Futaki invariants and harmonic metrics for the Hull-Strominger system

Abstract

The Hull-Strominger system has been proposed as a geometrization tool for understanding the moduli space of Calabi-Yau threefolds with topology change (‘Reid’s Fantasy’). In this talk we will introduce obstructions to the existence of solutions for these equations which combine infinite-dimensional moment maps, ‘harmonic metrics’, and a holomorphic version of generalized geometry. We will discuss the implications of these new obstructions in relation to a conjecture by S.-T. Yau for the Hull-Strominger system. Based on joint work with Raúl Gonzalez Molina, in arXiv:2303.05274, and arXiv:2301.08236.

Speaker

I am an Assistant Professor (Profesor Ayudante Doctor) at the Universidad Autónoma de Madrid, from September 2017. Previously, I have done postdocs at the ICMAT (Marie Curie Fellow, Severo Ochoa Fellow--Nigel Hitchin Laboratory), at the École Polytechnique Fédéral de Lausanne (Switzerland), at the Centre for Quantum Geometry of Moduli Spaces (Denmark) and at the Max Planck Institute for Mathematics (Germany). I obtained my PhD in 2009 at the Universidad Autónoma de Madrid.

My research is in the areas of differential geometry and algebraic geometry. The problems I study are mainly in complex geometry (Kähler and hermitian), and have strong links with geometric analysis and mathematical physics. The main research line I have carried out is the study of geometric structures and moduli spaces. Current projects include special metrics and connections in Kähler geometry (constant scalar curvature Kähler, Hermite-Yang-Mills, vortices, Hitchin equations) and their relation to stability conditions in algebraic geometry (GIT), moduli spaces (bundles and varieties, Higgs bundles, wall-crossing), special holonomy and mirror symmetry (Calabi-Yau, G2 geometry, Strominger system, generalized geometry, T-duality, vertex algebras).