evolution of agent i with this interaction, the same for agent 2, the same for agent n. And so basically the fact that I'm summing over all the agents, this is summarized by these signs here which is just saying that, okay, I'm doing the same for all the agents. So basically this is the kind of equation we are interested in. And let me show you a particular case which is what we call the Excelman-Kraus dynamics. Well, it's the case where you are saying that your interaction coefficient has a particular form. It looks like that. And what does it mean? It means that basically you are saying that your interactions, they only depends on the distance between opinion. So for instance, you are just saying that, well, I decide that if two agents have two opinions which are too far away, they do not interact. Or for instance, if they discuss, it will not impact their opinion. It will not make it change, which makes sense. In real life, if you are discussing with a person which has opinion which are very too far away, you do not share any value, it's less likely that they will manage to make you change your mind. So that's the spirit of this one. Okay, so here I will talk about system on graphs. So, okay, let me first say that I'm not a specialist of graph theory. I'm just talking about them because basically this is the structure which naturally appears when you are interested into this type of systems. So, okay, a quick introduction. A graph, this is a mathematical structure that you can use to model pairwise relations between objects. So, of course, it's natural with what I have just explained. So basically, you have two notions which are important when you are interested into a graph. You have the vertices or the points, the nodes. So here you have the blue circle. And the edges, which are the straight lines which connects or do not connect some vertices. So for instance, here you have a connection between those two vertices, but you do not have one between those two. Okay, so this is the natural structure which appears. So why am I talking about that? Because for instance, let me show you an example of a system I will be interested in. This is what we call the L nearest neighbor interaction. So basically we're saying that when we are considering agent I, well, it can only interact with the L agent to his right and the L agent to his left. Okay, so for instance, all of us in this room, at first I put all of you in a straight line and I'm telling you, okay, you can only interact with the two people to your right and the two people to your left. Okay, and you cannot interact with anyone else. So the equation, if you write the equation, it looks like that. Okay, so this is nothing else than the fact that you sum over all the agents that you can interact with. So the L to your left and the L to your right. And so here there is something that is interesting, because actually this is significantly different about what I've been talking about before. In the previous case, at the beginning actually everyone was able to interact with everyone. The only things that mattered was to know the distance between two opinions. As soon as your opinion were close enough, you were able to interact. So everyone could interact with everyone. This is significantly different in that case, because actually, well, you can have two opinions which are the same. Still, if at the beginning you were not seated two seats close to the person, you will not be able to interact. So basically, we are saying that not everyone can interact with everyone. So, well, basically there is a network, there is a graph underlying the interacting system, which describes the interactions which are possible or not. So this is how it naturally appears. Okay, so I will write what I call the classical opinion dynamics models that I've been describing so far. And now I will show you a variant which actually corresponds to the one that I particularly study. So this is a variant of this model, which is the following. So we are still interested into the opinion of each agent. But now we are introducing a new variable, which is what we call MI, which is the agent's weight. So basically, this represents the charisma or the popularity of a person. Okay, so the bigger your weight is, the more charismatic, the more popular you are. So now you have two variables of interest. And so the equation that you will study now is the following. Well, we are saying that the interaction coefficient aij, so the interaction of j on i, it is nothing else than its own weights. And it makes sense because basically we are saying that, well, the more charismatic, the more popular someone is, the bigger it has an impact into making the opinion of the person change. Okay, and the second equation of our model is the following. So it's just to say that we decide that the charisma, the popularity of person, it's not fixed over time. So basically it can evolve. So you can start being popular and then lose popularity and regain popularity, et cetera, et cetera. And it only depends on, well, the opinion and the weight of all the other agents. Okay, so this is the model that I've been particularly working on. And so, okay, let me say another word about the graph. What I didn't say here before is that actually there exists two types of graphs. There is undirected graph and directed graph. In that picture, this is actually undirected graph, meaning that when you have a connection between two vertices, it's actually on both ways. It means, for instance, if it's vertices one and two, that one act on two and two act on one. This is symmetric. But sometimes you have directed graph where you have to take care to the direction. And for instance, it's not because one act on two, that two act on one. So this is the difference between directed and undirected graph. First point. Second point is that actually what I didn't say, what I also didn't say, is that here it's what we call unweighted graph. So basically, you are just interested into knowing if you have an interaction or not. Okay? It's binary, one or zero. But with weighted graph, you are not only interested into knowing if there is an interaction or not, but you are interested into the weight of this interaction, because basically you have interaction which matters more than other ones. Okay? And so in my case, I will be in the case of directed weighted graph, meaning that I rewrite my equation which is right here, and now I represent the graph associated to my equation, which is, for instance, this one with three