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Mathematics

A formula that worked

Academic flexibility and internationalization are part of IMPA's formula for success

Class taught at the institute's building, in Horto, a neighborhood in Rio de Janeiro: open to math prodigies, like IMPA's famous student Artur Ávila, winner of the Fields Medal

LÉO RAMOSClass taught at the institute’s building, in Horto, a neighborhood in Rio de Janeiro: open to math prodigies, like IMPA’s famous student Artur Ávila, winner of the Fields MedalLÉO RAMOS

from Rio de Janeiro  

On a trip to Rio de Janeiro in the early 1980s, the economist José Alexandre Scheinkman, from Rio de Janeiro, decided to visit the new headquarters of the Brazilian Institute for Pure and Applied Mathematics (IMPA), a four-story glass building located in the Horto neighborhood, on the edge of the Atlantic forest between the Tijuca National Forest and the Botanical Gardens. Then a professor at the University of Chicago, he had maintained ties with the institute since the late 1960s when he undertook a master’s degree there in parallel with an economics undergraduate degree at the Federal University of Rio de Janeiro (UFRJ). He was also a visiting professor at IMPA in 1978-9. But that was not an entirely disinterested visit.

Scheinkman was having trouble understanding a paper on the mathematical theory of chaos, which he wanted to apply to an economics problem. He intended to knock on the door of Jacob Palis, an old acquaintance and one of the most famous professors at IMPA, who would certainly explain the details of the article to him. “I knocked and a huge man opened the door and said, in English, that Professor Palis was traveling,” recalls Scheinkman, 68, now a professor emeritus at Princeton University and professor at Columbia University in New York. “Then he introduced himself: his name was Floris Takens.” The Dutch mathematician was the author of the article that had led Scheinkman to the Institute. Takens, who did research with Palis and was spending some time in Brazil, explained the paper personally.

IMPA facade

LÉO RAMOSIMPA facadeLÉO RAMOS

The economist’s experiences illustrate three characteristics that, over more than six decades, have been incorporated into IMPA’s DNA: the recruitment of promising young students, the lack of concern for academic formalities, and the internationalization of its faculty and student body. Founded by three researchers in 1952, the institute, which has an annual budget of R$35 million from the Ministry of Science, Technology and Innovation (MCTI), currently has 48 full-time researchers on the payroll, 18 of which are foreigners. About 40% of its current 154 graduate students are from overseas, many from other Latin American countries. Among the 60 post-doctoral researchers, the story is not much different: 40% are Brazilian, 60% are foreign.

A page on the IMPA site—updated every month—lists the number of visiting researchers teaching classes or doing research in the Horto building. In August 2015, there were 51 names on the list, 12 from Brazilian institutions. “IMPA is an international leader, both in research and in mathematics education,” says Argentine Matias del Hoyo, a specialist in geometry, who received a grant for up to three years to work as a visiting researcher and professor. “The Institute has resources and stands out due to the excellence of its researchers and its very active environment, with conferences and visitors throughout the year.”

IMPA’s reputation for excellence extended beyond academics when Rio de Janeiro native Artur Ávila, one of the leading products of the extensive genealogy of mathematicians who have graduated from the institute (744 master’s degrees and 401 doctorate degrees have been awarded during its six decades of operation), became the first South American to win the Fields Medal, the most prestigious international mathematics award, in 2014 (see the interview with the researcher in Pesquisa FAPESP Issue No. 223). The story of Ávila, 36, now an extraordinary researcher at IMPA and director of research at the Centre National de la Recherche Scientifique (CNRS) in Paris, is typical IMPA. He finished his master’s degree while still in secondary school, at 18, and finished his doctorate at 21, together with his bachelor’s degree at UFRJ.

