Susanna Zimmermann, understanding birational transformations
Susanna Zimmermann is a Professor of Fundamental Mathematics at Université Paris-Saclay, within the Orsay Mathematics Laboratory (LMO - Univ Paris-Saclay, CNRS). A specialist in algebraic geometry, she is interested in birational geometry, algebraic groups and real algebraic geometry. Recipient of the CNRS bronze medal in 2020 for her work on groups of symmetries of algebraic objects, she has also been a junior member of the Institut Universitaire de France (IUF) since 2022.
If Susanna Zimmermann chose to study mathematics after her high school diploma in Switzerland, it was initially to have no regrets. "At the time, I was interested in everything: psychology, geology, archaeology and mathematics. But of all these disciplines, mathematics seemed the most challenging," recalls the lecturer. So, to avoid any future regrets, she decided to try mathematics first! While she had originally planned to go into finance to work in insurance, Susanna Zimmermann eventually decided to focus on mathematical research. "I had met some PhD candidates and their work intrigued and attracted me," she explains. After completing her thesis in birational geometry in 2016 in Basel (Switzerland), she chose to do her postdoctoral internship at the Paul Sabatier University in Toulouse, under Professor Stéphane Lamy, whose work was thematically close and from whom she knew she would learn a lot. The young researcher’s career flourished and, shortly after completing her postdoctoral internship, she was recruited as a lecturer at the University of Angers, where she spent five years until she obtained her Accreditation to Supervise Research in 2021. Subsequently recruited as a professor at Université Paris-Saclay, in 2022 she joined the Orsay Mathematics Laboratory (LMO - Univ. Paris-Saclay, CNRS) where she is currently conducting her research.
Immersed in birational geometry
Explaining Susanna Zimmermann's research field is no easy task, since, as she herself admits, "it really involves pure abstraction, in birational geometry". This means envisioning a sphere and placing it in Susanna Zimmermann's hands. What will she do with it? "I am interested in the symmetries of the sphere. For example, I can perform rotations around axes that I determine myself, but I can also choose to pierce the sphere and stretch it to obtain a plane, because geometrically the sphere and the plane are not so different from each other. In practical terms, I am interested in the properties of these types of symmetries, known as birational transformations," explains the lecturer. Why study these properties? While we know the sequences of special symmetries that generate symmetries of the plane, we know nothing about the sequences of special symmetries that generate the symmetries of space. "By learning more about the specific properties of birational transformation groups, it becomes possible to determine the relationships between different algebraic varieties," adds Susanna Zimmermann.
A CNRS medal and an ERC grant: recognition of initial results
When embarking on research in fundamental mathematics, it's hard to know if and when results will emerge. For Susanna Zimmermann, the initial results were not long in coming. "In collaboration with Jérémy Blanc from the University of Basel and Stéphane Lamy from the University of Toulouse 3, I solved a conjecture that had been open for almost 150 years, demonstrating the existence of subgroups with special properties within the symmetry group of higher-dimensional spaces," says the lecturer. This work earned her the CNRS Bronze Medal in 2020. One success leading to another, Susanna Zimmermann secured an ERC Starting Grant in 2023. "With this grant from the European Research Council and as a member of the Institut Universitaire de France, I benefit from a significant reduction in teaching. This enables me to recruit young researchers for postdoctoral internships, travel, carry out projects with colleagues abroad, and in short, to devote myself fully to my research, which has always been my priority."
The importance of building a community
Susanna Zimmermann could not envisage conducting research without engaging in dialogue with the broader mathematics community. "It is crucial to work on communicating your thoughts and results to other mathematicians and, conversely, to try to understand their research and results. This dialogue is essential, because it is within this exchange that the questions which may become our future research topics are born, and hypotheses are formed, sometimes leading to solutions, sometimes to new questions." This is why Susanna Zimmermann is always keen to increase her collaborations in France, but also in England, Switzerland and the United States, where she keeps in contact with numerous researchers. "I am also fortunate to work on a research theme that is supported by a sizeable and very dynamic community," the lecturer enthuses.
Making mathematics more inclusive
It is therefore hardly surprising that Susanna Zimmermann is passionate about breaking down barriers that could potentially deter entry into her field. While she was still a lecturer at the University of Angers, she contributed to the creation of a master class in the first year of a master's degree in mathematics, giving priority to women. "Although open to all, the aim was for at least half the participants in this master class to be women. The two main courses were taught by female mathematicians. The idea was to show everyone, both men and women, that women have their rightful place in research and a lot to contribute," she recalls. Susanna Zimmermann would like to see more such initiatives in the future. "In my opinion, the issue of inclusivity is not limited to the place of women; it concerns all minorities, ethnic or social, for whom the path to research can sometimes be more complex. I'm convinced that for research to be healthy and rejuvenate the dialogue that sustains it, it needs this diversity within."
Ambassador for the Maison Poincaré
While research and dialogue with her peers remain her top priorities, it is also important for Susanna Zimmermann to take the time to share her passion for mathematics with a wider audience. It is with this intention that she is currently ambassador for the Maison Poincaré, a museum associated with the Institut Henri Poincaré where mathematics comes to life. "In this museum, which I promote to the media, we welcome mathematicians, offer exhibitions and organise discussions to enable everyone to understand the approach of today's researchers and discover the history of mathematics through cultures and the arts. I believe that it is a way of showing that mathematics isn't necessarily what we might think it is, and that it has something exciting to offer everyone," concludes Susanna Zimmermann.
