General Events - Department of Mathematics

Title: Parameterized and isolated points on curves
 
 Abstract: Let C be an algebraic curve over Q of genus at least 2, i.e., a 1-dimensional negatively curved complex manifold defined by polynomial equations with rational coefficients.  
 A celebrated result of Faltings implies that, despite the hyperbolicity of C, all algebraic points on C are organized into families of nonnegative curvature.  We explore how these families provide insight into the arithmetic of C and give applications to the study of elliptic curves. This talk is based in part on joint work with A. Bourdon, Ö. Ejder, Y. Liu, and F. Odumodu, with I. Vogt, and with I. Balçik, S. Chan, and Y. Liu. This talk will be suitable for a general audience.