Can You Deform a Plane into a Saddle Surface?

This lecture from the Colloque des sciences mathématiques du Québec (CSMQ) features Sándor Kovács from the University of Washington exploring the nuanced question of whether a plane can be deformed into a saddle surface. Discover how the answer varies depending on whether surfaces are considered as topological spaces, differentiable, complex, or algebraic manifolds, and whether open or compact versions are being examined. Follow along as Kovács reviews various mathematical possibilities before delving into the specific case of projective complex manifolds. The presentation illuminates key challenges in the classification of higher dimensional algebraic manifolds, discussing both resolved issues and emerging challenges in this mathematical domain.