'My only superpower is not giving up,' says IMPA PhD.

Having recently earned her doctorate in mathematics from IMPA, Clarice de Souza Ferreira Netto, from Cabo Frio (RJ), is still surprised by the achievements she has gained in her professional career. For someone who attended modest, unremarkable public schools in the Rio de Janeiro Lakes Region, certain accomplishments were unimaginable.

"I've always studied in public schools, from kindergarten to doctorate. But they weren't star public schools, the kind that produce medalists for the Brazilian Mathematical Olympiad (OBMEP), the ones that top the lists of those accepted into university… I studied in regular schools. That's my basic education," she says. "I'm nothing special: I didn't come from a prestigious school, I didn't win any Olympic medals, my family is normal, from the working class. My only superpower is not giving up."

Armed with this perseverance, the doctoral candidate, daughter of public school teachers, completed another important stage of her education. On October 13th, she defended her thesis "Compatibility of Nijenhuis operators with Dirac structures and Courant algebroids" via videoconference.

Clarice defines the last ten years of her life, encompassing her time from graduating in mathematics from the Federal Fluminense University (UFF) to her doctorate at IMPA, as an "emotional rollercoaster." "I was incredibly happy many times. I made many friends, traveled to other countries, learned so much, solved so many problems, connected deeply with so many stories…," she recounts.

Her first international trip came thanks to mathematics, through the "Science Without Borders" program, which she participated in during her undergraduate studies in 2012. The Cabo Frio native lived for a year in Madrid, Spain. "It was a defining experience in my academic life. There I participated in a 'scientific initiation' program that lasted the last two months, where I learned about the area of symplectic geometry, in which I am still working today. My supervisor, David Martin de Diego, introduced me to Paula Balseiro, who would become my master's thesis advisor, and she was super important in my journey," she recalls.

The doctoral student felt the impact of gender inequality in the field.

But, in addition to having great experiences, the doctoral student felt the impact of gender inequality in the field, which brought her unpleasant situations. “I lived through complicated moments, ranging from doubts about my intellectual capacity to harassment. The effect of this on me was a total lack of confidence in my intellectual ability, but each woman feels it in her own way,” she shares.

The support of some colleagues and professors along the way, however, partially eased these difficulties. “I was fortunate to find wonderful people who trusted me while I doubted—or rather, was absolutely certain that I wasn't capable. One of them was my master's thesis advisor, Paula Balseiro. If I am here today, it is because she believed in me and dedicated time to teaching me what she knows. She is a great inspiration to me.”

Involved in the discussion about gender inequality in science, Clarice helped organize the 1st IMPA Meeting of Women Mathematicians in May of this year. “The meeting was wonderful. It’s very important to have a space to share our stories and encourage the creation of new ones.” She believes that this type of initiative is growing and may signal a change in the landscape. “It’s part of the current moment where more women are accessing this space, which was once completely dominated by a profile different from ours.”

Her own personal journey symbolizes this change. “It’s been more than 10 years dedicated to professional growth, trying to be part of an intellectual elite that wasn’t designed for a woman who came from regular public schools. The place I occupy today, the title I just earned, wasn’t meant for me. This wouldn’t naturally be my place. But here I am,” she celebrates.

Thesis deals with Poisson geometry

Supervised by IMPA researcher Henrique Bursztyn and co-supervised by Thiago Drummond, a professor at the Federal University of Rio de Janeiro, the doctoral candidate's thesis falls within the area of Poisson Geometry. During her postgraduate studies, Clarice studied the compatibility of Nijenhuis operators with Dirac structures and Courant algebroids. “I explored properties and examples of these new geometric structures obtained from Dirac structures and Courant algebroids by adding 'extra information' given by the Nijenhuis tensor. I addressed results such as integration and their relationship with holomorphic Dirac geometry in the thesis.”

My interest in Dirac structures began during my master's degree and was further explored during my doctoral studies. "I really enjoyed the topic because it has a connection to classical mechanics, since in some cases the Dirac structure describes an integrable system," he explains. "In my doctoral studies, I explored these structures from a more geometric point of view, setting aside their physical application for now. The results of my thesis opened up many avenues; I have interesting questions to answer for many years to come."

Like many of his colleagues, the Covid-19 pandemic interfered with the development of his doctoral research. Besides delaying his defense, it affected the dynamism of conversations with his thesis advisors, which previously took place "at any time in the IMPA hallways" and then became scheduled via online platforms. "The blackboard and casual conversations were missed. The pandemic changed the pace of work and access to good mathematical discussions, necessary for the development of any research project. It affected the building of work partnerships, attending conferences. I lost contact with several colleagues. All of this weighed negatively."

In this context, close contact with the advisors was a strong ally in the endeavor. “Being Henrique's student was a unique opportunity for learning and exchange. Because of him – who guided me so well throughout this process, gave me an interesting problem to work on, and has such a unique network of collaborators and former students – I see a path to follow. Thiago, my co-advisor, was the most pleasant surprise of my doctorate. Initially, we weren't going to work together, but he appeared at the right time and was fundamental in getting me here. Very patient, he was always willing to listen to me talk, even if I couldn't formulate a mathematical sentence that made sense. I am very grateful to both of them; they are an example for me.”

Passionate about the learning process, Clarice intends to continue her academic research now that she has completed another chapter of her journey, and to give back, in some way, the public investment she received during her education. "I love always learning, discovering something new, even if it's tiny. I still have a lot to learn and contribute to my field," she concludes.