The sector of Functional Analysis and Applications has been active at SISSA since 1978, the year SISSA was founded. Its permanent staff consists of 12 permanent members, and of a number of postdocs and associates.

The research activities of the sector include the study of a wide range of nonlinear problems in the areas of the calculus of variations, and of partial and ordinary differential equations. The applications of interest to members of the sector are mostly in the area of Control Theory and of the Mechanics of Materials.

The sector offers two Ph.D. degrees, in Mathematical Analysis and Applied Mathematics, which are legally equivalent to the Italian title of "Dottore di Ricerca in Matematica".

In the first 25 years of activity of the sector, about 90 students have been granted a PhD degree. Half of these graduates are now professors in either Italian or foreing universities.

The sectors of Functional Analysis and Application and the sector of Mathematical Physics, together with the School of Mathematical, Physical and Natural Sciences of the University of Trieste are responsible for a joint curriculum within the Master Degree in Mathematics offered by the University of Trieste.

### Mathematical Analysis

The activity in Mathematical Analysis is devoted to various research topics dealing with nonlinear ordinary and partial differential equations. In particular, the following topics are studied: stability and instability properties of finite and infinite dimensional Hamiltonian systems; singular perturbations and stationary waves of nonlinear Schroedinger equations; geometric analysis; transport theory; ordinary diff equations; hyperbolic sytems and conservation laws.

The permanent staff consists of 4 professors whose research is funded by some grants coming also from several collaborators.

The research activity takes also advantage by a broad network of collaborations at international level, and this allows a remarkable mobility of the researchers as well as of the Ph.D. students.

### Applied Mathematics

Image courtesy of T. Shield, Univ. of Minnesota

The activity in Applied Mathematics is devoted to several problems in control theory, in system biology, in multiscale analysis, and in mechanics of materials. On the one hand new mathematical tools are developed for the study of these problems, which require advanced techniques from differential geometry, ordinary and partial differential equations, and the calculus of variations. On the other hand this knowledge is applied to the formulation of new mathematical models and to the numerical solution of concrete problems.

The scientific staff of the activity in Applied Mathemathics consists of 3 professors and 5 researchers, helped by some scientific collaborators with temporary contracts.

The activity in Applied Mathemathics offers a Ph.D. degree in Applied Mathemathics, which is legally equivalent to the Italian title of "Dottore di Ricerca in Matematica". Several international connections ensure that researchers and students are in steady contact with the most active research centres in these fields.

Moreover, Dr. Claudio Altafini coordinates the research group in System Biology for the Ph.D. curriculum in Functional and Structural Genomics, jointly organized with the Neurobiology and the Statistical and Biological Physics sectors. This activity is also part of a cross-disciplinary teaching offer: "Approaches to Bio- and Neuro- Theory".