Venue: Tencent Room: 726 401 885, Code:061901

Abstract: In this talk, we give an overview on the interaction between convexity and positivity in algebraic geometry. We will discuss a somehow universal structure theorem with the flavor of elementary convex analysis, and show how it appears (and implies new geometric results) in the study of Minkowski's existence theorem, Zariski decomposition of cycles, pluripotential theory, etc. In particular, we discuss how convexity tools can be applied to the study of positive cycles on a smooth algebraic variety.