Tamás Darvas
University of Maryland, College Park, USA

We show that the volume of transcendental big $(1,1)$-classes on compact Kähler manifolds can be realized by convex bodies, thus answering questions of Lazarsfeld-Mustata and Deng. In our approach we use an approximation process by partial Okounkov bodies, and we study the extension of Kähler currents.

(Joint work with R. Reboulet, M. Xia, D. Witt Nystrom, K. Zhang)