Leadership in Research and Training
Maintaining an international footprint and partnering with other research groups and institutions are essential activities in order to keep abreast of recent developments in applied analysis, be in a position to identify cutting-edge mathematical questions, and remain a global leader in the training of postdoctoral fellows and graduate students, always cognizant of the various research opportunities at the interface between the mathematical and physical sciences and engineering. As Director of the CNA since 1998, Fonseca is actively engaged in searching for new opportunities, facilitating existing collaborations, and helping build new bridges between different institutions in the United States and Europe, thus guaranteeing and securing the center’s reputation as a national and worldwide asset in the education and training of a new generation of researchers well informed and well positioned to respond to those challenging areas of materials science, solid state physics, and biotechnology that are at the forefront of mathematics today. The CNA works to deepen its existing collaborations and cultivate new opportunities through the co-organization of conferences, workshops and summer schools, as well as providing mobility for postdocs and advanced graduate students.
Fonseca is the Principal Investigator (PI) of the $5 million, 5-year National Science Foundation-funded PIRE (Partnerships for International Research and Education) on "Science at the Triple Point Between Mathematics, Mechanics and Materials Science" (http://www.math.cmu.edu/PIRE/). Many contemporary problems in new advanced materials relate to variation in length, time scales, and variations inherent in their fabrication and function. Resolution of these problems requires predictive theories for these complex systems that in turn require advances in mathematics. In this PIRE project an international network of prominent mathematicians from four U.S. institutions, six European institutions, and a multinational industrial partner, will build on decades of collaboration and training at the interface of mathematics and materials sciences that have yielded many achievements at the forefront of sophisticated new mathematics and simulation methods.
The project will focus on four principal research areas:
Collaborators on this PIRE project include four U.S. institutions: Carnegie Mellon University (PA), California Institute of Technology, New York University, and University of Minnesota; six European institutions: University of Antwerp (Belgium), University of Bonn (Germany), Max Planck Institute
for Mathematics in the Sciences (Germany), International School for Advanced Studies (SISSA)(Italy), University of Oxford (UK), and the University of Warwick (UK); and an industrial partner: Robert Bosch GmbH (Germany and USA).
International School for Advanced Studies (SISSA) in Trieste. This is a continuing exchange agreement beginning in 2005 per which postdocs and researchers of each institution will visit the other for a period of one month between January 2006 and December 2008. This project had the financial support from the Italian Ministry of Education and Research (MIUR) in the amount of 14,940 euros, and of SISSA in the amount of 8,500 euros. One CNA postdoc and two Co-PIs spent one month at the SISSA, and the CNA had (and has) annual visits from at least 2 SISSA researchers.
The CNA and the SISSA are now partners in the recently NSF awarded PIRE on Science at the Triple Point Between Mathematics, Mechanics and Materials Science. See http://www.math.cmu.edu/PIRE/index.html.
The Max Planck Institute for Mathematics in the Sciences in Leipzig (Germany), the Mathematical Institute at the University of Oxford (UK), and the University of Boon together with the Hausdor Center for Mathematics in Bonn (Germany), have re-structured previous interchange agreements with the CNA through the current CNA NSF PIRE award on "Science at the Triple Point Between Mathematics, Mechanics and Materials Science".
The University of Naples (Italy) and the CNA signed an agreement in 2012 to facilitate the mobility of young researchers between the two institutions.
In 2012 the Center for Nonlinear Analysis agreed to participate as associate organization in the research project "Mechanics of Complex Materials", managed by the Italian Ministry of Education, University and Research, under the scientific responsibility of Professor Cesare Davini as coordinator of the Research Unit of Udine (Italy). This agreement was also extended to the University of Trento (Italy), under the same grant proposal.