On 6 July, at VNUHCM–University of Science (HCMUS), doctoral researcher Nguyá»…n Thị Thanh Lý successfully defended her doctoral thesis in Mathematical Analysis. The thesis, entitled “Ulam-Hyers stability of some functional equations and applications”, was completed under the academic supervision of Associate Professor Nguyá»…n Văn DÅ©ng and Associate Professor Lý Kim Hà.

The doctoral thesis focuses on the stability of several vital classes of functional equations in modern analysis, including generalized multilinear functional equations, generalized quadratic functional equations, generalized mixed additive–quadratic functional equations, and generalized cubic functional equations in quasi-Banach and quasi-p-Banach spaces. These research areas hold significant importance within functional equation theory and functional analysis, helping to clarify problems regarding the stability of solutions under the influence of small deviations or perturbations.

Utilizing research methodologies from modern analysis and the stability theory of functional equations, the thesis establishes sufficient conditions for the Ulam-Hyers stability of the aforementioned classes of functional equations. The achieved results not only extend the scope of application for numerous previously published works but also provide fresh approaches to studying stability within generalized spaces.

Among the prominent outcomes of this research is the formulation of corollaries for multiple special cases of functional equations, alongside answers to several open questions in the field. Furthermore, the doctoral researcher constructed counterexamples and illustrative examples to clarify the limitations of the theoretical findings and evaluate the applicability of the proposed methods.

The research findings have been published in three international scientific papers indexed in the Web of Science (WoS), comprising one Q1 journal article, one Q2 journal article, and one Q3 journal article.

In terms of scientific significance, the thesis contributes to developing the stability theory of functional equations in generalized spaces, whilst providing further theoretical tools and illustrative examples that can be inherited, extended, or applied in related research directions. The results and approaches presented in the thesis can also be further developed to investigate the stability of other classes of functional equations in quasi-Banach, quasi-p-Banach, and more generalized spaces.

On 30 November, doctoral researcher Nguyễn Cảnh Hùng successfully defended his dissertation at VNUHCM-University of Science. His thesis, entitled ‘Existence of Solutions and Duality for Several Classes of Nonsmooth Optimisation Problems,’ was completed under the supervision of Dr Thái Doãn Chương and Assoc. Prof. Nguyễn Lê Hoàng Anh.

The dissertation conducts a deep investigation within n-dimensional Euclidean space. The methodology employed a blend of established tools from variational analysis alongside novel techniques derived from semi-algebraic geometry.

The primary aim of the work was to establish the theoretical foundation for the existence of optimal solutions and to characterise the properties of the solution set, and to construct a comprehensive system of optimal conditions for a class of optimisation and robust optimisation problems where the objective function presents as nonsmooth and non-convex.

Academically, the work offers important new contributions, particularly in tackling the challenging and practically significant area of robust optimisation. The author introduced the concept of a ‘generalised tangent manifold at infinity,’ which furnishes an effective mechanism for investigating the lower boundedness of the infimum value. Building upon this, the dissertation demonstrated the equivalence between key stability properties, including robust M-tameness, robust properness, and the robust Palais–Smale condition, thereby establishing new results concerning the existence of solutions.

Alongside the investigation into the existence of solutions, the dissertation completed the theoretical landscape by formally constructing the duality problem. The author clarified the close relationship between the original problem and the dual problem through rigorous results covering weak duality, strong duality, and inverse duality. For problems incorporating functional and set constraints, necessary and sufficient optimal conditions were also rigorously established, drawing upon the concept of generalised convexity.

The dissertation’s results were highly praised by the Committee for both their urgency and potential applicability. The successful establishment of optimal conditions and the detailed analysis of solution existence are fundamental to the modelling and resolution of complex real-world problems. Furthermore, the innovative methods developed within the dissertation open up promising avenues for future research in related fields, such as asymptotic analysis, multi-objective optimisation, and the development of new sub-differential variations.

To realise the goal of achieving at least one field ranked in the world’s Top 100 by 2030, as directed by the Central Steering Committee for Science and Technology Development, 17³Ô¹Ï National University Ho Chi Minh City (VNUHCM) organised a seminar on 29 October 2025. The event was titled ‘Orientation and Development of Training and Scientific Research in Mathematics for the 2026–2030 Period, with Vision to 2045.’

