Abstract: 

Pluripotential theory is well-developed for positive closed currents of bi-degree (1,1), corresponding to currents of hypersurface type. However, the theory is significantly less understood in higher bi-degrees. In this talk, we will present recent advances in this area of research. We will explore the theories of super-potentials and densities for currents, with a particular focus on intersection problems. Applications to complex dynamics, foliation theory, and aspects of complex analysis will be discussed, along with some open problems. This presentation is based in part on joint work with Bianchi, Kaufmann, Nguyen, Rakhimov, Sibony, and Vu.

Dinh Tien-Cuong is a Vietnamese mathematician educated by the French school of mathematics, and Provost's chair professor at National University of Singapore (NUS). He held professorship at Pierre and Marie Curie University (2005–2014), part-time professorship at Ecole Polytechnique de Paris (2005–2014) and at Ecole Normale Supérieure de Paris (2012–2014). He is known for his work on Several Complex Variables and Complex Dynamical Systems in Higher Dimension.