The interplay of modeling, analysis and computation is at the very core of modern applied mathematics a key to R/D in modern technology. It is thus naturally beneficial for institutions in LFR to foster the development of this triptych. For some years now, the Institute of Applied and Computational Mathematics in FORTH, Crete has been developing a group and an infrastructure in the direction of modeling and computation for evolution problems. The interests of IACM range from the analysis and computation of hyperbolic and kinetic partial differential equations to issues of homogenization and random Wave Propagation. The scope of the planned visit to FORTH, Crete will be to transfer expertise in modeling and analysis of hyperbolic and kinetic problems. The interface of the fields of hyperbolic and kinetic pdes is naturally tied to manifold issues of multiscale analysis and computation, which are in turn central to technological problems of both "industrial sectors" (rarefied gases, plasmas, materials) as well as "society oriented sectors" (e.g.imaging, seismology). The proposed project will be an important step to advance existing research programmes as wells as to develop expertise in new important problems in theoretical and computational hyperbolic systems. In particular during the stay of A. Tzavaras in IACM-FORTH the main directions of research will be
-numerical methods for conservation and balance laws
-methods in high frequency asymptotics
-numerical and analytical methods for hyperbolic multiscale problems. It is expected from both the proposer and the host institution that the proposed project will contribute greatly in the development of Applied and Computational Mathematics in Crete towards becoming an internationally competitive Research node in this area.