We hereby illustrate the objectives of the project, divided into two main strategic aims: “Advanced education” and “Mathematics of complex systems”.
Among the most successful objectives pursued with conviction by the Department there are the training of Master’s and Ph.D. students to an excellent level of scientific knowledge and the integration of young researchers in a context favourable for their full scientific growth. An advanced course offer with a broad educational range and an intense seminar programme are essential in order to implement tangible strategies in support of advanced education, as well as the participation of students and young researchers interested in starting or developing further a career oriented towards mathematical research. In this respect we have set the following objectives:
- Appeal and internationalisation of the Ph.D. Programme We deem important to further enhance the internationalisation of our Ph.D. Programme, both by trying to draw in students coming from abroad and by increasing the student exchange with Ph.D.’s of other universities. The development potential in this direction can be observed from the numerous existing agreements for the exhcange of Master’s students with universities abroad (ETH, EPFL, Université de Genève, University of Bonn, Université Paris Cité, Ecole Polytechnique, French Scuola Normale’s, Hokkaido University double degree programme).
- Increase in the number of young researchers We aim to significantly increase the total number of young researchers, Ph.D. students and research associates, which is still low in some research areas and does not always reach the minimum critical mass necessary to foster scientific vibrancy.
- Strengthening of the advanced course offer The remarkable educational effort of the Deparment has meant that in recent years Ph.D. courses and some Master’s Degree courses were held by professors in addition to their ordinary educational responsability. Courses maintained an excellent level of delivery and were sufficiently numerous, however the planning of the offer was at times a source of problems due to the difficulty in locating the necessary resources. We consider this a critical issue that needs to be addressed with energy via the recruitment of new professors and a robust programme of visiting in order to grow and consolidate the advanced course offer.
The achievement of these objectives, together with the high level of research activities of the Department and the proximity to the Scuola Normale, can make Pisa a reference point for doctoral and post-doctoral studies both nationally and internationally.
Mathematics of Complex Systems
An important challenge of modern science, which also explains various strategic directions taken by NRRP (National Recovery and Resilience Plan), is the understanding and the forecasting of the behaviour of complex systems, such as those emerging in the climate change, epidemic, life science, economic and social, machine learning and artificial intelligence models. These systems are characterised by a high level of dimensionality and from the variability of the constituent parameters. The understanding and the forecasting of the macro emerging behaviours and of their sensitivity with respect to the parameters defining a system are crucial to the study of a complex system. This aspect poses significant challenges both in the theoretical study and the development of suitable numerical methods. Some groups of the Department are already active on these topics, in particular with regards to mathematical models for applied sciences and data analysis. The research group in celestial mechanics has a long experience in the field of solar system dynamics and orbit and space mission calculations, and on these subjects it has already won two European Marie-Curie projects, and several projects with ASI (Italian Space Agency) and ESA. The group of mathematical physics has been enriched by the recent hire of an expert in problems in materials science and biological models (Muratov). The Analysis group has among its members experts in the study of statistical properties of dynamics, partial differential equations, calculus of variations, free boundary problems and shape optimisation. The big advancements in data analysis and artificial intelligence observed in recent years require advanced mathematical tools for the understanding of the fundamental mechanisms regulating these phenomena. This research field is relatively new, even though some members of the Department can already offer meaningful contributions. Specifically, the expertise in the study of multi-component agent-based systems, rough path theory and the probabilistic approach to optimal transport has achieved recent results in reinforcement learning (Agazzi, Romito), the asymptotic study of neural networks and manifold learning (Trevisan). The expertise in algebraic topology is very promising for applications in topological data analysis, especially considering the support that can be given computationally by the group of numerical analysis, thanks to their vast experience in numerical methods for higher-dimensional systems and complex networks. Furthermore, thanks to the recent creation of the advanced course in “Data Analysis” focused on the mathematics for machine learning, the Department is training students in the fields of statistics and of the theory of machine learning, which are highly sought-after by firms specializing in data analysis. We deem strategic for our Department to strengthen and expand the research activity and the educational effort in the mathematics for complex systems, setting the following objectives:
- Development of the research activity The main objective is the development of the scientific activity related to the study of complex systems in order to make the Deparment a reference point in these research areas. The growth in modelling and computational expertise will play a key role towards reinforcing and extending the collaboration efforts with other research centres and the industrial sector. This objective will be achieved via the recruitment of new researchers and the strengthening of the knowledge base already available to the Deparment, through the invitation of experts and the organisation of classes, workshops and conferences.
- Students and young researchers training Another objective, closely related to the previous one, is the training of students and young researchers, via the increase in the educational offer on these topics. We anticipate this will raise the appeal of our Degrees and Ph.D. Programme, with a resulting increase in the number of students coming from other universities.
Plan of action
This is the list of the main action points that will be carried out to reach the set objectives:
A key point for the success of the project is the recruitment of new staff. During the project lifespan we aim to hire a good number of external researchers, young and with a high-profile scientifically, and to offer them “tenure track” and permanent positions. Staff hired with this process will be integrated both toward working on research lines already being developed by the groups of the department, and toward contributing to the progress of the research lines described above. It is important to highlight the possibility to have the central offices of the University co-finance the recruitment of the teaching staff with 3 positions for “tenure track” researchers.
Appeal and internationalisation of the Ph.D. Programme
We aim to enhance the offer of the Ph.D. Programme to improve its competitiveness internationally. The actions we deem of paramount importance to this end are the increase in the duration of the scholarships from 3 to 4 years, the supply of additional scholarships (indicatively 2 per year), and the increase in the funding provided by each scholarship. In addition, we aim to increase the funds available to the mobility of Ph.D. students.
The offer of post-doctoral positions is rather limited and we consider a priority its upgrade to international standards. This initiative is fundamental to the objective of an increased internationalisation of the Department. The actions regarding the Ph.D. Programme and the post-doctoral grants require also an upgrade to the current structures that at present are considered undersized.
Advanced course offer
The increase in the educational offer of the Master’s Degree and the Ph.D. Programme will be achieved first of all with the recruitment of new staff, who will be able to contribute directly to the supply of advanced courses and also to free up resources currently employed in different study courses. Moreover, we aim to finance an intense programme of visiting fellows, to teach courses and to interact with the students, researchers and professors of the Department.
Classes and workshops
Annual classes will be organised targeted towards Ph.D students and young researchers; furthermore, the organisation of international conferences will be promoted and, at least biennially, one will be organised on topics related to the mathematics of complex systems.
Working group for the collaboration with businesses and other institutions
Creation of a working group to promote the collaboration between the Department and external companies, tasked with handling the communication with the firms and with drafting the cooperation agreements on the topics of research and development.
Relationships with schools
Development of the connections and collaborations with schools by means of training activities for teachers and orientation events (stages, laboratories) on the project topics aimed at high school students.
The creation of new spaces and the rationalisation and renovation of existing ones are fundamental to the purpose of the project. To this end, we expect the integration of new bodies on the roofing of the building totaling a surface area of approximately 200sq m, to be realized according to the principles of sustainable and bioclimatic architecture. Existing spaces will be reorganised and the furniture will be renovated in order to make them more functional.
Research on complex systems requires computing resources that can allow the manipulation of a numerically large amount of data. In particular, we expect the purchase of a GPU server to increase the computing power at disposal of the Department, and the purchase of a server for the maintenance of the computing resources of all students and teaching staff.