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Trends in Non-Linear Analysis in Discussion

Trends in Non-Linear Analysis in Discussion
By José Matias* and Marco Morandotti**, organizers of the Workshop

participants TNLA 2014 The workshop “Trends in Non-Linear Analysis” took place at Instituto Superior Técnico of the Universidade de Lisboa (IST-UL) on July 31 st and August 1 st , 2014, with the aim of bringing together leading experts and young mathematician researchers to present and discuss recent developments in non-linear analysis.
The workshop was very successful, it gathered more than 35 participants and it offered a space for engagement in discussions about the latest findings in a number of different directions in non-linear analysis, including homogenization, non-local variational problems, mechanics of defects in materials, fractures.

The research network of the CMU Portugal/UT Austin project “Thin Structures, Homogenization, and Multiphase Problems” (FCT-UTA_CMU/MAT/0005/2009) was pivotal in enabling this workshop, through the partial support of 6 keynote speakers (Bouchitté, Fonseca, Mascarenhas, Morini, Piatnitski, Zappale), and 12 young researchers (whose participation was supported by the Center for Mathematical Analysis, Geometry and Dynamical Systems -CAMGSD). We also acknowledge support from the CMU Portugal/UT Austin project “ Degenerate elliptic and parabolic equations and its applications to front propagation ” ( FCT-UTA_CMU/MAT/0007/2009).

The workshop fits squarely within the scope of the CMU Portugal collaboration, and facilitated the tightening of the networking between the Portuguese and Carnegie Mellon researchers in the field of Mathematics, and by stressing once more the success of this partnership, that will continue strong beyond the sun setting of this project. It is our strong belief that it should continue even after the deadline of the project. Indeed, at the conclusion of the workshop several open problems were identified that still need to be addressed and solved, and such a thriving project is one of the best ways to bring together top class researchers to develop science.

There are many open problems, for instance in the field, of homogenization, dynamics of defects in solids, fractures, the theory of A­ -quasiconvexity, that are worth investigating and will contribute to further develop science and its applications to physical and engineering problems.

* Instituto Superior Técnico of the Universidade de Lisboa (IST-UL)

** Post Doc in Mathematics at Instituto Superior Técnico of the Universidade de Lisboa (IST-UL) and Carnegie Mellon University (CMU)