Delivering the opening remarks, Prof. Nguyá»…n Thị Thanh Mai – Vice Chancellor of VNUHCM stressed that Mathematics holds a foundational role in innovation and digital transformation—the pillars of national science and technology development. Investment in the field of Mathematics aims not only to enhance the quality of training and research but also directly serves the national development strategy for science and technology and higher education.

At the seminar, experts analysed the current status of Mathematics training and research within the VNUHCM system and proposed numerous development solutions. For example, Dr. Võ �ức Cẩm Hải (VNUHCM-University of Science) suggested recruiting approximately 150 high-quality research personnel during the 2026–2030 period, striving to achieve 2,250 international publications, 75% of which belong to the Q1–Q2 group, and forming at least five strong research groups. Furthermore, Assoc. Prof. Trần Vũ Khanh (VNUHCM-International University) proposed building an academic brand identity by organising annual international conferences, publishing a dedicated Mathematics journal, and developing a “Chair Professors� programme to enhance global recognition. Meanwhile, Dr. Phan Thành An (VNUHCM-University of Technology) highlighted three development pillars: interdisciplinary/applied Mathematics, strong theoretical Mathematics, and effective support mechanisms from VNUHCM.

Vice Chancellor Nguyễn Thị Thanh Mai announced that VNUHCM is developing a project to improve university rankings, identifying Mathematics as a priority field for investment. The goal is to triple the number of international publications, particularly Q1 articles with international co-authors, thereby improving the academic reputation index—a crucial criterion in global rankings.

Concluding the seminar, she affirmed VNUHCM will continue substantial investment in human resources, financial capacity, and mechanisms to position Mathematics as a spearhead field, aiming for the world’s Top 100. This event serves not only as an opportunity to review the current status of Mathematics at VNUHCM but also lays the foundation for a methodical development strategy, contributing to asserting the position of Vietnamese higher education on the international academic map.

On 10 October, the Faculty of Mathematics and Computer Science at VNUHCM-University of Science (HCMUS) convened a seminar to introduce postgraduate scholarship programmes, featuring an academic address by Professor Shang-Yuan Shiu from the Department of Mathematics at National Central University (NCU), Taiwan. This event constituted a key component of the NCU delegation’s official visit and working agenda at HCMUS.

The session drew attendance from lecturers, researchers, and students from the Faculty of Mathematics and Computer Science. During the address, Professor Shang-Yuan Shiu delineated postgraduate education and scholarship prospects at NCU, underscoring the university’s robust international orientation regarding Mathematics, Data Science, and Artificial Intelligence (AI). Funded by the Ministry of Education of Taiwan, these full and partial scholarships seek to recruit exceptional researchers from Southeast Asia—specifically from 17³Ô¹Ï—thereby affording students entry into an advanced, multicultural, and globally integrated academic sphere.

Subsequent to the introductory remarks, Professor Shiu presented an academic lecture titled ‘Mathematical Formulation of Diffusion Models in Generative AI.’ The discourse offered an analytical survey of the mathematical underpinnings of diffusion models, elucidating the forward–reverse mechanisms inherent in data generation while highlighting the function of probability and stochastic analysis in the advancement of next-generation deep learning algorithms.

A dynamic dialogue ensued between Professor Shiu and the attendees, yielding novel interdisciplinary perspectives that bridge pure mathematics, data modelling, and AI technologies. This exchange granted HCMUS lecturers, researchers, and postgraduate students a venue to investigate contemporary research trajectories and deliberate on prospective avenues for collaboration with an international subject matter expert.

An interactive discussion following between Prof. Shang-Yuan Shiu and participants.

The seminar served not only to fortify research and education cooperation between HCMUS and National Central University but also to reaffirm the commitment of HCMUS to global scientific integration. Furthermore, the proceeding demonstrated the University’s sustained endeavour to broaden the institution’s international academic network and establish a high-calibre, forward-looking, and sustainable postgraduate research environment.