Prof. Dr. Sc. Pham Hoang Hiep was born in 1982 in Hai Duong. He earned his bachelor’s at Hanoi National University of Education in 2004, completed his PhD thesis at Umea University, Sweden in 2008 and obtained Habilitation à diriger des recherches at Aix-Marseille University, France in 2013. From 2005 to 2014, he served as a lecturer and researcher at the Hanoi University of Education. Since 2015 to present, he is a researcher of the Institute of Mathematics, Vietnam Academy of Science and Technology. He and collaborators have had 37 scientific papers in mathematics journals (33 papers in mathematics journals in ISI list) about Complex analysis and geometry, a Monograph, two books for undergraduate and graduate courses.
Work
Demailly, J. P., & Phạm, H. H., 2014. A sharp lower bound for the log canonical threshold. Acta Mathematica, 212(1), 1-9.
Log canonical threshold is a real number that measures the singularity of an holomorphic function in Complex analysis and geometry. Let a holomorphic function on a complex manifold X with dimesion . A problem of mathematics is to understand the singularity of a holomorphic function at a point which the function vanished at this point. In algebraic geometry, mathematicians investigated the log canonical threshold which is an invariant number with the charge coordinate and measures the singularity of a holomorphic function at a point . Log canonical threshold is the correct upper bound of the numbers so that is integrable with respect to the Lebesgue measure on a neighborhood of the point . The plurisubharmonic function is the main research object of Pluripotential theory and is an important function class that has many applications in complex analysis and geometry. Log canonical threshold is generalized to the class of plurisubharmonic functions. Let be a plurisubhamonic function on the complex manifold X, log canonical threshold of at the point is defined as the correct upper bound of the numbers such that is integrable with respect to the Lebesgue measure on a neighborhood of the point . The result of the article is to study the best estimate of the canonical threshold with the system of Lelong numbers of plurisubhamonic functions.