 Okay, so I'm here with Ingrid Del Vachy who's visiting the ICTP for the scientific council meeting Yes, and I thought it was a good opportunity to chat with her about many things So maybe we can start about Your Interested math how that come about I mean your background I see well The first thing I have to confess is that I have no degree in mathematics. Oh My yes, my my my degree is in theoretical physics and But in Belgium where I was educated you see a lot of mathematics as a physicist and I did in the first two years actually wanted to see what I could do the double degree and So I took also the math courses. This would be sort of an undergraduate level Yeah, the undergraduate level and then the so undergraduate degree was four years and the first two years I took the all the math courses as well and then after that it became too much because the physics teaching was very heavy We had a third year in physics was extremely heavy because well, we had 13 different courses in physics and so But I don't regret having all that physics because I think it gives me a different way of looking at things And then I learned a lot of higher-level mathematics later Because I was interested I've always been interested in mathematics because I've always been interested in why things work and Figuring out how but I am physics was also a big interest So you would say that the physics background suddenly has a lot of influence had a lot of influence in your later career it did because it it's really a I Find it much easier to understand physics arguments and physicists than most mathematicians do Especially in the US where it's possible to get a math degree without even having taken any physics, which I find mind-boggling But it also give me a different way of looking at things and then I in my research Mostly known for mathematical tools and mathematical approaches to image analysis and signal Compression and so in that setting I talk a lot with electric engineers but having this physics background gives me a different way of looking at them than they do and I find that very useful And how was your experience going through school and his career? How is it compared to now? Yeah, well, it's always hard to compare because I am comparing I Was in oh my god, I was in elementary school 50 years ago. So comparing something is half a century ago in In a country that has changed a lot and in which education system has changed a lot. So Actually, I went I had all my elementary and So elementary and then secondary education in all-girls schools so Because that was the standard thing in Belgium and so and I think that may have had an influence too because many Many many women feel that as a woman interested in mathematics, they were always the odd one out People interested in math are always already exceptional Way more than they should be because math is really interesting to everyone But but then to be a woman among them And so I never had that because it was all girls anyway So there's only until high school. I mean well until college Even it was was all So it was in college by then I was really if I then encountered the attitude that People thought I couldn't be good in math because I was I was a girl by then I mean, I just thought you jerk I didn't it didn't engage on me. It's the same way. So So I never thought about the fact that because I was a girl I would be expected to know I mean just never so the school was very Positive behind your interest in math already. Yeah, your high school. Yes, I mean and science in general and and and my my my father was very much supportive of Interest in the sciences actually I Without my father's influence I might have gone for math straight away, but he always had wanted to be a physicist really I mean he came from what was his profession. He wasn't an engineer and a mining engineer He his parents were a very blue color. They came from a mining region in Belgium his father worked in a glass factory not in in the mines, but so when His when the teachers have told My grandparents that this was a smart boy. They should let him study They only knew of two professions where people went to college. I mean and one was medical doctor and My father couldn't stand the sight of blood So that was kind of exclude and then they knew about engineers. And so I mean it was never a question I mean if he was going to study it was going to be an engineer and it's only after he finished his studies that He also went to polytechnic where everybody became an engineer that he realized that there were many more things Physics would have been really probably his first love. So it must have been very exciting for your father to see you Yeah Well first study physics and then I shifted to mathematics, but yeah, he was it was very They were very happy about it. My mother had hoped that I would become an engineer. She thought a scientist She said just it's only barely better than being an artist. I mean you want me to make a living She said So she finds out very funny now Yes So As well as being a professor of mathematics now at the University you were the former chair of the International Mathematical Union. Yes, so how was that experience? That was a very interesting experience, but it was also very intense. It was very interesting because The International Mathematical Union is mostly known among mathematicians if it's known at all as the organization that Organizes the Congress every four years and the Congress has a very high visibility It gives high awards and things like that, but it has many other roles and which I found much more Challenging than that because organizing the Congress Once you've put together the program committee and a local organizing committee is something of which the I knew has an oversight role, but it doesn't The day-to-day so they today and it's set up in that the way that the executive committee should not have An integrity role in the organizing. I mean, there's a kind of independence between an executive and Legislative and the practical of actually running it and and so so the The the the statutes are made up in such a way that there's independence of the organizing committee and Program committee from the executive committee of the IMU, but so the the executive committee also is very involved in activities of the IMU in developing countries and in Good having a good relationship with the council on mathematics instruction and And I thought those were two aspects that are close to my heart and That I really am committed to and that's why I agreed to serve as this president It was a four-year commitment So it was really it took quite a bit of your time and energy. Yeah, it's it's well And actually it takes time but also a lot of energy especially in the last year, which is the Congress here coming up to the Yes, then then it takes a lot and I was gonna ask you about I remember you gave a talk here some time ago Possibly for the Ramanutian Prize And you mentioned an interesting anecdote because you you have your work has to do with Images. Yes, right? There's something about grass and your I see yeah, so Some of the constructs that I have built I mean so I've built the work I'm most known for is work on wafle bases and those are used in the Image compression algorithm JPEG 2000 the standard which are actually used. Yeah, but they used but they they're not used in your Wanted shoot camera those use the oldest standard JPEG the JPEG 2000 was a standard while that's now 15 