agents. Well, as I explained to you, the action of one on two, the weight which is associated is nothing else than the weight of one, which is M1, and the action of two on one, the weight which is associated, it's M2. So you can ask yourself two types of questions when you are interested into, well, there are more than two types of questions, but I have an interest of two types of questions. So the first one are self-organization. So basically, you are wondering what happened in long-time behavior. Okay? So for instance, in the case of Excelman and Chaos Dynamics, it has been studied and we know that actually naturally, what we obtain is what we call consensus. Basically, the agents, they are trying to reach the same opinion, naturally. And other case which is, which appears, it's what we call clusters. So the same, but actually you, at the end, you have a finite number of opinion. So the population divide into different groups. And at the end, they have reached common opinion, but a finite number of opinion. Actually, this is not the type of question I've been working on. The, yeah? Yes. This is the case where everyone interacts with everyone. Absolutely. So actually, this is not the question I've been working on. The question I've been more interested on are what we call large population limits. So basically, we are wondering what happens when n goes to infinity. So what is the interest of this type of question? Well, it's the fact that as you have seen, I have one equation by agent. So if I have a huge amount of agent, I have a huge amount of equation. So if you want to, for instance, solve it by computer, well, it will cost you a lot of energy. Okay? The interest of this type of question is actually to trade this huge amount of equation to only one equation, not on the same quantity, but only one equation, which happens to be what we call partial differential equation. And as it was said in my introduction, this is my specialty. This is my field. Okay? So this is the type of question that I've been dealing with for the special class that I've shown you, the special social model that I've shown you. Okay. And to finish, I will talk to you about two examples of social dynamics. So the first one is the case where you decide to divide your population into K groups. And into each group, you have two type of people. You have leaders or you have followers. Okay? And you cannot switch levels. You are either one or the other one. And for instance, we can decide, so this is a model that we built to do some simulation. You can decide that, well, the weight of a leader will increase proportionally to its own weight and to the total weight of the followers of this group. And the weight of a follower will decrease proportionally to its own weight and to the total weight of the leaders of this group, for instance. Okay? And, okay, so this is what I just wrote here. Well, this is what this formula means, nothing else. Okay? This is the dynamic that describe exactly what I've written here. And if you do some simulation, well, here, this is my position which evolved over time. And here, this is my weight which evolved over time. And you can see if you start, for instance, with one group of 20 agents and 10% of leaders. So you have two leaders and the rest are followers. You can see that, well, you reach consensus in that case. And what is interesting is that the consensus that you reach is actually a position which is not so far away from the initial position of the leaders of the population. So basically, the population is trying to reach an opinion which is not so far away from the one of their leaders. Okay? And at the end, the total weight, the total popularity is divided split between the two leaders and in the model we have built, well, the follower, at the end, they have zero popularity. Okay? Okay. With the second example, now this time we have two different groups. So we have 10 agents in one group, 10 agents in another one, and we have one leader by group. Okay? And here you can see that in that example, there is one leader who takes more weight than the other one. It's actually because this is a leader which is popular among people who has a big weight. So basically this is a leader with popular among popular person. And so this is why he's taking more of the weight. And this is why the consensus is reached at the position which is close from the leader or the first group. And we actually do not care of the leader of the second group because this is a leader in people who are not so much charismatic. Okay? So this is what we observe. So basically it corresponds to the intuition that we could have for this model. And let me finish with the following model, which is a second example that we called the list influence, gain influence. Okay. So we're interested into this quantity, the influence of j on i that I did not like that. And we're interested then into EI, which is the sum of all the influence on i. Okay? So I'm interested into all the influence that I will get. And now we, so we have that for each agent. Each agent has a total influence on him. So we can do a mean and average with this quantity. Okay? And we want to compare those two things because in our model we're saying that, for instance, how your charisma popularity will evolve. Well, basically if you are less influenced than the regular one in the population, well it makes you gain popularity. Basically I'm saying that if you are reluctant to conspiracy theory, if you are harder to convince, et cetera, et cetera, it will make you more popular. On the contrary, if you are more influenced than the regular person on the population, it will make you lose popularity. So basically if you are very easy to convince, it will not make you a popular person. Okay? So this is what the model described. And this is a simulation. In that case, well actually you observe clusters. So at the end there are three different opinions in the population. And this is an example of how the weights of the different agents can evolve. And I think I will stop there. Thank you for your attention. Thank you, Natalie, for your wonderful talk. Now there's actually a bit of time for some questions. So please raise your hand so I can reach you with the microphone. Thank you. So if I understood correctly, opinion is measured on a one-dimensional scale. So that applies for say politics. Are you of the left or are you of the right? Exactly, for instance. How about, could we generalize this to two-dimensional or n-dimensional? For example, you like jazz, you