Mr. Umut Selvi centers on advanced mathematical structures, focusing on algebraic geometry, matrix theory, and their applications in both theoretical and computational mathematics. His doctoral and postgraduate work explores the geometry of Lie algebroids and non-Newtonian parallel surfaces, contributing to a deeper understanding of modern geometric frameworks that bridge algebra and analysis. Selvi has co-authored several studies on spectral norms of circulant matrices involving Chebyshev polynomials and Fibonacci quaternions, providing explicit formulas and extending the theoretical foundations of matrix norms. His research in these areas enhances the computational methods used in engineering and applied sciences. Additionally, his collaborative book chapters and editorial contributions in mathematical publications such as Mathematical Methods for Engineering Applications and Recent Developments in Mathematics reflect a strong engagement in the dissemination of mathematical innovation. Through presentations at international conferences, including those on geometry and mathematical education, Selvi has shared insights on generalized multiplicative cross products, Euclidean norms, and Lie algebraic structures on vector spaces. His work emphasizes analytical precision, structural symmetry, and the unification of abstract algebraic concepts with geometric intuition, advancing the field of pure mathematics with applications in natural and computational sciences.