Our research explores advanced problems in string theory and quantum field theory, with particular emphasis on the deep connections between geometry, symmetry, and quantum dynamics. We study dualities, conformal and topological structures, and the behavior of quantum fields in curved or otherwise nontrivial spacetimes. Our work develops both analytical and perturbative methods to investigate scattering amplitudes, anomalies, effective actions, and the emergence of holographic descriptions. Through these efforts, we seek to illuminate how fundamental theoretical frameworks encode quantum and gravitational interactions, unifying insights from high-energy physics, modern mathematical structures, and contemporary approaches to quantum gravity.