like classical music, you like rock and roll. And you know, it's not just left and right. It's on a plane, at least one in a space. Actually in our paper, our results are in RD. I just shown you pictures in one dimension, but it works in higher dimensions. Any more questions? How did you measure the stability of each opinion? What do you mean? Well, there is a variation of the opinion according to time, according to the surrounding. Yes. So, do you have a kind of parameter which characterizes this evolution both in time and both in space, I would say. So if you, you didn't localize the people in space. Okay. You didn't do that, you did not do that. To change the, to change the... I mean, each people as a localization in the free space. Yes, for instance. Okay. And so, do you take into account of this localization? Yeah, we're really tracking the position in the space. Yeah. This is, so, yes. So, I didn't see that. Okay, go. So, I'm interesting when you have this convergence, we see like two convergence of opinions and what is the stability of this? Is there a way you can get out of that? Okay. So, maybe this will answer your question. I don't know. So, let's first say I didn't work on the emergence of patterns. So, maybe I'm not sure about everything I'm going to say. But the thing is, for instance, what I can well explain is how in one cases you have consensus and how sometimes you have cluster, for instance. Well, the cluster, they appear when, so we're in the context of Excel Man-Cross Dynamics. They appear when basically your interaction function is compactly supported. As soon as it compactly supported, you will... Basically, you are people from the population which will never see each other. And so, this is why you have different opinion. But as far as I understood, if you're not compactly supported, the more... You have some decreasing or non-increasing assumption to have. But as soon as you're not compactly supported, the natural behavior is consensus. You observe the same pattern, for instance, with the second order models. So, with the birds, actually, where you are not tracking the opinion, but now you are tracking the position and the velocity. The natural behavior pattern that you will observe is that they align their velocity. This is the equivalent of consensus. So, this is the same type of model. So, this is very stable, I guess, if you answer your question. This is what you naturally observe as soon as you have the right assumption on the interaction functions. I'm not sure I answered correctly the question. Okay, one last question. But have you oscillation, like in chemical oscillation? To the convergence? Permanent oscillation. Permanent oscillation. Like in chemical? I don't know. I don't know if you converge through oscillation, but all I know is that you have a limit. Okay, but I cannot characterize the way you converge to it. So, do you have a concrete example in life where you tested your model on some particular thing? Yeah, that's a good question, actually, that I have been asked a lot. This is one of the things that I would like to do. I have an interest in social medias, so I would like to develop the medias to, for instance, typically our model where you are taking into account charisma. This is something that you can parameterize on social media. It means you can take into account the number of followers, the reaction to your post, how much people interact with them. This is concrete measure that you can use to feed your charisma parameters. So this is something that I would like to do, but so far I haven't started. All right, thank you for the questions and Veronica. Thank you Dimitri. Thank you very much to Natalie for her exposure and for sharing her experience with us. I am Veronica Fantini, I am a mathematician and post-doctor here at IHS, and I work on geometry, on problems related to mathematical physics. I am happy to be with you today because I think it's a great opportunity to talk about maths but also to share our experience of researchers with a large audience. And this second part of the event is designed in the format of the podcast Tete a Tete Chercheuse in which Natalie exchanges with researchers and researchers to make people know the world of research, and also present the possibilities that open to them after the high school. And as you have heard before, this part of the event is in French because it will be a special episode of the podcast of Natalie. And for this reason, we will also record the part concerning the questions. So if you don't want to appear in the podcast, when you ask a question, we will have to specify it. And now I would like to introduce Tina Anikoka. She is post-doctor at the Borelli Center, the Mathematics Laboratory of the Paris-Saclay UNS. Tina is the Aurea of the Prix-Jean-Talon, for the FEM and the Science of the UNESCO Foundation, with the Academy of Sciences. Tina works on the treatment of images, and more particularly on the development of algorithms capable of detecting the classification. She collaborates, in particular, with the police and journalists who sensibilize and form the issues of the verification of information. In addition, she actively transmits her knowledge to the people, first to the UN and the UN. Tina, Natalie, I will leave the floor to you. Thank you very much Veronica for the introduction. Indeed, I am pleased to talk to you today with Tina Anikoka. Tina, I discovered you during the exhibition that you gave to the Mathematics Assistants that I loved, and I invite you to watch them. They are available in replays. And so I immediately started with you when you gave me the honor to participate in this event. And so I thank you for accepting my invitation. Indeed, our exchange will be built on the same format as the podcast, so we will start by talking about your course, then we will be interested in your life as a researcher and we will finish with your white card. So starting with the first part, can you briefly introduce us to your general course of high school to the doctor and we will come back on a specific topic afterwards. So first of all, thank you for the invitation, thank you for the invitation to the podcast. So in high school, I know that this part is not very interesting, I was not a very good student, I was a good student in the subjects that I apparently chose, this is what was written on the bulletin, and the subjects that I chose were Mathematics, well English, sports, that's the other subjects, but it was especially the subjects that caught up with everything. So