Notices of the American Mathematical Society
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A Few Words About IMPA and My Relation with the Institute
About eight months ago, I had a great surprise when I opened my email and saw that Ben Jaye, one of the editors of this Early Career section of the Notices of the AMS and, more importantly, a friend, had invited me to write about the place where I work: the Instituto de Matemática Pura e Aplicada, better known simply by its acronym, IMPA. Located in Rio de Janeiro, Brazil, IMPA is a mathematical institute whose main focus is to produce high level mathematical research, to educate the new generation through its graduate programs, and to promote and disseminate mathematical knowledge in our society. The institute has around 50 full-time professors and offers master’s and doctorate degrees in pure and applied mathematics with a current student body of around 150 students. The institute runs around 10 weekly seminars in different areas of mathematics and it is the venue for over 10 events every year including conferences and workshops. As a consequence, IMPA has a continuous flow of researches from all over the world visiting it, which creates a very rich environment for its students and faculty members. The institute also plays an important role in Brazil’s society by organizing events such as workshops designed for high school teachers and the Olimpíada Brasileira de Matemática das Escolas Públicas (OBMEP), which is currently the largest mathematics olympiad in the world with over 18 million students taking part in it every year.
IMPA’s main entrance.
Despite the fact that writing an essay of this sort is something that goes way beyond my expertise—there is a very good chance that the last time I wrote a nonmathematical essay was for my university entrance exams—I accepted Ben’s invitation and hope this can be of use to the math community, especially to early career fellows who are not very familiar with Brazilian mathematics and/or IMPA. As the attentive reader may have already noticed, it took me eight months to start writing this piece. While one could attribute this to the usual procrastination that afflicts us all from time to time, I will argue that this has more to do with my insecurities regarding the “style” and “structure” that this text would have. Regarding the chosen style, it already must be clear: informal. As for structure, I think I should start with the basics.
Who am I and what is my relation with IMPA?
My name is Bruno de Mendonça Braga, but most of my friends call me Braga. I am from Rio de Janeiro, Brazil, and did both my undergraduate and master’s studies in the Universidade Federal do Rio de Janeiro (UFRJ), the federal university here in Rio. Despite IMPA being in my home town, the first encounter I had with it was in January of 2009, during my masters at UFRJ. IMPA’s classes are always open for students from other institutions to attend, but the months of January and February, during our summer in Rio, are very special at IMPA: the institute offers around 20 different graduate courses in pure and applied mathematics and it sponsors dozens of students and professors from all over the world to come visit IMPA. During the summer of 2009, I took functional analysis, with Benar Svaiter, and I can confidently say that this ended up changing my life; not only did I have a great summer and love the lectures, but functional analysis also ended up becoming my research field.
After my master’s degree, I decided to cross the equator and do my PhD in North America. The motivation for the 21-year-old version of myself to make this move was not based purely on mathematics; besides IMPA, Brazil has many other excellent places I could go to in order to pursue my doctorate such as the aforementioned federal university of Rio (UFRJ) and the Universidade de São Paulo (USP), the state university of São Paulo. My decision was mainly driven by a strong internationalization desire. Besides the personal aspects of it—I was young and wanted to get to know more about the world, master a new language (still working on that part), etc.—I also believed that it was very important to be exposed to the international mathematical community as much as possible. Fourteen years later, I cannot stress enough how much I believe that my young self was correct and I would highly encourage young researchers everywhere to do the same; the world is bigger (and often more interesting) than our backyards. During the twelve years I spent in North America, I obtained two PhD diplomas, from Kent State University (KSU) and the University of Illinois at Chicago (UIC), and had two post-doctoral experiences, from York University (YU) and the University of Virginia (UVA).
In 2022, after over a decade above the equator, I was finally able to return back home. While my time abroad was fantastic both mathematically and personally (I never thought I would meet my now wife in Kent, Ohio), it had always been my dream to be able to return back home and be able to contribute to Brazil’s mathematics. After a short period at the Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), a Catholic private university in Rio with a fantastic mathematics department, I got a tenure-track position at IMPA and I have been here for two years now. Earlier this year, in our summer program of 2024, I was in charge of teaching the functional analysis course here at IMPA. It was quite special for me to be able to return to this course now on the opposite side of the classroom.
The early ages of IMPA
IMPA was founded in 1952 by the astronomer Lélio Gama and the mathematicians Leopoldo Nachbin and Maurício Peixoto as the first research unity of the then recently created Conselho Nacional de Pesquisas (CNPq), a sort of Brazilian version of the National Science Foundation (NSF). Gama was IMPA’s first director (1952–1966). Nachbin, a functional analyst, later became the first Brazilian to be invited to speak at the International Congress of Mathematicians (ICM) in 1962 and Peixoto, a dynamicist, became the second in 1974. It took decades for the then recently created institute to consolidate itself, become a leading center in the development of mathematics in Brazil and, later, establish its international excellence. For instance, it wasn’t until 1962, ten years after its birth, that the institute opened its graduate program—it should be said that (due to the beauty of modern bureaucracy), IMPA needed the help of UFRJ to officially grant its students their diplomas up to 1971, when the institute finally obtained the autonomy to issue its own diplomas. It also wasn’t until the 70s that IMPA started to have its own full-time permanent faculty; up until then its members would be affiliated with other institutions or have short contracts which would be renewed every few years.
