A Tour through Algebraic Geometry

Date: 15 - 19 September 2025

Location: Cortona, Italy

Algebraic geometry, a foundational discipline that studies geometric objects defined by polynomial equations (algebraic varieties), continues to be one of the most vibrant and dynamic areas of contemporary mathematics. It is at the forefront of numerous exciting developments, many of which intersect with and draw on other branches of mathematics, including topology, differential geometry, and commutative algebra. These interactions foster new insights and advance our understanding of complex geometric and topological structures.

This conference, celebrating Alessio Court’s contribution to the field of algebraic geometry, will include topics that reflect the breadth of these developments, showcasing cutting-edge research at the confluence of algebraic geometry and related fields. In particular, recent advances in the theory of moduli spaces, singularity theory, and mirror symmetry are reshaping our understanding of algebraic varieties, with profound implications not only within mathematics but also in related areas of physics and string theory. The growing synergy between algebraic geometry and adjacent disciplines, such as category theory and representation theory, has opened up fresh avenues for exploration, and has led to new tools and techniques that promise to yield deeper results in both pure and applied mathematics.

The conference will highlight these trends, which attest to the continued relevance and vitality of algebraic geometry today, and have grown out of foundational work carried out by Corti among others. The talks and discussions will present some of the most exciting open problems in the field and explore future directions of research in algebraic geometry in its dialogue with other areas of mathematics.

CMI Enhancement and Partnership Program