# FCT GFM Evaluation, 2008

**Unit name:** Grupo de Física-Matemática da Universidade de Lisboa (MATH-LVT-Lisboa-208)

### Evaluation Panel (Unidade I&D visitada em: 19-02-2008)

- (c) Irene Fonseca
- (r) Richard Smith
- (r) Konstantin Mischaikow
- (r) Mete Soner
- (r) Tom Laffey
- (r) Martin Golubitsky
- (r) Tamas Terlaky
- (r) Gerard Besson
- (r) James Cummings
- (r) Vivette Girault

(c) Coordinator; (r) Reviewer

### General Comments*

This is a compact research unit group with 13 members organized in three groups. Recently, they have gone through a substantial reorganization: one group just joined and the other joined two years ago. The main focus is applied mathematics and applications of mathematics in physical sciences. Group has produced high quality research and organized several exciting seminars. Although the number of doctoral students is low, the Unit is actively involved in post-doctoral education and recently secured four Ciência 2007 positions.

Research productivity is impressive both in quantity (more than 70 papers) and in quality (Acta Math., ARMA, and J. London Math. Soc.,etc). Also the members are well connected with many research centres around the world and they have high international visibility.

While rating this Unit excellent the panel also observed that a research Unit of this size could only have limited impact. However, the Unit serves the mathematics community in Portugal with numerous excellent seminars and workshops. Also they are actively involved with other researchers in the country in research and in other scientific activities.

### Specific Group Comments*

- [RG-MATH-LVT-Lisboa-208-2123] Molecular Dynamics of Complex Systems
This very small research group consists of one senior member, two postdoctoral fellows and two graduate students. During the evaluation period two doctoral theses were supervised. Main scientific activity of the group is centred on simulations of many body interacting systems. This is clearly an important area of research. Indeed, many scholarly publications resulted and were published in top journals in the general area of physical chemistry.

This group joined the Unit recently. Their research interests rest well within the scientific mission of the Unit stated above. However, one outside reviewer questioned the rationale behind supporting this research activity within mathematics. On the contrary, the panel takes the view that this is a unique opportunity to strengthen the ties between the applied mathematics and the computational chemistry communities. However, this will require a directed effort.

- [RG-MATH-LVT-Lisboa-208-2485] Analysis and Geometry in Mathematical Physics
Research of this group can be grouped in two general areas: dynamical systems and quantum physics. In particular, they work on deformation quantization, Yang-Mills theory, eigenvalues of operators from a computational point of view, special functions and dynamical systems. Their research productivity on these topics is very impressive, although sometimes concentrated on a small number of journals. There are 6 members in the group, one post-doctoral fellow and two students. Two theses were supervised. Overall, this is an excellent group with high research productivity.

In addition, they were quite successful in securing outside funding. One of the senior members of the group is in the Steering Committee of an ESF Programme in Spectral Theory and PDEs (SPECT). One other member is funded by ESF through the project "Quantum Geometry and Quantum Gravity" for the period (550.000 Euros). They also secured a small grant from the Clay Mathematical Institute.

- [RG-MATH-LVT-Lisboa-208-2511] Stochastic Analysis, Path Integrals and Applications
This research group has been the core of this Unit over the years. It consists of four senior members and supervised three master theses during the period of this evaluation. Their main scientific focus is the applications of stochastic analysis. They were involved in several applications including,

- non-equilibrium statistical physics,
- phase-space geometry,
- exciting new results by randomization of geometric tools of classical mechanics,
- Feynman path integrals.

They have been actively involved in organizing international conferences both in Portugal and abroad including the ICPM 2003 conference in Lisbon and a satellite workshop of the International Congress of Mathematicians in 2006. They participate in many international networks.