in fact, the question was totally natural, I made a physical preparation, because in fact it was great, for me it was the continuation of high school with only the subjects that I liked, so more French history, philosophy, etc. And I would not have been able to do the faculty, I know that this is an important question, because people wonder if I'm doing faculty or not, I love faculty, if I could have done 10 years of faculty, I would have done 10 years of faculty, and I think it's easier than the faculty, I would have really been disqualified, I disqualified very easily, and I think that at the faculty I would not have I would not have attended the class, I would not have succeeded, there we are really well set up, I loved it, I loved it so much that I did not do what I had to do, that is to say I did not decide from a school where I wanted to go, I did 5 degrees, so I did 3 years, but because I would have continued if I could still, and we said to myself, we still have to choose schools, we have to look, and well, it's true that if I had been admissible at the UNS, I would have gone, but I had indeed looked only at the UNS and Polytechnique, because I would have been there anyway, I would have done 3 years. There, I, we said to myself, but clearly there too you chose subjects, in fact I was much better in computer math than in physics, and so then I went to an information school, I did not know at all, I did not want to leave the Paris region, it seemed to me very far, but the NCMAG, which is a school of computer engineering and applied mathematics, I loved it there too, it's really only subjects that I liked that I did at school, and there we do a lot of computer, we do a lot of mathematics, and I also did a research master's in applied mathematics, in addition of the NCMAG, so it's really the two aspects that I liked the most, all the names I chose, but it was perfect. Okay, after your school? After my school, I came back to the island of France, because Grenoble is nice, my 3 years here, where I was supposed, so I did a stage in medical imaging, because my mother is a doctor, my father is an automatic researcher of the mechanics, it was the good mix of the two, and I had to pursue a big thesis there, but in fact, I would have met, but life made me meet other people who talked to me about imaging, because today, it's more of a falsification detection, but it's really digital imaging, so photography, etc. and that was my topic of TIPE in preparation, my first love of imaging, so I couldn't refuse, here at the hidden NS, so I started at the hidden NS, and I ended at the hidden NS, where I am today. Okay, great, and at the time, where you were in high school, you already knew the medical research? Yes, so my father is a researcher, so he was a researcher, a research director at the Inria-Rocancourt. Yes, but did you know specifically what it meant? Yes, because I went with him, I was not very serious, I never was, I didn't pay attention to my notes, the competition, everything, I'm not a scholar, exactly. And so not that my primary mother, when we were, we were late, my father said, we're going to work, so we went to register, but it was very, very, very good, because I hated going late, it was too stressful, he said to me, come, let's go to Inria, so it really happened to me, once a month, in the year, to go do the research, I mean, I quit my job, almost, and so I knew that, my mother was a doctor, but she was working a lot in medical research, so I didn't know any other job than research. Okay, and did you project yourself at the time? Well, I projected myself in, I had never thought so much, at the time, still today, I do that, I know it's not good, but so I didn't project myself, but on the other hand, what I did, so I was working today too, is that in the stages I did in engineering school, so I did a start-up stage, in a big company where I did research, so as I knew that it was the research world, I saw my parents, I wasn't convinced with that, so in a start-up, I had trouble with everything that was marketing, I needed to understand everything and I didn't understand that people didn't want to understand, and they didn't want to understand, they wanted to sell often, so I had trouble with that, and in the big company, I found it very good, we have a lot of means, we do real research, but everything is closed, so I work on this equation, I only work on this equation, I don't know how to do a single thing, but I do a lot of things, and I found that in the team where I am, in the training team of the Borelli Center of the UNS, I can do a lot of things, it's very varied, and that's what I saw through my father, so I knew that there was something that was better, that's why. So if you don't project yourself, at what time, if you know that then that's what you want to do. So I did start-ups, I did business, I did a year, before I started my thesis, I did a year of research engineer, and that's where my domain also applies to social networks, even me who applied to social networks, because at first it was image treatment, the mathematical aspect, and when I saw that I could understand what I like with what I do, knowing that I had always done what I needed, what I didn't know how to do something else, but it was really, it added legitimacy in what I brought to the team. And that's where I realized that I can never disconnect because in my everyday life I can apply the maths that I do in my everyday life, so it was a whole. I thought, that's it, public, where I do things where I don't have to lie to sell it, where it's useful, all that, I liked it. You found the right place to correspond. So you supported a thesis entitled the secret life of jpegs, falsification detection via compression traces. Can you explain to us briefly what your thesis is? Yes, it's much more easy than what you think. It's really, for the moment, I really like my... Of course, during the 4 years of my thesis, we do a lot of things, but in my thesis, I put something that is quite consistent, so I really talked about the treatment of images. I work with digital images like those used to film, to take pictures, etc. And these images, I spent some time learning, and every day, how these images are formed. These are digital images. When the light enters the lens and arrives on the sensor of your device, whether it's a portable phone or a camera, we get the light that arrives on the sensor, we get photosite photos. Visually, these photosites are not visible. Nobody immediately sees what has been