The Role Of Mathematics in the CMU Portugal Program

   Mathematics is a science that studies patterns and structures, and it is about performing logical analyses, deductions and calculations within those patterns and structures. The notion of ‘computing’ alone would not have made sense without Mathematics, and it was the analysis of mathematical methods by mathematicians, philosophers, logicians and engineers that led to the concept of ‘programmable computers.’ 

In Portugal, José Miguel Urbano, full professor at the Universidade de Coimbra, has recently taken on the challenge of leading the Mathematics area in the CMU Portugal Program, succeeding to Diogo Gomes, professor at the Instituto Superior Técnico of the Universidade de Lisboa (IST-UL). 

One Plus One Equals Many 

“I see Mathematics as an area on its own within the CMU Portugal Program,” states José Miguel Urbano, “but for me the best thing about the Program is that it strengthened the relations between mathematicians in Portugal and at CMU.” According to the researcher, “that has brought additional notoriety to the area and has enabled a number of collaborations with top mathematicians at CMU, and that is outstanding.” 

“We mathematicians have always had some problems finding applications for our work because we have a tradition of fundamental research as opposed to applied research,” the researcher explains. “This happens because mathematical applications are not immediate.” But did you know that the mathematics of error-correcting codes is applied to CD players and to computers, or that the pictures from distant planets sent by Voyager would not have their crispness and quality without Mathematics?  

“We have been doing a great effort to change this tradition of uncooperativeness. In the UT Austin Portugal Program, for instance, we have been applying our work in the medical imaging area. So it’s possible and I think we can go down that road with the CMU Portugal Program as well,” he states. 

An Opportunity to Get the Work Out There 

“We have three ongoing projects within the CMU Portugal Program, one of them in financial mathematics. Basically, researchers involved in these projects have been producing research papers,” he explains. But more than that, the fact that people, professors, students, and post-docs have the opportunity to spend some time at CMU, through the Faculty Exchange and the dual degree programs, “is a way of getting collaborations going and of getting the work out there,” he adds.  

 

 Rita Goncalves Ferreira 
Rita Ferreira, advised by Irene Fonseca (CMU) and Luísa Mascarenhas (Faculdade de Ciências e Tecnologia of the Universidade Nova de Lisboa – FCT-UNL), and Robert Simione, advised by Diogo Gomes (IST-UL) and Dejan Slepcev (CMU), are the two alumni of the dual degree Ph.D. in Applied Mathematics. “I think that while some people view programs like CMU Portugal with some doubt and keep their distance, others see them as an opportunity,” the professor explains, adding that “I think we have been collaborating at the same level, although we don’t have infrastructures as developed as American universities do.” 
 Robert Simione 

Post-docs have also been an important way to foster and strengthen collaborations in Mathematics between Portuguese universities and CMU. The post-doc Marco Morandotti, mentored by José Matias (IST-UL) and Irene Fonseca (CMU), started his post-doc at CMU and then came to Portugal, in the scope of the research project “Thin Structures, Homogenization, and Multiphase Problems,” carried out under the CMU Portugal Program. While in Portugal, Marco had the opportunity to teach Recitations for the course "Complex Analysis and Differential Equations,” and was involved on the organization of the Workshop“Trends in Non-Linear Analysis,” at IST-UL, among other research activities. 

The Program provides access to a world-renowned university, it is an opportunity to leverage the science made in Portugal. According to José Miguel Urbano, “those who have had the opportunity to participate in the CMU Portugal Program brought a lot of notoriety to their research, and even the conferences that we organized together brought more attention to these researchers and their work. Without the CMU Portugal Program, this would not have been possible.”  

The Next Step for the Future 

The next step now is promoting projects involving both mathematicians and scientists from other areas. “Although mathematicians find it hard to collaborate with other scientists sometimes, that’s something we would like to work on in the future,” he adds. Because there has been a shift in the Program’s goals with the new phase, “now we want to try to identify potential collaborations and projects to which mathematicians can provide some relevant input and contributions,” he concludes. 

September 2014

Projects approved in the Call 2009 in Applications of Mathematics Thematic Areas, in the framework of the Carnegie Mellon Portugal Program and UT Austin-Portugal


Degenerate Elliptic and Parabolic Equations and its Applications to Front Propagation more
Diogo Gomes (IST/UL) and Dejan Slepcev, David Kinderlehrer (CMU)

SANAF: Stochastic Analysis and Numerical Approximations in Mathematical Finance
more
Cláudia Philippart (IST/UL) and Dmitrry Kramkov (CMU)

Thin Structures, Homogenization and Multi Phase Problems more
Luísa Mascarenhas (FCT/UNL) and Giovani Leoni, Irene Fonseca (CMU)

Related Articles: 

    Trends in Non-Linear Analysis in Discussion
    Irene Fonseca Receives Highest Faculty Distinction at Carnegie Mellon
    Robert Simione Successfully Defended his Ph.D. Dissertation
    Rita Ferreira personal webpage