years old that Was meant to go beyond the JPEG standard and it does for instance, it allows Compression at bigger factors than the standard JPEG But with very graceful degradation meaning if you only I mean with JPEG if you go much much more Lower bit rates than what the JPEG normally does you get not very good yes, and while while the degradation is much more gradual with JPEG 2000 and it also Focuses it it has a Multi-resolution feature to it meaning that where you have sharp edges it uses Building blocks that are very very small and very local and where not it uses only very smoother building blocks and So the artifacts in an image because you always have artifacts if you start compression Look very different from JPEG to JPEG 2000 and that gets to that anecdote. I mean JPEG 2000 standard is used for a lot of internet applications, but it's also used in digital cinema Standard used in in the United States and Europe for digital movies And it's also used by ESPN for their sports transmissions And so when we have bought about five years ago a very large television screen when this was not as much But they were not as affordable as now we had bought it for a special reason I was going to be away from home for several months and I wanted my husband to have something nice to watch his sports and So While that we had this screen and my husband was watching a Premier League game And I noticed going by the artifacts and I said oh my god I said they're using wavelets. They're using JPEG 2000 and my husband said Yes, yes, he was following the game. He says how do you see that? I said look here in the grass He says who cares about the grass? I mean and of course, that's exactly the point Nobody cares about the grass and so that's why you could get away with how your compression I say because nobody would notice people would notice this players and So you could accommodate that in your compression So to what extent did your mathematical work that is now used in these Artifacts as you're saying Was correlated to the actual application what came first and how it's It was I had nothing to do with the standards meetings standards meetings are something that's half scientific half political really because Standard is first coal is written out and then people Submit solutions and they get together and there's a whole jockeying because people like to get some of their intellectual property And so on so I had nothing to do with that, but I had published earlier mathematics Wavelets and and they were very much my work was very much motivated by applications to image compression Because Wavelets had emerged in the 80s as a kind of synthesis from ideas from computer graphics from computer vision from physics from mathematics and and so there was a whole intellectual mixing that went on and that led to this building of of of Wavelets But if you then wanted to use them for signal analysis They turned out that you you had this beautiful algorithm But in practice you had to truncate because everything was infinite infinite filters And so you had to truncate them and well that it was not as precise anymore or does nice anymore and and everybody kind of Seem to take this in stride like I mean yes Math is beautiful, and if you want to really apply it It's going to get dirty and that is pretty anymore, and I've never believed that I never I mean I felt look The fact that we want these applications is going to put us some conditions Let's take those seriously Let's say if we want those conditions can we then still build that beautiful framework so I kind of turned the whole thing upside down and it turned out you could and But the end construction were functions. I mean in the end I built bases of functions Just like the original Wavelet bases did but they were not functions for which you have not the expression I mean so you built them from the algorithm up and But you could still you you had all all the rest of the beautiful mathematical structure So interesting in this in this case the the actual application was the one that Yeah So show the way for them a different mathematics. Yes And and then and then when I wrote out the paper Although I published it in a mat journal It was very important to me that they would allow me to print the tables of the actual numbers used for the filters Because I knew I wanted it to be something that engineers would be able to use and I knew that they would recognize these tables I published tables in the same formats as they found them in their papers Because I had seen them there and so I and actually that was a good move because that really made a difference in many engineers Who are not interested in all the mathematical details that went around it, but they used the filters And they probably wouldn't have if I just indicated how to compute them, but not compute So this probably is more Gaps between disciplines that we are aware of Yeah, and I think it's because I came from a non-traditional background and And I was I have no inhibitions about talking with people in other fields that that it was easier for me to make that bridge Very nice. And so a final question You know, we are ICTP which one of its missions is to help science in the developing world But in general, well, what would be your advice to somebody young that is considering going into mathematics and doesn't quite know Oh well mathematics is such an incredible cool subject if you think about it because you You figure things out by thinking you solve problems by thinking now, of course, there's a lot of mathematics that has been Developed already so it's good to learn a lot of mathematics But it's it's good to to learn and to realize that this mathematics is not something that is just Molitic and given I mean, yes, it takes people to build it. First of all, we've built it It's not I do not believe in this concept of mathematics exists and we discover it I mean, I think we we build it and actually one reason the fact that I work on on these these building tools for technological applications has something to do with that because Everybody agrees that the way of life constructed are things I constructed people don't really see those as things that existed floating in The universe and I found them But that's because I they use for technological applications If they have been something for physics people would have more fun that they were found now The reason people think that you just discovered them is that you have this incredible feeling of surprise and admiration and wonder when you find something you say, oh wow That was there But it feels exactly I've worked in mathematical physics I've worked in more pure mathematics the feeling is always the same whether you work on these technological things or you work on mathematical physics or you work in the excitement is still the same excitement and the feeling of wonder is the same so That feeling is it's just We judge a lot on how we feel when we see things and if you think about it feelings are just a kind of Shortcut that evolution has made up to give us quick insights and feelings about facts, I mean I'm not talking about love. Yes. Yes, I mean and Doesn't mean this if you have the same feeling after you found after you've solved the mathematical problem as When you discover a new flower Doesn't mean that both of them are discoveries. It just mean that you have the same feeling I see and so But it's still a wonderful thing very good. Well, thank you very much in great