recorded at this level. There is a series of operations that are done, a series of mathematical operations. And in these operations, there are, for example, mosaics, for example, it's a very complicated interpolation, but either an interpolation works, we can calculate the means, it's really accessible to all. Then, we have a white balance, we have shapes, functions that are applied to our image, color images, three matrices, functions, things are really very simple, until we have a nice image and then it is often saved in JPEG format. In JPEG format, I found a way, I didn't present it to my thesis, but as soon as I can talk about my thesis, I do it like this, I explain it by saying that an image takes a lot of space on the computer, in memory, I take your sheet, imagine everything, you can take a sheet, you have a large sheet of size A4, it takes a lot of space, it's an analogy, it takes a lot of space on the computer. So what we do, automatically, is that this image is compressed, for example, in JPEG format, and the analogy works, if I tell you to take this sheet, it takes too much space, you will answer me, it's enough to apply it. So I will apply it, I will get something that is applied, but I don't see the inside anymore. So that's something that even in my colleagues, they don't always think we are always an image in JPEG, and the image is, you have to open the sheet to look at the image, it is passed by a compression stage. So in fact, all the operations I talked about before, and that one, it's really operations like life operations, we can say an image, life, and I was interested in detecting the life of an image, so we have an image, and I want to know what happened to it. And here for the JPEG, the analogy works well, I don't even need to explain, but if I see an image, really like a an analogist who analyzes a corpse, I will open it because it will be compressed, so I will open the image, and I will look at it, and the difference I will observe in relation to before, on a sheet it is seen, on the image it is not necessarily seen, but me with mathematical processes I see it, I will observe traces of fold that I have there, that I didn't have before. I can detect it and know if the image has been compressed, I can even say with what parameters, because there are more complicated parameters, etc. Then, if someone makes a falsification, for example, add an object outside, it's like if we cut a piece and paste it on this photo our object outside, we will see that in this part there is no trace of fold, no trace of compression in the rest, yes, if I, well, we can all have fun imagine all the scenarios possible, we can all have fun with this analogy, and then, if I want to share this image for example on social networks, or send it to someone, I will record it under formage IPEC, so I will fold it, and I will send it to someone, and in the area, for example, falsified, I would have players that don't match, or less players than in the rest, etc. And well, I found the analogy, I don't have, of course, there are other methods that work and the particularity of my team and my thesis is to have used maths, really a statistical evaluation to be sure that if, for example, there is no trace, yes or no, in a reliable way, for example, there are methods that work very well in this state, or to know if an image has been folded, they fold it and see if it looks like before or not, but it's purely, well, you have to interpret, you need a human to interpret all that and that's why my algorithms were included in a tool called InfitWeVerify, it's a free tool put in place by the FP for all the fact-checkers, well, for everyone, but it's the fact-checkers, the journalists who verify the effect, who use it, so in addition to other tools that, of course, have this reliability problem, but like that, they are sure of the result, it's the same for the scientific police who can spend hours looking at an image but who need to know if it's reliable or not, because we can't say... You can imagine why. And indeed, it's used for, so my particular algorithm is used by everyone, because it's available online by the journalists, etc., by the police, and in more than 40 countries. So you can know with certainty if it was falsified or not, can you know the nature of the falsification? For example, concretely, you have a photo and you say, this object, it's sure it was added, can you do it? I can't know 100% that something was falsified, because I always do the analogy like that, for example, it's only the compression traces that I'm going to analyze, and the anomaly is in there, but there can be other anomalies, for example, sorry for the analogy, but you can be sick and you go to the doctor, he's going to make you a radio, a radio can be perfect, but you have to do an IRM. And in addition, something I didn't tell you about, but in the traces of the player and the inconsistencies of the player, there are always limitations, but I know them. So I know there's a chance on 64 that, for example, the two traces of the player coincide or things like that, and I can't say that, for example, but I can say what's disturbing, so yes, I can interpret it much more than methods that say, here, it's weird, because there are methods like that, or big black box that say here it's weird. OK, thank you very much. We're going to move now to your current research life, so I like to ask this question, for someone who has no idea what our job is, can you explain what your days look like? So? I'm going to ask this question, and every time, apparently, I already said it, I don't have a very classic profile, so I'm going to answer anyway, but that's it. I have four aspects in my life of well, in a week, I do research, of course, I do teaching and diffusion, I do framing, stage art and PhD, and I do a lot of framing, project coordination, etc. And in general, well, that's it, in fact, to make a lot of information, I have my order, but I always have it with me and I can work wherever I want, so that's also what's nice. So, in particular, I get back to work two days a week, maximum, to chat with others. And otherwise, the rest of the time, we're very, even before COVID, we've been very visible, with people all over the world, even colleagues who spend three months a year in other laboratories, etc. And even my teaching, so I give classes, during my time, I give classes to children at the MIS, it's the house of initiation and sensitization to science, so it's scientific workshops we do with children from CE2 to the third, they