Por Giosuè Muratore (CEMS.UL).

A¹-homotopy theory, introduced by Morel and Voevodsky, provides a powerful motivic framework that bridges algebraic geometry and the methods of classical topology. By extending the toolkit of algebraic geometry with concepts from homotopy theory, this approach has opened the door to a wide range of applications across the field. In this talk, we will outline the fundamental ideas behind A¹-homotopy theory and explore its relevance in enumerative geometry, highlighting recent developments and results.