The award recognizes his work on algebraic geometry: "There are a number of spaces that appear naturally in theoretical physics. You want to understand some very complex physical phenomenon and you model it with equations. These have multiple possible solutions that can be arranged in a space. In order to understand the complex geometry of these spaces, which are a 'whole' that evolves over time, I brought a particle physics tool, the 'topological theory of quantum fields'. That allows us to understand the solutions in parts : I obtained a series of numerical invariants, some polynomials, that characterize the extent to which this space is complex, with the hope of understanding how things can happen in the Universe".
Are these spaces realities that occur in the Universe, extremely complex places like singularities or event horizons, or are they still more conceptual?
Very good question. It's even more conceptual. It is not about understanding the Universe itself, event horizons and singularities, but about understanding phenomena that occur on top of the Universe. You want to understand how a magnetic field propagates, and in that equation, the Universe is the fixed data, while the phenomenon occurs above.
How do you go from research like this to machine learning?
When I finished my thesis at the Faculty of Mathematical Sciences of the Complutense University of Madrid, I started that job at the Polytechnic. One of the areas in which I work is recommendation systems: I connect to Netflix, and the platform, based on my consumption patterns and through cross-matching algorithms between user preferences, must be able to decide which movies suit me. to like it more even though I haven't seen them.
I also work on gender violence recidivism prediction systems. The idea is that, when a woman goes to report a sexist assault, the Police collect the circumstances surrounding the case in the VioGén system and obtain an estimate of the probability that the assault will be repeated. The system is a pioneer in Europe and it is one of the ones that works best, but we wanted to add Artificial Intelligence to refine the statistical prediction with Big Data, improve it by 10-13%, and give what we call a more accurate Minority Report.
It is inevitable not to think then of Minority Report, the dystopia in which the Police predicted crimes before they occurred.
What VioGén tries to do is in that line, anticipate a recidivism of macho aggression. But the story and the film have a bias: their moral is that "people are being blamed before they commit the crime, and if so, they are not really guilty." Here it is not about blaming anyone before, but about offering additional protection to people who are already victims. The currently implemented system collects a lot of data, 38 indicators of the circumstances of the victim, the aggressor and their relationship, and it has been proven that it reduces the incidence of gender violence.
But there are problematic aspects: first, unfortunately, that it does not work in the very high number of cases in which it has not been reported first and the aggression is fatal. Another critical point is that it is difficult to measure its effectiveness: if there is no recurrence, have your additional measures been successful or did you make a mistake in the prediction? It's like the uncertainty principle of quantum mechanics: if you intervene to protect the woman, you change the outcome.
The mathematician José Ángel González-Prieto. Fundación BBVA
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— MS04 (9 days until b-day) Sun Jul 25 15:33:45 +0000 2021
There is a social paradox with data collection: If I open Netflix and it has agreed to your suggestion, I am delighted, even though I am handing over personal information that would otherwise shock me.
The concern that society has for the processing of its data is indeed a paradox. I understand it, but you also have to understand the dilemma and the different use. By entering Netflix, I agree to provide my data so that it can recommend the movies I like and in return I pay the monthly fee. But I disagree that my data is sold to an American company so that they can sell me insurance. That is the real social problem, the unexpected use that ends up in a Cambridge Analytica, designing an electoral campaign.
It is striking how his research profile combines theoretical aspects and practical solutions within the same discipline of mathematics.
It is true that on many occasions mathematicians tend to specialize in a specific area and stay there. I was fortunate to win a place in Computer Science at the Polytechnic after finishing my thesis at the Complutense Faculty of Mathematics. That postdoctoral paradigm shift, leaving your circle of trust, moving to the practical approach, made me open my mind and understand that there were other very important problems to solve, and that I could take what I had learned during my doctorate in algebraic geometry to export it. to 'machine learning'.
I also try to go back and forth: take applied questions and bring them to the theoretical world to try to understand the ways in which a theorem is understood. And it is a very natural path: we mathematicians like to live in the glass tower, in a mixture of the theorem that you write in an article and the thousands of pages that you have written before and thrown in the trash because they were the wrong proof. But those leaves are still analogous to the experiment that a biologist does in the laboratory.
It is not usual for someone of such a research level to stay in Spain. Have you found here all the opportunities you were looking for?
Not at all. I think that in Spain there are very few opportunities and typically excellent scientists and researchers are thrown out. Going abroad for a postdoctoral period is an excellent formative experience, but it should be optional like any other, and with a clear path back. I was very lucky, I practically stayed for a carambola. I try to make many stays but of short duration to interact with research groups.
Unfortunately, due to the pull policies that exist, many people are expelled from the system and go to other countries to carry out high-quality science that we are losing here. And this is also part of the social conception: people must understand that it is much more important to bring a scientist back from Germany than Cristiano Ronaldo from an English team.
Jon Asier Bárcena Petisco, postdoctoral researcher at the Autonomous University of Madrid; Xavier Fernández-Real, postdoctoral researcher at the Institute of Mathematics of the École Polytechnique Federale de Lausanne; Mercedes Pelegrín García, postdoctoral researcher at the LIX Computer Science Laboratory of the École Polytechnique (Paris); Abraham Rueda Zoca, postdoctoral researcher Juan de la Cierva-Formación at the University of Murcia; and María de la Paz Tirado Hernández, a postdoctoral researcher at the University of Seville, are the other five winners of the 2021 Vicent Caselles Awards.