Research Interest

  • Number Theory

    Number theory is an ancient branch of mathematics that deals with properties of integers, such as prime numbers and divisibility. Number theorists study a wide range of problems, from basic questions about the integers (such as Goldbach's Conjecture) to more advanced problems that involve modular forms and elliptic curves. Number theory also has important applications in cryptography, coding theory, and computer science.

  • Group Theory

    Group theory is the study of symmetry and the properties of groups, which are sets of elements that can be combined under certain operations. Groups are used to model symmetries in physics, chemistry and other fields. The study of groups is also important in the study of algebraic structures, and it is widely used in many areas of mathematics, physics and computer science.

  • Graph Theory

    Graph theory is a branch of mathematics that deals with the study of networks of objects, where the objects are represented by vertices (or nodes) and the relationships between them are represented by edges. Graphs can be used to model many different types of relationships, such as social networks, the internet, and transportation systems. Graph theory has many important applications in computer science, operations research, and network science. It is also used in the study of algorithms, complexity theory, and cryptography.

Advancing mathematical fundamentals and real-world applications of Number Theory, Group Theory, Graph Theory, Topology and Abstract Algebra.

Our research mission is to advance the fundamentals of number theory, group theory, and graph theory through rigorous mathematical inquiry, while also exploring the practical applications of these theories in fields such as artificial intelligence, cryptography and computer science. We aim to tackle some of the most challenging open problems in these fields, such as the Riemann Hypothesis in number theory, the classification of finite simple groups in group theory, and the study of complex network systems in graph theory. Our research effort will be guided by the principles of interdisciplinary collaboration and innovation. We will strive to make significant contributions to the understanding of these theories and their applications by leveraging the latest techniques and tools from various disciplines.

We will collaborate with researchers from other fields such as computer science, physics and engineering to explore the potential of these theories in solving real-world problems. For example, in number theory, our research will focus on developing new methods for primality testing and factorization, which have important applications in cryptography and computer security. In group theory, we will study the symmetries of physical systems and explore the potential applications of group theory in quantum computing. In graph theory, we will study the structure and properties of complex networks, such as the internet and social networks, and explore the potential of graph theory in machine learning and artificial intelligence.

Our research effort is expected to have a significant impact on both the theoretical foundations of these fields and the practical applications of these theories. By solving open problems, we aim to deepen our understanding of the mathematical properties of numbers, groups and graphs and to develop new methods and tools to analyze large and complex systems. We also expect that our research will have a positive impact on the society by providing new solutions to critical problems in areas such as cyber security, transportation, and communication networks.