Tesis
THESIS PREDEFENSE -- Hybrid Spaces on Deligne-Mumford stacks and degeneration of measures
Ponente: Bilson Castro ()Director/es: José Ignacio Burgos (ICMAT-CSIC)Fecha: viernes 13 de febrero de 2026 - 10:30Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
In this talk, we present the construction of a hybrid space associated with a compact complex manifold \(X\) together with a simple normal divisor \(D\). The notion of hybrid arises from the fact that this space combines aspects of complex geometry and polyhedral geometry. Once this topological space is established, we study its fundamental topological properties, which lead us to formulate and prove a continuity theorem for measures on the hybrid space.
After developing the theory in the case of complex varieties, the next step is to extend the construction to the setting of toroidal Deligne–Mumford stacks over \(\mathbb{C}\).
The construction of these spaces and the resulting theorems are broadly motivated by the connection between amplitudes in quantum field theory and string theory. In particular, the hybrid space associated with toroidal Deligne–Mumford stacks, such as the moduli stack of stable curves of genus \(g\) with \(n\) marked points, offers a natural geometric setting in which the computation of amplitudes in these physical theories can be understood as integrals over a hybrid space associated with the moduli stack.
