From June 26-28, 2024, the Vietnam Institute for Advanced Study in Mathematics (VIASM) hosted a mini-course on rational algebraic surfaces and birational maps between them. The course attracted nearly 30 participants, including lecturers, researchers, and students - both undergraduate and postgraduate - from various universities and institutes nationwide.

Assoc. Prof. Dr. Le Minh Ha, VIASM Managing Director, delivered the opening speech for the course.

The course provided a robust introduction to foundational concepts, offering a blend of broad overviews and in-depth insights into key principles and applications. Prof. Alberto Calabri of the University of Ferrara, Italy, delivered a series of engaging lectures that covered essential and advanced topics.

Prof. Alberto Calabri from the University of Ferrara, Italy

The series of lectures included:

- The complex projective plane, its blowing-up at finite points; divisors, linear systems, and intersection forms; some examples of rational surfaces, such as: Hirzebruch-Segre surfaces and elementary transformations between them; 

- Definitions and properties of del Pezzo surfaces, quadratic Cremona maps, de Jonquieres maps, and Cremona equivalents of plane curves; 

- The characteristics of the base locus of a plane Cremona map, Noether's inequality, Hudson's test, and a classical proof of the Noether-Castelnuovo theorem.

The course was a resounding success, marked by enthusiastic participation and dynamic discussions between attendees and the lecturer. The knowledge and skills gained will offer a solid foundation for the participants' future careers and further research in algebraic mathematics.

Here are some photos from the course: