Research departments

Department of Algebra and Number Theory

The Department of Algebra and Number Theory was renamed the Department of Algebra in 2005, at the same time the Department of Number Theory was established. Over the years, the department has been headed by Professors Ngo Viet Trung, Nguyen Tu Cuong, Le Tuan Hoa, and Phung Ho Hai. Several former members of the department have become professors abroad, including Prof. Dinh Van Huynh (USA) and Prof. Nguyen Viet Dung (USA). The department's staff regularly engage in short-term and long-term academic exchanges abroad.  

Department of Mathematical Analysis and Differential Equations

The Department of Mathematical Analysis was established in 1998, bringing together Institute staff researching various directions in mathematical analysis. Mathematical analysis is a very broad field, so the research carried out at the department is correspondingly diverse. Several department members currently head state-level research projects and serve as the core of numerous research groups that include staff from various universities and other research institutions. Many staff members teach Analysis as well as other courses at universities and have supervised numerous PhD candidates and master's students.  

Department of Geometry and Topology

Main research directions of the department Global Milnor fibration, topology and geometry of polynomial mappings. Positivity theorems and applications in polynomial optimization. Dynamical properties of polynomial mappings. Real analytic geometry. Geometry and topology of hyperplane arrangements, fundamental groups and homotopy type of hyperplane complements. Chern-Simons type invariants of 3-manifolds. Representation spaces and character varieties of fundamental groups.  

Department of Discrete Mathematics, Probabilily Theory and Statistics

In 2025, the Department of Discrete Mathematics, Probability and Statistics was formed from the merger of two departments: the Department of Mathematical Foundations of Computer Science and the Department of Probability and Statistics. 1. The Department of Mathematical Foundations of Computer Science was formed in 1970, originating from the Automata Theory and Formal Languages Group (led by Dr. Do Long Van) within the Cybernetics Section (headed by Prof. Phan Dinh Dieu). In 1975, the Department of Discrete Mathematics was established with core staff including Do Long Van, Pham Tra An, Ngo Dac Tan, Le Cong Thanh, and Nguyen Huong Lam. In 1998, the department merged with the Center for Applications of Mathematics in Technology and Management, officially becoming the Department of Mathematical Foundations of Computer Science, headed by Dr. Ngo Dac Tan with Dr. Pham Hong Quang as Deputy Head. Subsequent heads of the department were Dr. Le Cong Thanh (2002–2010), Assoc. Prof. Phan Thi Ha Duong (2010–2021), and Dr. Tran Nam Trung (2021–2025). The department has maintained a continuous seminar for more than 50 years, with lecturers from many universities. Its main research directions include computational complexity and models of computation, cryptography and applications (Phan Dinh Dieu, Pham Tra An, Le Cong Thanh), coding theory and automata (Do Long Van), Hamiltonian cycles and graph theory (Ngo Dac Tan), as well as discrete dynamical systems, combinatorics and complex networks (Phan Thi Ha Duong, together with Tran Thi Thu Huong, Pham Van Trung, Nguyen Hoang Thach, Do Duy Hieu). Several department members have actively participated in the activities of the Vietnam Mathematical Society, the journal Acta, the Institute of Mathematics, the UNESCO Mathematics Center, and the France-Vietnam Research Unit of CNRS. The department has carried out dozens of state- and ministry-level research projects, in cooperation with the Government Cipher Committee, Hanoi University of Science and Technology, Paris 6 and Paris 7 Universities, Nice Côte d'Azur University, ENS Lyon, and others. The department has trained dozens of PhDs and master's graduates, organized international schools and conferences, and made active contributions to the development of discrete mathematics and theoretical computer science in Vietnam. 2. Alongside the founding and growth of the Institute of Mathematics, the research field of Probability and Mathematical Statistics has been gradually built and developed. When the Mathematics Research Department at the Committee of Science and Technology was established at the end of 1967, the Probability and Statistics research group was born, with its first members being Tran Manh Tuan, Pham Tra An, and Dang Han — the first generation of probability and statistics staff, trained domestically at Hanoi University. During this period, alongside the task of raising professional qualifications like all staff of the Mathematics Department, the probability and statistics group took part in several projects applying mathematical statistics to practice, such as using statistical methods for product quality inspection, developing tailoring standards, and light-rain forecasting, among others. Training activities at the department were also strengthened; during these years, 6 PhD candidates of the department successfully defended their doctoral theses at the Institute of Mathematics: Nguyen Van Toan (Hue University), Cao Van Nuoi (Danang University), Nguyen Thanh Binh (Thai Nguyen University of Education), Tran Trong Nguyen (National Economics University), Tran Quang Vinh (Hanoi National University of Education), and Nguyen Thi Thuy Quynh (Academy of Finance). The department also taught probability and statistics courses to master's students at the Institute of Mathematics, and supervised more than 35 students who successfully defended their master's theses there. In addition, department staff have taught and trained PhD students, master's students, and undergraduates at Hanoi University of Science, Hanoi National University of Education, University of Engineering and Technology, Hue University, Vinh University, and several other research and training institutions across the country. The department helped organize and chair the 2nd National Conference on Probability and Statistics (Ba Vi, 2001), the Winter School on Probability and Statistics (Vinh, 2003), the 3rd National Conference on Probability and Statistics (Ba Vi, 2005), and the 4th National Conference on Probability and Statistics (Vinh, 2010). The department maintains broad relationships with numerous institutions and universities worldwide, through cooperative exchange and training activities between department staff and foreign partners and colleagues in France, the USA (Tuan, Thao), Germany (Thu, Cong, Duc, Son), Japan (Tuan, Thu), Poland (Thu, Luu, Phuc), Sweden (Phuc), Italy and Russia (Cong), Canada, the Netherlands, Taiwan, Singapore, Malaysia, Indonesia, and Thailand (Thao). Despite going through various ups and downs, the Probability and Statistics group has made many contributions to the research, application, and teaching of probability and mathematical statistics in Vietnam, helping to raise the standing and reputation of mathematicians both domestically and internationally. Probability and Mathematical Statistics are important branches of Mathematics, playing an essential role in the overall development of science. In this new period, the group continues to strive to further strengthen its scientific and professional role within the mathematical community in particular, and within the country's broader economic and social life in general.    

Department of Optimization and Scientific Computing

The Department of Numerical Analysis and Scientific Computing is responsible for research in the fields of Numerical Analysis and Scientific Computing. At the same time, the department's members continue to research and develop scientific topics that had already been of interest before the department was established. Over the years, the department has regularly held the "Numerical Analysis and Scientific Computing" seminar. The department's staff have published research on Numerical Analysis, Scientific Computing, and several related fields in international journals. Alongside research and teaching in Numerical Analysis and Scientific Computing, the department's staff continue to develop traditional research directions (applied analysis, optimization, variational inequalities, control theory, etc.) and have achieved good research results.