Seminar on Complex Analysis and Complex Geometry - Spring 2019

Friday, March 8, 2019, 10am-11am, Room AH 303

Title: Unique continuation at the boundary for a class of elliptic equations

Speaker: Shif Berhanu, Temple University

Abstract: We will discuss results on unique continuation at the boundary for a holomorphic function of one variable. Applications to unique continuation for CR mappings and extensions to a class of second order elliptic partial differential equations will also be presented.

Thursday, April 18, 2019, 10am-11am, Room PGH 646A

Title: Stability, complexity of rational points and arithmetic of linear series

Speaker: Nathan Grieve, Michigan State University

Abstract: I will survey concepts that are near to K-stability and which have origins in toric geometry. A main goal will be to explain their role in measuring arithmetic complexity of rational points, for example questions in Diophantine approximation for projective varieties. There are also important connections to measures of growth and positivity of line bundles. These arithmetic results build on a number of earlier related works including those of Ru-Vojta, McKinnon-Roth, Evertse-Ferretti and Fujita.