For its first few decades, IMPA did not have its own headquarters and it physically moved addresses a couple of times, sharing its facilities with a couple other entities such as the Centro Brasileiro de Pesquisas Físicas (CBPF), the Brazilian center for physics research. Finally, in 1981, during the term of Lindolpho de Carvalho Dias (who was IMPA’s director for 22 years), IMPA opened its first campus in Jardim Botânico, a very pleasant neighborhood of Rio which still maintains a large amount of its original Atlantic Forest. This gives the neighborhood, and, in particular, IMPA, a very bucolic atmosphere (or at least as bucolic as a place in a city with over 6 million people can be). The institute is located in a very privileged spot surrounded by forest and it may be the only place on earth in which monkeys come to watch symplectic geometry classes through the windows on a regular basis.
Artur Avila giving a colloquium at IMPA.
Another important figure in IMPA’s history is Elon Lages Lima. Besides its mathematical research, Lima was arguably the most prolific Brazilian writer of mathematics textbooks and had deeply impacted the development of Brazilian mathematics as a whole. Lima was also the institute’s director at three distinct occasions; from 1969 to 1971, 1979 to 1980, and 1989 to 1993. Interestingly, Lima was responsible for introducing the future Fields Medalist Stephen Smale to Peixoto, who later invited Smale to spend a year at IMPA. It was during this first visit to Brazil that Smale obtained the proof for the Poincaré conjecture for dimensions greater than four; and the best part—as Smale himself has already said—this happened on the beach of Copacabana.
French mathematics also played a very important role in the development of IMPA and its internationalization. The reason for that is quite curious: up until 2001, France had mandatory military service and one of the ways accepted by the French state for young researcher to escape (this punishment) was to be an exchange researcher abroad. During this period, IMPA was fortunate enough to attract many incredible researchers such as Christian Bonatti, Etienne Ghys, and the fields medalist Jean-Christophe Yoccoz.
From 1993 to 2003, Jacob Palis was IMPA’s director. Palis, a brilliant dynamicist and former student of Smale’s, also served as president of the International Mathematical Union (IMU) from 1999 to 2002, and as president of the Brazilian Academy of Sciences from 2007 to 2016. Palis led the institute through a very important change in its legal status which remains until now: IMPA moved out from CNPq and became a Social Organization under the auspices of the Ministry of Science, Technology, Innovations and Communications (MCTIC) and the Ministry of Education (MEC) of Brazil. The technicalities of such change are out of the scope of this piece, but, in my point of view, this (bureaucratic) move has been excellent for the development of the institute: it gave IMPA much more autonomy and allowed it to shape itself in a more attractive way internationally.
IMPA’s modern days and future
After Palis, César Camacho acted as the director of IMPA from 2004 to 2015. With the already mentioned changes in IMPA’s legal status, this period was very important for IMPA to consolidate its internationalization. The institute renewed its faculty with the hiring of many young researchers and finally was able to begin hiring regularly on the international job market. In 2004, IMPA signed an agreement with the Centre National de la Recherche Scientifique (CNRS), the main research agency of France, and it became part one of CNRS’s Unité Mixte Internationale (UMI). As a result, CNRS members frequently come to IMPA and work here for extended periods of time. Due to IMPA’s strong link with Yoccoz, the UMI was named after him when he passed away in 2016.
In 2014, Artur Avila, a professor here at IMPA and former student of the institute, became the first Brazilian to be awarded a Fields Medal. More than merely the first Brazilian to be honored with this prize, Avila is also the first Fields Medalist who completed his entire education in a developing country.
Marcelo Viana, a former doctorate student of Palis, became IMPA’s director in 2015 and he has been in this position to the present date. Viana, a renowned dynamicist and laureate of the prestigious award Grand Prix Scientifique de la Fondation Louis D., has been crucial to some of the latest achievements not only of IMPA, but of Brazil’s status within the mathematical community worldwide. The International Mathematical Olympiad (IMO) was held in Rio de Janeiro in 2017 and, in 2018, it was time for the ICM to be held in Rio. Still in 2018, IMPA and the Sociedade Brasileira de Matemática (SBM), the Brazilian mathematical society, led the candidacy of Brazil to enter Group 5 of the IMU: this is a selective group of the 10 nations in the world with the most developed mathematics according to the IMU.
Earlier this year, in 2024, IMPA took yet another important step in its history: the institute opened its undergraduate program, IMPA Tech. As stated in its name, IMPA’s undergraduate program will have an important focus on the new uses of mathematics in our society and aims to become an important engine in the new hub of technology being created in Brazil—this does not mean students interested in pure mathematics are not highly welcome to the program as well, on the contrary! The new undergraduate institution has an uncommon entrance pathway. It will annually select up to 100 students from all parts of Brazil mostly based on their performance in several olympiads, such as the mathematics, physics, and programming olympiads. Although it is still too early to know how things will develop with IMPA Tech, its future surely looks bright!
IMPA Tech earlier this year before classes began.
Final words
IMPA is a prestigious center for mathematics located in Rio, Brazil, which has been exponentially growing and contributing in a fundamental manner to Brazilian mathematics and science as a whole—IMPA’s presence actually goes way beyond Brazil’s border and the institute works as a mathematical center for all of Latin America. IMPA highly encourages people from everywhere to apply to its graduate programs and has been consistently hiring a couple of new professors every year in the international job market. If you are in either of these categories, we would be very pleased to consider your application! Last, but definitely not least, Rio is a wonderful city which combines everything a big city has to offer with incredibly beautiful nature. Even if you do not plan on applying for a position here, IMPA and Rio are definitely worth a visit!
An ugly day in Rio.
Bruno de Mendonça Braga is a professor of mathematics at IMPA. His email address is demendoncabraga@gmail.com.
Article DOI: 10.1090/noti3093
Credits
Figures 1–3 are courtesy of IMPA.
Figure 4 and photo of Bruno de Mendonça Braga are courtesy of Bruno de Mendonça Braga.