On March 18, 2025, the Vietnam Institute for Advanced Study in Mathematics (VIASM) successfully organized the workshop "Complex Analysis and Pluripotential Theory", attracting the participation of many students, graduate students, mathematicians, and researchers. The workshop created a dynamic academic environment where mathematicians could engage in in-depth discussions, share ideas, and establish connections to foster research collaboration opportunities in the field of Complex Analysis and Pluripotential Theory.

Participants at the Workshop

During the workshop, speakers presented their most recent research and current projects. The program began with a talk by Professor Pascal J. Thomas from Paul Sabatier University, Toulouse, France, on "Weak Triangle Inequality for the Lempert function." His presentation provided deep insights into the necessary conditions for a Lempert function to satisfy the triangle inequality.

Professor Pascal J. Thomas, Université Paul Sabatier, Toulous, France

Continuing the program, Professor Le Mau Hai (Hanoi National University of Education) discussed the relationship between convergence in (ω,m)(\omega, m)(ω,m)-capacity and the convergence of the corresponding Hessian operator on compact Kähler manifolds in the class of functions E(X,ω,m)\mathcal{E}(X, \omega, m)E(X,ω,m).

Professor Le Mau Hai, Hanoi National University of Education

Doctor Nguyen Van Phu (Electric Power University) presented improved results on subextension and approximation of m-subharmonic functions, comparing them to the subextension and approximation of plurisubharmonic functions. His results did not require assumptions such as relative compactness of small domains within a larger domain or continuity of boundary values.

In his talk, Professor Nguyen Quang Dieu (Hanoi National University of Education) introduced new improvements in solving Monge-Ampère equations by employing capacity convergence—a novel technique compared to the commonly used approach of proving existence via the Schauder fixed-point theorem.

Professor Nguyen Quang Dieu, Hanoi National University of Education

Professor Phung Van Manh, Hanoi National University of Education

Associate Professor Phung Van Manh (Hanoi National University of Education) provided an overview of orthogonal polynomials, covering univariate orthogonal polynomials, multivariate orthogonal polynomials, orthogonal polynomials on the circle, on the parabola, on cubic curves, and, notably, recent results on orthogonal polynomials on quartic curves.

The workshop concluded with a presentation by Associate Professor Nguyen Xuan Hong (Hanoi National University of Education), who discussed an extension of Demailly’s strong openness conjecture concerning level sets of plurisubharmonic functions.

The workshop provided a comprehensive overview of the latest research in Complex Analysis and Pluripotential Theory. The dynamic exchange of ideas proved invaluable, both for clarifying existing concepts and inspiring new research trajectories in these mathematical domains.

The speakers discuss at the workshop