Impa's library: 60,000 items for 48 professors, 154 graduate students and 60 post-doctoral researchers

LÉO RAMOSImpa’s library: 60,000 items for 48 professors, 154 graduate students and 60 post-doctoral researchersLÉO RAMOS

“We don’t place a priority on academic formalism here, we’re more flexible,” says César Camacho, general director of the institute, who has dual citizenship: Peruvian (he is from Lima) and Brazilian. “Additionally, in mathematics, talent often appears early.” Camacho was accepted into IMPA’s master’s program back in the 1960s, without having completed his undergraduate degree in physical sciences and mathematics at the National University of Engineering, in Lima. Brazilian legislation does not allow individuals without an undergraduate degree to receive a graduate degree. Therefore, IMPA lets its students in this situation study for their master’s or doctorate degrees, but only apply to validate their graduate degrees after the students formally complete an undergraduate degree.

The number of scientific articles published by IMPA researchers in peer reviewed journals seems modest when compared to the figures for the biological sciences but, according to the institute, they are similar to those from the world’s top mathematics departments. According to IMPA’s 2014 management report, which used data extracted from MathSciNet, a publication of the American Mathematical Society, its faculty published 76 papers in 2012, an average of 1.65 articles per professor. The mathematics department at Princeton University had the highest average, 2.1 articles per researcher, with 88 papers published that year. In terms of impact factor, each IMPA article was cited 1.46 times according to a weighted average, surpassing important mathematics research departments, such as the University of California at Berkeley (1.41) and the University of Cambridge (1.30). Princeton also headed this ranking, according to the IMPA report, with 2.59 citations per paper.

IMPA clearly has international prestige, especially after the Fields Medal. But in the ranking of the world’s best institutions of higher education with mathematics programs, published in 2015 by the British consulting firm Quacquarelli symonds (QS), IMPA holds a modest position: between 301st and 400th place, behind the University of São Paulo (USP) and the University of Campinas (Unicamp), both between the 51st and 100th place, and UFRJ (151-200) and the Federal University of Minas Gerais (251-300).  “I do not agree with this comparison. It involves institutions with different structures. The result is unreliable,” says Palis, director of IMPA from 1993 to 2003 and current president of the Brazilian Academy of Sciences (ABC). The assessments of the USP and Unicamp mathematics departments also seem to be distorted downward. Brazilian mathematics as a whole has great international prestige.”

Director César Camacho...

LÉO RAMOSDirector César Camacho…LÉO RAMOS

Palis believes that IMPA’s success can be explained, in part, by its discreet trajectory and slow growth, but marked by good management and administrative continuity. “If IMPA had started out large, perhaps it would not have become such a success,” he says. As the first research unit established by the National Council for Scientific and Technological Development (CNPq), the institute was founded in 1952 by three renowned researchers: Lélio Gama, an astrophysicist and mathematician who served as the first director, a position he held until 1965, while also heading up the National Observatory; Leopoldo Nachbin, a mathematician, also one of the founders of the Brazilian Center for Physics Research (CBPF), with good connections abroad; and Maurício Matos Peixoto, who developed the field of dynamic systems, in which Palis, Ávila and other IMPA mathematicians work. After Gama, IMPA had only four more directors. From 1965 to 1993, two individuals led the institution, alternating back and forth: Lindolpho de Carvalho Dias and Elon Lages Lima, the latter still a professor emeritus. Then came Palis, and now Camacho.

Before definitively establishing roots in the pleasant Horto neighborhood in 1981, IMPA had three temporary addresses. During the first five years, it occupied a CBPF room in Praia Vermelha. From 1957 to 1967 it operated out of a mansion in the Botafogo neighborhood, and then in a building in downtown Rio de Janeiro until it moved to its own building at the current location. The facilities changed as the institute grew. At the turn of the 21st century, already in the building on Castorina Street, it had 31 resident researchers. In 2001, during Palis’ administration, a structural change gave it even more administrative and scientific autonomy: The institution became a social organization (OS), a non-governmental non-profit legal entity, funded, basically, through a management contract with the MCTI. “We spent a year discussing whether or not we should become an OS,” recalls Luiz Velho, coordinator of Visgraf, the computer graphics laboratory founded at IMPA in 1989.

