Mathematics


Interdisciplinary research,
education and capacity building


The CoLab Mathematics Program

This program builds upon the collaborative programs in Mathematics between Portuguese Universities and the University of Texas at Austin. In the first 5 years this cooperative initiative involves the Institute for Computational Engineering and Science http://www.ices.utexas.edu/ (ICES) and the Department of Mathematics (math.utexas.edu) http://www.math.utexas.edu/of at UT-Austin and mathematical research centers and groups in four Portuguese universities, namely at the Mathematics  Department http://www.math.ist.utl.pt/Department of Instituto Superior Tecnico (IST)http://www.math.ist.utl.pt/(IST) of the Technical University of Lisbon, the Mathematics Department  http://mat.fc.ul.pt/pt/ of the School  of Sciences http://www.fc.ul.pt/ of the University of Lisbon (FCUL), the Mathematics  Department http://www.dmat.fct.unl.pt/ of the School of Sciences http://www.fct.unl.pt/ and Technology of the New University of Lisbon (FCTUNL), and the Department of Mathematics of the School http://www.mat.uc.pt/ of the School of Sciences and Technology http://www.fct.uc.pt/ of the Universidade de Coimbra (FCTUC). In this second phase of the program the Mathematics Department of the School of Sciences of the University of Porto will also be one of the main partners.
This collaboration between UT Austin and Portuguese institutions was extremely beneficial in a number of fronts.  Portuguese and UT-Austin faculty strengthened their academic connections, resulting in a number of joint publications, joint post-doc positions, long-term visits by Portuguese faculty members to UT-Austin, and ongoing research projects; a number of very strong Ph.D. students have been recruited, some of which are now close to graduation; by organizing workshops and schools in various areas of mathematics, especially in applied areas (for instance, mathematical finance and control, optimization and machine learning, kinetic and statistical methods for complex particle systems, imaging sciences and medical applications, to name just a few) the program has increased the international recognition of Portuguese scientists, as well as bringing to Portugal top researchers in a diverse class of topics.  Finally, through this collaboration with UT-Austin, Portuguese MSc students in advanced training courses through The University of Texas at Austin Research Training Group program were involved in areas as diverse as multiscale modeling and analysis or financial mathematics.  
 
Accomplishments
During the past five years through this program 13 Ph.D. students and nine post-doctoral fellows have been recruited from countries such as Armenia, Brazil, Italy, Iran, Lebanon, Portugal, Spain and the United States, as well as involving other Ph.D. students and post-docs in research projects.  At the current time, seven research projects have been approved.  More than seven Portuguese faculty members spent extended periods (between 1 month and 1 semester) at UT- Austin.  A large number of publications (more than 50) have already appeared in international mathematics journals, have been submitted or are in the final stages of preparation as a result of collaborative research or research projects. During the first phase of the program 12 international schools and workshops were organized for researchers at all levels.  In addition, more than 20 Portuguese undergraduate students have participated in research training groups.
Goals 2013-2017
During this period the plan is to increase and strengthen the existing collaborations, by
1)    Continuing to attract strong Ph.D. students and post docs, which are strengthening the research capability of Portuguese universities and thus creating critical mass in key areas of mathematics. 
2)    Increasing the number of Portuguese faculty members involved in long-term visits to UT- Austin, thus contributing to the internationalization of Portuguese scientists
3)    Promoting events such as schools and workshops in both pure and applied topics in order to enhance Portuguese research capacity, capitalizing on the presence of qualified and well trained doctoral students and post-docs.  
4)    Using the UT-Austin expertise, help to promote high quality and high impact research in interdisciplinary applied areas such as mathematical finance and optimal control, vision and medical applications, complex particle systems and social network applications, and optimization and machine learning, which it is hoped will contribute in a very positive way to the Portuguese economy and society.  
5)    Promoting the collaboration between the mathematics UT-Austin|Portugal program and the CMU|Portugal program.
 
Actions
Ph.D. Program
The dual-degree Ph.D. programs will be continued and structured along the following guidelines:
The CoLab Ph.D. Program in Mathematics is a collaborative Ph.D. program between the participating Portuguese Institutions and The University of Texas At Austin (math.utexas.edu). The students in the program will study both at The University of Texas at Austin and at one of the Mathematics Departments of the partner Portuguese institutions. Under this program, students will spend part of their time at UT-Austin where they will have the opportunity to pursue a dual degree between UT-Austin and one of the Portuguese universities. In order to qualify for the dual degree, students will have to fulfill the academic requirements of both the Portuguese university and UT-Austin.
The typical Ph.D. student will spend his/her first year in Portugal, by the end of which she/he will complete the qualifying exams. In the second year the student will be at UT-Austin and at the end of that year will take the candidacy examination. The last two years will be dedicated to research. Typically the student will spend the third year in Austin and the last year in Portugal.
Post-Doctoral and Faculty Exchange Program
In order to build a successful collaborative research project there needs to be a strong component of joint research at the junior and senior levels. Accordingly, there will continue to be a regular exchange of post-docs, junior faculty members, and senior faculty members to foster the development of common research interests and projects.
Research Projects
It is anticipated that there will be two open research calls in order to support competitive, high quality collaborative research between Portuguese and international partners.
Events and initiatives
In order to promote collaborative research the plan is to continue to organize an annual workshop and training course on key areas of mathematics. In addition, an annual postdoctoral academy will be organized that will bring together post-docs, Ph.D. students and faculty members.  Finally there is a plan to organize a periodic meeting in Portugal of all Ph.D. students, post-docs and faculty members involved in the program in order to stimulate the collaboration between Portuguese institutions.
It is expected that efforts will be undertaken to further enlarge the scientific committee to enhance the academic diversity by including additional members from Portugal and the United States academic community.