Colloquium| Institute of Mathematical Sciences
Time：16:00-17:00, August 8 Thursday
Location：Room S408, IMS
Speaker: Mario Garcia-Fernandez, Universidad Autonoma de Madrid
Abstract: The Hull-Strominger system of partial differential equations has its origins in string theory in physics, and it was first considered in the mathematics literature in a seminal paper by Li and Yau (JDG 2005). The mathematical study of this PDE has been proposed by Yau as a natural generalization of the Calabi problem for complex non-Kähler manifolds, and also in relation to Reid’s fantasy on the moduli space of projective Calabi-Yau threefolds. Conjecturely, the Hull-Strominger system hosts a generalization of mirror symmetry, where `mirror pairs' (X,V) <-> (X',V') are given by Calabi-Yau manifolds X equipped with a holomorphic vector bundle V.
In this talk I will discuss the construction of new examples of solutions of the Hull-Strominger system on non-Kähler torus bundles over K3 surfaces. These solutions are comparatively much simpler than the solutions constructed in the same manifolds by Fu and Yau (JDG 2008) via the complex Monge-Ampère equation. We will apply our construction to find the first examples of T-dual solutions of the Hull-Strominger system on compact non-Kähler manifolds with different topology.