At the time, the principal concern was that this legal form would represent a gateway to the privatization of public research. “We use the OS regime in a responsible way here,” says Velho. IMPA’s management agreement with the MCTI establishes 18 annual goals to be met by its faculty, such as the publication of a given number of articles in top international journals and the graduation of a certain number of master’s and doctoral students.

...researcher Jorge Zubelli ...

LÉO RAMOS…researcher Jorge Zubelli …LÉO RAMOS

The Brazilian Association for Synchrotron Light Technology (ABTLuS), in Campinas, was the first research institution to convert to an OS and sign a management agreement with the MCTI.  In obtained this legal status in January 1998. Today, five research institutions associated with the ministry have adopted this system, which lets them establish their own rules and procedures, different than those governing the public sector. “A bad institution doesn’t become good because it turned into an OS,” said Carlos Américo Pacheco, general director of the Brazilian Center for Research in Energy and Materials (CNPEM, the successor to ABTLuS), the organization that administers the National Synchrotron Light Laboratory (LNLS) and three other laboratories. “OSs have a management agreement with a clear mission that gives them freedom to pursue their goals and avoid, for example, premature job security, which could result in lack of ambition in some cases. But not all research institutions need to operate under this regime.”

One of the reasons why there are few OSs linked to the MCTI, according to Pacheco, was the legal uncertainty during more than 15 years regarding the legality of management agreements entered into by these entities and the Brazilian government. A lawsuit that questioned the constitutionality of these OSs acting in areas that would normally be the responsibility of the government—such as health, education, research and environmental conservation—was filed in 1998. In April 2015 the Federal Supreme Court ruled on the issue and decided that OSs are legal.

...and Visiting Professor Matias del Hoyo—a Peruvian-Brazilian, a Brazilian and an Argentine, respectively; IMPA's faculty is increasingly international

LÉO RAMOS…and Visiting Professor Matias del Hoyo—a Peruvian-Brazilian, a Brazilian and an Argentine, respectively; IMPA’s faculty is increasingly internationalLÉO RAMOS

One of the advantages of being an independent legal entity is the ability to define its own policies for hiring and remuneration. The careers of the mathematicians hired by IMPA are divided into nine salary levels, three each for each of three research positions (assistant, associate and full researcher). The lowest pay level, that of the assistant professor at level 1, is R$16,700 per month. The highest, for a full professor at level 9, is R$22,900 per month. “IMPA had a good start and was well implemented. Its qualities were given an extra boost when it became an independent legal entity,” says physicist José Fernando Perez, former FAPESP scientific director and the oldest of the 10 members of the institute’s board of directors, a new body established when it became an OS. “Today it has the flexibility that public universities do not have to hire and fire faculty.”

When he decided to quit his job at Microsoft Research, in the Seattle area of Washington State, and return to Rio de Janeiro in the late 2000s, computer engineer Diego Nehab, 38, had two good job offers in academia: one from a private university and one from IMPA. The latter paid 30% more and offered other comparative advantages. “IMPA has many ties to colleagues abroad. Since I lived in the United States for a long time, all of my contacts were also outside Brazil,” says Nehab, who completed his doctorate at Princeton before joining the software giant and has been an associate researcher an IMPA since 2010.

International visits by staff researchers are facilitated by the adoption of a more flexible school calendar. Nehab, for example, has to teach during two of the three terms of the school year at IMPA. He can choose between teaching his courses in January and February, during the summer program, from March to June, or from August to November. That way, if he chooses to teach a summer course, he has one semester free to focus exclusively on research and potential travel. “IMPA receives many visitors and allows researchers great freedom to travel,” says Frenchman Hubert Lacoin, 30, a specialist in probability theory with emphasis on physics problems, hired in October 2014 as an assistant researcher.  One hundred candidates participated in the selection process that resulted in the hiring of Lacoin and the German Oliver Lorscheid, 37. Seventeen were from Brazil; the rest were foreigners.

