Title: Examples of Lefschetz fibrations with infinitely many sections
Abstract: A Lefschetz fibration M^4 \to S^2 is a generalization of a surface bundle which also allows finitely many nodal singular fibers. Work of Arakelov and Parshin implies that holomorphic Lefschetz fibrations of genus g \geq 2 admit only finitely many holomorphic sections. In this talk, we will show that no such finiteness result holds for smooth sections by giving examples of genus-g (g \geq 2) Lefschetz fibrations with infinitely many homotopically distinct sections. This is joint work in progress with Carlos A. Serván.