Special Session 22

Singularities in Algebra and Geometry

Organizers: Bruna Oréfice Okamoto (Federal University of São Carlos, Brazil), Luiz Hartmann (Federal University of São Carlos, Brazil), Mauro Spreafico (University of Trento, Italy)

MSC codes: 32S-XX, 58K-XX

Description:

Singularity Theory is a branch of Mathematics that studies non-smooth phenomena, investigated from different perspectives within Geometry, Topology, and Analysis. The two constituting fields of this special session, algebraic geometry and geometric analysis, intersect on various levels and in particular are connected by the celebrated Atiyah-Singer index theorem, which equates the topological and analytic index with crucial consequences in both fields. The purpose of this thematic session is to bring together researchers working on singularities from complementary perspectives in algebraic geometry and geometric analysis, providing a focused setting for the presentation and discussion of recent results. The session aims to encourage interaction between specialists at different career stages and to promote the exchange of methods and viewpoints across the two areas. By concentrating on concrete problems, established techniques, and current developments, the session seeks to strengthen existing connections between the fields and to support the gradual development of a shared framework for the study of singular spaces.