Corridor in the IMPA building, in Horto: shorts and a relaxed atmosphere

LÉO RAMOSCorridor in the IMPA building, in Horto: shorts and a relaxed atmosphereLÉO RAMOS

IMPA researchers work in 11 mathematical subfields: algebra, analysis and partial differential equations, computer graphics, fluid dynamics, holomorphic dynamics and complex foliations, mathematical economics, differential geometry, symplectic geometry, optimization, probability and dynamic systems/ergodic theory. A joke often heard in the corridors of the institute is that, for a long time, IMPA stood for institute of pure and abstract mathematics. Today, the joke does not apply as much. Applied mathematics has gained ground during the last two decades. The Laboratory for Analysis and Mathematical modeling in Applied Sciences was established four years ago, and develops and uses mathematical tools to solve problems in different industries, such as oil, financial markets and public health. “We would like to have more students in our area,” say researcher Jorge Zubelli, laboratory coordinator.

Walking through the institute’s hallways, an environment in which mathematics is framed by the sounds, scents and views of the Atlantic Forest, is an introduction to the IMPA style of teaching and doing research. Conversations in Spanish, French and English merge with the Portuguese heard in the large break room, which usually fills during intervals between classes and events. A blackboard hung in one corner of the room gives the break room an almost academic air. “I also want to do my doctorate here,” says Jennifer Loria, in a mixture of Portuguese and Spanish. The woman from Costa Rica began the master’s program in January 2015 after contacting a Brazilian researcher two years earlier during an international mathematics olympiad. At 24, she is a little older than most of her classmates. “The environment here is beautiful and the people are warm.” Women are a minority at IMPA: only one professor and 12 graduate students, less than 10% of all students. Of current post-doctoral researchers, 10 are women.

From the large classroom windows at IMPA you can see the surrounding forest, just outside the building walls. When a professor pauses in his explanation in front of the blackboard, one can hear the noise of monkeys in the nearby trees if one is lucky. Even in autumn or winter students or young professors can be seen wearing shorts. If one wants silence, the library provides it. In addition to archives containing 60,000 items, including both classical and modern books and mathematical journals, the visitor can read in a large hall with a view of the Tijuca Forest and the Rodrigo de Freitas Lagoon.

Arturo ...

LÉO RAMOSArturo …LÉO RAMOS

IMPA’s excellence has allowed it to do something rare in the Brazilian academic arena: attract private contributions, a common practice in the university environment in the United States. Today, endowments represent 2% to 3% of the institute’s annual budget. The months that Ávila spends in Brazil, for example, are financed by a donation from Armínio Fraga, former president of the Brazilian Central Bank and partner in an investment bank. Ávila holds the title of extraordinary researcher and holds a chair at IMPA named in honor of the banker. In April 2014, the Marinho family, owners of the Globo group, whose headquarters is located in the Botanical Garden neighborhood, donated 250,000 m2 of land next to the IMPA building to the institute. The area is covered almost completely by Atlantic Forest, which cannot be cut, and involves numerous restrictions in terms of building possibilities. However, on the edges, in sections that have already been partially altered, there is space to build a new building. “We plan to build housing and expand our facilities,” says the director, Camacho. The high cost of housing in Rio de Janeiro is a problem for students and visiting professors that spend time at IMPA.

The Moreira Salles family, which was the main shareholder of Unibanco, now part of Itaú, also supports IMPA. The filmmaker and journalist João Moreira Salles came into closer contact with the institute in 2009 when he began preparing the profile of the mathematician Artur Ávila to be published in his magazine, Piauí, the following year. It was through this profile that Moreira Salles established ties to IMPA’s administration. He and his brother Pedro organized a group of people who financed the Magnas Conference program that, from 2012 to 2013, brought seven top mathematicians, six of whom were Fields Medalists like Ávila, to the institute for a week of talks and interactions with students and researchers. The Moreira Salles family also helps out when IMPA visitors need housing. The filmmaker says that he is part of a group of people open to the idea of helping and supporting IMPA and the Mathematics Department at PUC-RJ.

...João Pedro...

LÉO RAMOS…João Pedro…LÉO RAMOS

“The people of Rio de Janeiro are increasingly interested in strengthening relations with IMPA. It is a center of excellence in research in Rio de Janeiro, when most are in São Paulo. We have a duty to help it,” says the filmmaker.

