The Department of Mathematics "Federigo Enriques" of the University of Milan has been awarded a special grant of the Italian Ministry for University and Research in the framework of the initiative “Excellent Departments 2023-27”. This is the outcome of an evaluation process involving all the university departments in Italy, based on research quality assessment and selection of future activity proposals. In the area of Mathematics and Computer Science only 11 departments have been awarded the grant.

The grant will be used for the implementation of several development plans:

1. hiring of high level researchers and professors;
2. offering of post-doc positions and additional PhD grants;
3. improving high level (Master and PhD) educational activities;
4. funding for new infrastructures, including computational and logistic facilities.

A central role will be played by the creation of a Departmental Center for Training and Research (the Center) whose mission is to promote organization of intensive research semesters. They will be devoted to research on timely topics on pure and applied mathematics with the aim of reporting on the state of the art in a particular field and to promote new research activities. They will include:

• long-term hosting of high-level scientific guests, aimed at collaboration with the researchers of the Department;
• organization of workshops and meetings;
• PhD courses;
• sustained seminarial activity.

The first intensive research semesters will benefit of existing ERC grants in the Department and will be devoted to the following topics:

• stability and instability in fluid-dynamics and dispersive PDEs and connections with turbulence;
• methods of homological algebra in algebraic geometry;
• interacting quantum systems beyond mean-field theories: a road to understanding quantum entanglement.

The activity will continue with high level programs focusing on other topics on pure and applied mathematics, or of interdisciplinary nature.

Intensive research semesters will be of great value to create an active and collaborative environment for scientific staff and to give new perspectives for education and training of students and young researchers, as well as to promote the international visibility of the Department. The Center is equipped with a Director, a Steering Committee and an external Advisory Board which includes first-class researchers from various areas. The Center will continue its activities beyond the five-year period of the grant, as an instrument to consolidate the activity of the Department as an excellent training and research institution.