The award will enable the researcher to develop a universal mathematical language that unifies the study of all possible geometries through a deformation connecting orientable and non-orientable surfaces. Topological recursivity is the universal procedure for calculating invariant properties of surfaces such as spheres or tori, but currently, there is no unified model for non-orientable surfaces, such as Möbius strips or Klein bottles.
García's project, REBORN, aims to establish a framework for calculating invariant properties of both orientable and non-orientable surfaces. The researcher, a professor at the Escola Politècnica Superior d’Edificació de Barcelona (EPSEB), proposes introducing a parameter to distinguish the type of surface, recovering the theory of orientable surfaces when the parameter is zero and that of non-necessarily orientable surfaces when it is one.
The objective is to obtain refinements of the Witten–Kontsevich theorem and Mirzakhani recursion, simplifying the understanding of continuous surface deformations appearing in quantum field theory and string theory models. This unified framework will establish connections between refinements of curve moduli spaces, providing new mathematical tools to study symmetries, dualities, and geometric structures.
“"When the parameter is zero, the theory of orientable surfaces is recovered, while when it is one, the theory of non-necessarily orientable surfaces is recovered."
Leonardo grants are financial aids for researchers aged between 30 and 45 to support individual research or artistic creation projects of an innovative nature, offering freedom and flexibility.