come in high school and we do a scientific subject, as I admit, in these past years. Obviously, it was on site, it was eight o'clock, and today, I give classes to journalists. This, on the other hand, is pure video conferencing, it's complementary information for a university degree. And so, it changes, but I always like to give this aspect of class and so my days don't feel like that, because I always have these four things there, but I try to have a rhythm of an afternoon where I keep it for myself and I don't get there. I have meetings all the time, in visual or in presence, and on Thursday I try to it always ends in a meeting, but I try to go on site, because that's what I really liked, when I saw my father working, it's the exchanges with others. So it's important to go on site, even if I change a lot, not on site. I can exchange. OK, so you're going to give us a nice panorama of all the things you do and what's the part of the research that you like the most? In which you enjoy it the most? Well, that's the part, working as a team, exchanging with the others, but not because we have meetings from time to time, even there, for example, you could exchange with me and we would talk about something that will later make me think about something and I want to develop it behind. So that's the part I like the most. Also the diffusion, when I give courses or conferences to younger people, I really like doing that. It takes time, but then it gives me an incredible energy. No, I don't think so. If just after, yes, then I rest, and I don't know, it gives me the strength to continue doing what I do. So I like that a lot, but otherwise, working as a team, doing links between things, I really like that. And on the contrary, are there things that you like less? I don't like the side writing articles for conferences because we have to publish, of course, because we have to share what we have discovered, and even it strengthens us to understand what we have done, the newspapers, etc. But it's the side of the deadline, I see it, I know there are people their method is not finished, they know it themselves. But I want to go to Singapore in November, so I have to submit to such a thing. And that, I don't like all that, but not at all. You mentioned it a little, but I admit, when I went to see your profile, I find it quite fascinating, the fact that you collaborate with the police and journalists. Can you tell us a little more about the situation? Yes. Unfortunately, it's not any police who is on the road or something like that. It's the scientific and technical police, like the experts of France. And it's the digital part. So it's not the part where they come to recover the DNA on crime scenes. And with them, we had already worked in the case of a project called DEFALZ, Falsification Detection. In fact, the INR had gathered in France who worked on this subject. And they were in our consortium, we were two of them. And they give us cases of use. They don't put us in front of our algos, because they don't have a public website, of course. They give us cases of use only in oral, because we can't look at the police images. So they describe things to you? They describe things. And it's not clear, because it's interesting. We have fake images. We have so many images, for example, and we want to make a trio of things like that. So we realize that there is all this, but it's quite vague. They don't give us images. So it's really cases of... We realize that they spend time, it's really people who spend more time than us on images. So it's interesting to tell them what we are able to do with images. At the moment, we only work on two projects. And another one, it's not without falsification, but it's a bit like my thesis, it's the improvement of the videos they receive. Because they receive a lot of media, of videos, for example, of people in the street who filmed something, but far away. And they use tools, really like in movies, to zoom in on a zone and make sure it's better resolved. So they make the best resolution and we have quite a few state of art on it. So we try to tell them the state of art, look at what exists, etc. All of that in European projects. And with journalists, they have European projects. We work with all the European laboratories who work on the verification of facts. So it's not just images and videos, it can also be tweets, messages, etc. And that's thanks to a meeting with Denis Tessou, the head of the media lab, of the FP, who set up this plugin where my algorithms were included. And not only he gives us the visibility, the utility to our work in the team, but he also gives us images. We can also find them, on social media, etc. But he has 500 fact-checkers who send him images every day. So we really have real cases. So you test them all. I was wondering when you explained, are you able to detect if an image is falsified? You explained with the image of the player. But if an image has been completely generated by artificial intelligence, are you still... Are you able to detect that? That's a great question of actuality. This algorithm is looking for local anomalies in the image. But what's interesting is that as I told you, this image has a normal digital image, a cycle of life, and they don't have these images. Each of these traces can be detected. That's what we're doing at the moment. We're looking at images that come out of these new tools and we observe that there are many non-natural things that can be detected but we still don't have methods that are able to say it's non-natural, it's obvious, because getting out a method that generates even if the fingers are not perfect or it's not serious, we can get out the method. In fact, it generates... it detects once, once, once over twice. It doesn't work. So it's a bit more difficult but we actually work on it. We're counting on you because we need you. After, they don't forget that every image is like a drawing. Thank you very much. We're going to conclude the conversation with your white card. What do you want to talk about today? Well, I wanted to talk about something that keeps me in mind that I already had the opportunity to present to a lot of different audiences what I was doing and I've never been able to ask a question, in general, people who invite me and ask me questions and they often ask me for example, why did you do maths? What made you do maths? You didn't find it weird to do maths as a woman or whatever. And I... I asked myself the question if I did for example, I don't know history, maybe we wouldn't