1. TS. Nguyễn Thị Ngọc Giao (Trường Đại học Bách Khoa - Đại học Đà Nẵng)
Topic: On plane Cremona maps of degree four
Abstract: We are interested in the birational self-maps of the projective plane over an algebraically closed field of characteristic zero (e.g. the field C of complex numbers). Such a map will typically be denoted by f : P2 P2 and it is called plane Cremona map. The set of all plane Cremona maps forms a group, which is called the plane Cremona group Bir(P2). Generators of Bir(P2) have been known for over a century now, by Noether- Casteln uovo’s theorem. In particular, we aim to classify plane Cremona maps up to linear equivalence. These problems are often complicated, even for small de grees. Indeed, the classification of quadratic plane Cremona maps was very well-known from the beginning of the study of plane Cremona maps, more than one hundred years ago. Nonetheless, the classification of cubic plane Cremona maps was only established a few years ago in 2013 by Cerveau and D´ eserti, and then in 2022 by Calabri and me. Our goal in this project is to classify quartic plane Cremona maps. Our classifications are based on studying the configurations of the base points of the maps. This is a joint work with Alberto Calabri

2. TS. Trần Thị Hiếu Nghĩa (Trường Đại học Sư phạm TP. Hồ Chí Minh)
Title: Algebraic structures of some families of constacyclic codes over finite fields
Abstract: Algebraic coding theory explores the branch of coding theory where the properties of codes are expressed through algebraic structures. The focus is on constacyclic codes, a direct generalization of cyclic codes, which hold a significant role in error-correcting code theory due to their efficient encoding via shift registers, making them particularly appealing in engineering applications. From a mathematical perspective, constacyclic codes are characterized as ideals in the quotient ring F[x]/<x^n - λ>, where F[x] represents the polynomial ring over a finite field F. Over the years, constacyclic codes over finite fields and their applications have been widely investigated. However, classification results for repeated-root constacyclic codes of length np^s have been achieved only for some specific values of n. The problems of describing the structure and computing the minimum distance of constacyclic codes over finite fields become more difficult as the code length increases. In this talk, I will briefly discuss recent findings by my collaborators and me on some families of constacyclic codes of length np^s over finite fields where we develop polynomial algorithms with computer assistance to investigate the structures and the Hamming distances of these constacyclic codes, including identifying their optimal codes.

3. TS. Hoàng Anh Đức (Trường Đại học Khoa học tự nhiên, Đại học Quốc gia Hà Nội)
Title: A study on the structure of reconfiguration graphs and related problems
Abstract: Over the past few decades, "Combinatorial Reconfiguration" has emerged in various areas of computer science. In a reconfiguration variant of a computational problem (e.g., Satisfiability, Independent Set, Vertex-Coloring, etc.), a transformation rule describes an adjacency relation between feasible solutions (e.g., satisfying truth assignments, independent sets, proper vertex-colorings, etc.) of the problem. Another perspective on these reconfiguration problems is through the so-called reconfiguration graph (or solution graph)--a graph whose nodes represent feasible solutions, with edges connecting nodes that can be transformed into one another by applying the given rule exactly once. A typical example is the classic Rubik's cube puzzle, where each configuration of the cube corresponds to a feasible solution, and two configurations are adjacent if one can be obtained from the other by rotating a face of the cube by 90, 180, or 270 degrees. A classic question is whether there exists a sequence of adjacent feasible solutions between two given solutions S and T. In the corresponding reconfiguration graph, this question is equivalent to deciding whether there is a path between the nodes representing S and T. In this talk, I will briefly summarize the work I have done in 2024 at VIASM regarding my proposed research entitled "A study on the structure of reconfiguration graphs and related problems".

4. TS. Nguyễn Tiến Tài (Trường Đại học Khoa học tự nhiên, Đại học Quốc gia Hà Nội)
Title: Stability of laminar flows in fluid mechanics
Abstract: The study of the stability of laminar flows satisfying a system of hyperbolic equations has attracted a lot of attention of physicians and mathematicians due to its appearance in numerous models in fluid mechanics, e.g. Rayleigh-Taylor, Kelvin- Hemholtz, Zeldovitch-von Neumann-Doring detonation. In this talk, we first describe the viscous Rayleigh-Taylor instability around a smooth increasing density profile. We develop a novel method, based on the operator theory, to prove the existence of infinitely many normal modes to the linearized problem. These normal modes, along with nonlinear energy estimates, help us to prove a general nonlinear instability, extending the previous framework of Guo-Strauss and of Grenier. Second, we extend the above study to other models in fluid mechanics, precisely Rayleigh-Taylor influenced by other physical parameters, and Rayleigh-Bénard thermal convection.