Specialization: Algebra, Combinatorics and Number Theory
The group’s work widely spans algebra, coding theory, cryptography, combinatorics, discrete mathematics, and number theory. We explore how number theory strengthens cryptography, coding theory enhances data security, algebraic geometry supports string theory, and graph theory advances network analysis in social and biological systems, showcasing the profound impact of mathematics on technology and scientific discovery.
- Non-commutative ring theory, module theory, endomorphism rings, Direct sum decomposition in some classes of modules as an application of Algebraic Coding theory.
- Algebraic and geometric structures that naturally appear in Mathematical Physics, particularly in (non-)associative algebras, algebraic Operads, Homotopy algebras, and related topics.
- Graph Theory, particularly algebraic, spectral, and chemical graph theory, with applications to large-scale complex networks arising in the computational, social, biological, chemical, and drug design.
- Design and analysis of algorithms with a focus on computational complexity and machine learning techniques.