Interview with Carolina Araujo, new holder of the Ramanujan International Chair

[Music] My parents are engineers. So I thought I was going to be an engineer. But then in the in the first uh the first two years of university, I tried many different things. I took classes in uh in engineering but also in mathematics and physics and chemistry. And then but since the first serious class that I took in mathematics I was I knew that that that was my path. So um then since then I haven't left math. [Music] Okay. So maybe to talk about algebraic geometry which is my area of research maybe I should talk about the different areas of mathematics more generally. So the way that I see this is um it's like our senses. So to to understand the world that we live in, we have all our we have a vision and smell and taste and and touch. And I think mathematics is the same. Uh we have there are many different mathematical senses that we can use to understand better a problem. And among these two senses there is geometry and there is algebra. So geometry is concerned with studying uh the the shape of objects. So we understand shapes, angles, distance and in algebra is a it's a different it's a different way of of understanding mathematics. It's a it's a it deals with manipulating symbols. So for instance, if you have an equation that you have to solve, sometimes there is a formula. So this formula is explaining us how we can manipulate the symbols in the equation in order to to come up with the answer. So this is this is how I sort of describe algebra in a in a sort of simple way and then in algebraic geometry we put these two senses together to better to better understand some of these mathematical objects. So for instance, sometimes you want to uh you would like to solve an equation or a system of equations, but this is very sometimes it's very difficult to solve it explicitly. However, the space of solutions, it it does have a a geometric manifestation. For instance, you have the you can write down the simple equation of a circle. So you can look at this from the point of view as of equation. There is there are some symbols that you know mean something. But it also if you look at the points that satisfy this equation this has the the shape of a circle and then in algebraic geometry we we often build the bridges between these two universes. So sometimes you want to understand the solution and you do so by understanding the the geometric behavior or sometimes you uh you would like to understand say the curvature of a trajectory and then you do so by analyzing the equation and and and the algebraic structure that is behind. So this is more or less what we do in algebraic geometry. We exploit this two senses. [Music] It was just much later after talking to many to many other women and and observing their their experiences that I realized that there were some um some injustices that were very much present. Even if for me maybe from my privileged point of view it was not clear at the first uh in the first moment. And then I think there was uh I think by um by being bit upset with these injustices and and I felt that then at some points I I in some moment I realized that I could do something that from my from my uh from from where I was now in my career I could do something to change the situation for for other women and then I I naturally embrace this this is I guess stronger than [Music] I have to say I love ICTP. It's a it's a wonderful place. I feel very inspired here. So I spent many I I visited ICTP many times and it always meant something very special for my research. uh so I made some some important breakthroughs while I was here at ICTP and so it was very very important for my research and also um I think the last time that I was here for almost 3 months it was um that's when I got into a new project and um and this is a project that is is really important to my uh to my research right now. So, this is it's always been a very inspiring place to be.