Algebraic geometry is one of the central areas of modern mathematics, interacting in many ways with other fields like differential and symplectic geometry, topology, number theory, combinatorics, and with theoretical physics. Research in algebraic geometry uses a variety of sophisticated techniques drawing inspiration from all these areas. Algebraic geometry remains a vibrant area of research that has witnessed ground breaking recent progress, for instance on the minimal model program, moduli spaces, or in combinatorial algebraic geometry.
The thematic semester will center on various aspects of the theory of moduli spaces, that is, parameter spaces in algebraic geometry. Moduli spaces appear naturally when one wishes to clarify all algebraic varieties of given numerical invariants. We will focus on some of the most prominent moduli spaces parametrizing concrete geometric objects, like algebraic curves, algebraic surfaces and abelian varieties.
During the semester, there will two major activities, each of two weeks, consisting of a school followed by a high-profile workshop on the following two topics:
- Moduli of curves, abelian varieties and \(K3\) surfaces.
- Algebraic surfaces and their moduli.
The first activity will highlight the enumerative and birational geometry of these moduli spaces, presenting modern techniques of geometric, combinatorial and tropical nature that led to decisive progress. The second activity will focus on modern techniques in the classification theory of higher dimensional algebraic varieties, highlighting connections to K-stability and singularity theory.