Eric Riedl, University of Notre Dame
"Plane curves, log tangent sheaves and the Geometric Lang-Vojta Conjecture"
In this talk, we describe two problems relating to plane curves, and describe how log tangent sheaves are key to solving both. First, we consider the natural question: when does the families of lines that intersect with a plane curve vary maximally in modulus? We show how the classical Grauert-Mulich theorem applied to the log tangent sheaf can solve this. Then we consider the question of the algebraic hyperbolicity of the complement of a very general quartic plane curve, and describe how we achieve an answer to this long-open problem, motivated by the Lang-Vojta Conjecture in number theory. This includes joint work with Xi Chen, Anand Patel, Dennis Tseng, and Wern Yeong.