ask the question. I don't know. Knowing that if we knew we would have to ask the question because at the same time, we qualified as historians because I detect historical images and I said if I could show that to my history teachers, it would be incredible. But I really don't understand what I said. I grew up in a bubble where maths was normal, it was too good, it was normal and today I realize that it's weird that I won't even go into a boy's field but even just to like maths apparently it's weird and that's what I really have trouble with and we are in France we had a lot of very well-known mathematicians and I did an investigation on what was asked of me so there are several profiles there are students I often see primary school students they often say I don't like maths everyone tells me it's not possible but surely I have to make an abstraction but I'm sure they know all my friends love maths I don't remember people who were not good, but it's not serious but there was no rejection as you can feel after yes that's it and then there are people who say the maths teachers they say it's because there are too many parkers after I was okay if I had bad hearing because I didn't learn parkers but it's okay because I have a good memory it's just that I didn't make the effort what was written in my brain but in maths I never learned anything so I never in the the adult lambda who ask me sometimes what do you do in life today I don't know if now I know, I tell them I detect or I create fake images but people don't like that so it's not a good idea it's not very popular so I tried image treatment it doesn't mean anything signal treatment I tried maths and I never I said I do maths and I do research in maths you tell me your maths teacher and then maybe no one will listen to your podcast but I saw once I said that to someone and I saw in his eyes if I was looking for new numbers new numbers I don't know for example applied it's not people don't know so now I say maths but also people I don't understand and so I tell myself why do they have this image if it's a bad image and it's the same even in the industrial context because we brought them to do a lot of I often talk to companies about projects they want ideas, we talk about them they want to put artificial intelligence because yes I could qualify as I do research in artificial intelligence but I don't really like this term I'm even going to create courses to explain what artificial intelligence is but the term it's very good but what people think is not correct and so I continue to say maths but even people who do companies that just left because they have people who can talk about artificial intelligence for example if we tell them that it's maths we want to do something like that we can do maths maths no no it has to be really all public and my white card I have a big question why are maths so negative and why so it's negative and when we think it's positive yes because it's elitist, there's nothing like that it's to select and me clearly if there was no maths I would have selected nothing but yes it's selected and it's optional I speak French I could have spoken in English but maths it allows me to speak I speak very digital so I speak on my phone I speak on my computer all that is maths I want to understand how it works trees, nature, physics all that is with the language so that's my big question so your white card is your question about the images the fact that you are in contact with a young public the fact that we do events like that it can help to change maths the image of maths so we're going to end this thank you very much Tina, it was a pleasure to chat with you Veronica, I'll talk to you ah yes, sorry so now, if you have any questions I would like to go to your hand I think I'll leave the mic to Tina to answer yes, so just the question has to be in the mic for the podcast no no no yes, thank you I don't know if it works yes, thank you for this interview very well done and to which you answered in a passionate way it's useless to emphasize the importance and utility of the field that you have chosen to apply your knowledge at least I ask you the question don't think about your image in astronomy in astrophysics because I think it's a passionate field and mathematics plays a big role thank you, yes I thought I thought because I have friends of my father who work at the CEA who told me that you can't do image treatment at NOE yes, today I'm doing image treatment for satellite images but I'm already doing satellite images but when I did the social media images and I approached journalists and the FBI where I found my place with my colleagues I think I'm more connected and it's true that it was easier I don't have an account of social media for example photography, I like it a lot it's part of my passions it's me who insisted to work on classic digital images and social media but today I have a doctor who works on satellite images and the images of telescopes it's like medical images I did but there's less variety and less aesthetic I like for example I often work on images that I take myself as an example and it's more complicated except if I go to an ERM or I use a telescope myself but it's the same domain and it's fascinating In the case of an image generated by a neural network a GAN is it the prototype of the falsified image or an artificial image can be if it hasn't been modified or photoshopped can be passed to be correct if we let the GAN run for a long time Thank you so to detect local anomalies it works for photoshop but it can also work with GAN or diffusion methods because we can write in the prompt select an image area and add a white cat in this image area if it's local for example the method with the traces to work because we'll see that the image has a historic and locally there's another if the image is generated by GAN or by diffusion by GAN we've already observed it's like adding an additional step in the chain it's so big that it's not visible and we observe for the GAN depending on which GAN we observe traces like pure traces I don't have analogies but we can detect these traces and say that it was generated by GAN in particular but what's complicated is that we're supposed to know all types of GAN generators and there are neural network methods that work like this as soon as a new method comes out and detects like this to say the diffusion method is the same but we've observed it's all recent we've observed last week that there would be traces periodical traces that are complicated to analyze we