Assoc. Prof. Nguyen Sum was born in 1961 in Binh Dinh Province. He graduated from Quy Nhon University in 1983 and defended his PhD thesis in 1994 at Ha Noi University before starting his career at Quy Nhon University to July 2018. He works at Sai Gon University from August 2018 to date. He compiled two curricula on “Linear Algebra”, published by Education Publishing House and also, published more than 15 scientific papers of high quality on international journals of high reputation. The papers are in the fields of studying the modular invariant theory, the Peterson hit problem and applications to homotopy theory.
Nguyen Sum, 2015. On the Peterson hit problem. Advances in Mathematics, Vol. 274, 432–489.
One of the key problems in Algebraic Topology is the problem of finding a minimal generating set for the polynomial algebra in k variables, regarded as a module over the Steenrod algebra. The problem was set by Frank Peterson and is called the Peterson hit problem.
The hit problem was explicitly solved by Frank Peterson for k = 1, 2 in 1987 and by Masaki Kameko for k = 3 in his Johns Hopkins University PhD thesis in 1990. In this work, the author studies the hit problem for k > 3.
The main result of this work is an induction formula on the determination of the generators of the polynomial algebra in k variables in terms of the generators of the polynomial algebra in k–1 variables. From which the hit problem is explicitly determined in some types of generic degrees. By using this formula, the author explicitly solved the hit problem for k = 4.