One side effect of the recognition achieved by Brazilian mathematics is that major international centers fight over the talents trained by IMPA. In September 2014, 35-year-old IMPA mathematician Fernando Codá, from the state of Alagoas moved to Princeton. Codá is considered a potential Fields Medal winner. The award is granted every four years to mathematicians under 40. Together with the Portuguese mathematician André Neves, Codá solved the Willmore Conjecture, one of the most challenging problems in geometry. “It’s normal to lose people. This is not a drawback,” comments Palis. “People leave, but they might return. Maybe we will receive a good donation to bring him back?” The next Fields medal recipients will be announced in August 2018 during the 28th International Mathematics Conference, which will take place in Rio de Janeiro. The mathematics party will be on IMPA’s home turf.

Studying during vacation

Summer courses attract young talent to IMPA

A gateway to graduate school admissions at IMPA—often used by students who have not even completed high school or who are still undergraduates—is IMPA’s summer intensive courses, offered in January and February. School holidays allow students from outside Rio de Janeiro and IMPA to attend classes more easily during this period. The courses are free and students can register though the institute’s site. In practice, the short courses serve as a test to see if the student is up to starting graduate work at IMPA, and count for credit if the candidate is accepted.

...and Maria Clara: IMPA students who are studying for their master's and bachelor's degrees simultaneously

LÉO RAMOS…and Maria Clara: IMPA students who are studying for their master’s and bachelor’s degrees simultaneouslyLÉO RAMOS

João Pedro Gonçalves Ramos, 19, from Rio de Janeiro, now a master’s student at IMPA, took two summer courses in 2013 (Real Analysis and Combinatorics I), when he was a junior in high school. He was accepted to the master’s program in October of the same year.” I had an 18-year-old friend enrolled in the doctoral program at IMPA. That’s why I knew one could do a master’s degree there without doing an undergraduate degree first,” says Ramos, who receives a scholarship of R$2,200 a month from the Rio de Janeiro Research Foundation (FAPERJ) and, in parallel, studies for a bachelor’s degree in applied mathematics at UFRJ.

Originally from Pirajuba, Minas Gerais state, Maria Clara Mendes Silva, 20, took a slightly more circuitous route before becoming a master’s degree student at IMPA in 2015. After distinguishing herself at several Brazilian Public School Mathematics Olympiads (OBMEP), a project implemented by IMPA in 2005 in which 18 million elementary and secondary school students participate annually, Maria Clara studied for a bachelor’s degree in science and technology for one year, 2013, at the Federal University of the ABC (UFABC) in Santo André, São Paulo state. But she soon realized that that was not what she wanted to study. Then she attended IMPA’s summer school in 2014, and was also admitted to the undergraduate program in mathematics at PUC-Rio.” I like the flexibility and lack of bureaucracy at IMPA,” says the student.

One of the difficulties faced by young students from outside Rio de Janeiro is finding a place to live at a reasonable price. A rented room near IMPA costs around R$700. Born in Lima, the master’s student Raúl Arturo Cháves Sarmiento, 17, has been rooming with his brother Enrique, 26, near the Botanical Garden, since March 2015, together with two other Peruvians. “Between 2012 and 2015 I attended four summer sessions at IMPA,” says Sarmiento, who is also pursuing an undergraduate degree in applied mathematics at the Getúlio Vargas Foundation (FGV) in Rio de Janeiro.

Most students who are accepted to the institute’s graduate programs prematurely were standouts at some OBMEP or at the Brazilian Mathematics Olympiad (OBM), an event also organized by IMPA for students in private or public schools who are studying at all levels, from elementary to university. “The main objective of the OBMEP is to encourage the teaching of mathematics in public schools,” explains Claudio Landim, associate director of IMPA and general coordinator of the Olympiads for public school students. “But this type of initiative helps us discover new talents.” In 2017, Brazil will host the International Mathematics Olympiad for the first time. Brazilian and foreign talents will be here.

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