don't know why they're there we don't know if it's because the methods have learned classical images and get traces of compression but badly, because they get them badly or if it's the network itself as it under-examples and enlarges the image several times if it's the one who introduced this period it's all the traces that we don't see in the image but now I see what I'm looking for and they're passionate Hello, thank you for this interview still a little on the same question if ever we have your algorithm that allows to detect falsifications and the generation of false images can we build a GAN that will produce images that you can't detect and if so the case is it complicated for you to publish your detection algorithms? Thank you, we often asked me if it wasn't dangerous to put these tools at your disposal because imagine you want to falsify an image, you're going to map the image and then you're going to pass the tests and check that it's good except that it's not possible to pass all the tests if for example you manage to coincide the worst traces because you understood everything in my presentation there's another trace that you won't be able to coincide until maybe the image doesn't make sense you won't be able to connect something where the colors don't coincide so that's not possible but in the images generated by GAN where everything is artificially generated and globally we could do something yes, it's easier even on a traditional image we could try to erase the traces that we detect and try to put real traces back we tried to do that theoretically it's possible the traces don't go too far because the image will go too far and put GAN or diffusion images theoretically it's possible to erase the existing traces if we manage to recalculate them and re-apply traditional traces of, I don't know, a Nikon device such a model such a particular objective and if we manage to do that, it's not bad then it's possible that someone actually comes up with an algorithm just enough for anyone to press a button and clean their image and yes, it's possible so my solution the solution that I think everyone agrees with in my field is that the images don't have to believe these videos I mean, in text, we agree when you send a message on social media you won't believe it even if I tell you something, I hope you won't believe it I tell you, it's super beautiful out there you'll all look at each other with the images and the videos it's the same, it becomes a drawing if we want but if we want to have a real image it would be necessary and technology exists, it can be called digital tattoo or watermarking or even to sign the file it would be like putting traces but to put them in the front by the camera or by the human who is on photoshop or every time there is an operation that is done, it adds to the data there was that, that, that that moment I don't know, we can't have all the information we want but it would allow to certify the image and that, technologically, we know how to do it there are even photos and devices that they do but we would have to we would have to say, we have to do that everywhere if the image has a signature that identifies it then, I don't know, the social media platforms will automatically put a green arrow that's just my idea I don't know, we would have to do that but yes, it's clearly to detect falsifications it's interesting, pedagogically, for children I love it, it's a very easy way to explain the maths the algorithms are useful in some cases of course I'm not saying that but the real use to solve the problem there is a way, but I'm not a minister or whatever so if there is no first question yes, to qualify your job I would say engineering engineering being a great engineer in the image I think we can identify my question will be very provocative the ontological framework think about it Yves Meier worked with the Chinese police I know Yves Meier from 2000, so Yves Meier he worked with the Chinese police I know him personally because he was at the Borelli centre in Cachan apart from making him a cuckoo and going to install me in his office when he wasn't there, I don't know I don't know what he's doing today I don't know thank you very much, Tina thank you Natali now I leave the stage to Pascal Massara the director of Mathematical Foundation Jacques Adama we were asked to speak in English but I feel better in French putting the nuances is easier in French than in English even if talking about maths I do it all my life in English but putting nuances is easier in French so thank you first to the interpreters thank you to IHES to have made this event possible I can tell you that every time I put my feet here, I learn something so that's very good the IHES is very happy to join this event and the common concerns of IHES and the IHES about the disparity that we all see between men and women in general about sciences and mathematics in particular with the IHES IHES took the bull by the horns he took an interpreter equal to plus infinity to pass his number of permanent professors from 0 to not 0 the FMJH does its best to take care of this problem and the problem of diversity so we have a program called FMJHCR to to put more diversity in the student population and in the young researchers so it's a bit like that that we see things we tried to take modest but meaningful initiatives to change things we noticed that as in the companies the green platform plays as the level of study of more and more young women and so we created a junior prize that is for young women at the end of the year and at the beginning of master at a time when there are still young women who do mathematics so it's one of the initiatives we also introduced the mentor at the level of the license to try to convince young women that there was an avenue for them in mathematics and in mathematical research so you were a perfect advocate to explain all the diversity that can be seen in subjects to approach through mathematics and I would just like to say that the reasons for which we can want a world which is more diverse and more open we can say that a world more open more diverse is a world which is more fraternal and after all why not relate to this idea but it's also for a pragmatic reason that is to say that we notice that more diversity is also more creativity and that mathematics itself will benefit from this greater diversity and once again, thank you to the IHS for making this event possible and I wish that we continue in the same direction to try to make this double cause progress that's it