An introduction to the Strominger system
Student No.:50
Time:Tue/Fri 9:50-11:25, 2017-06-20~2017-07-04
Instructor:Mario Garcia Fernandez  [ICMAT (Madrid)]
Place:Conference room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-6-20
Ending Date:2017-7-4



The Strominger system of partial differential equations arises in supergravity in physics, where it describes supersymmetric vacua in compactifications of the heterotic string theory. Its mathematical study was proposed by Yau as a natural generalization of the Calabi problem, and in relation to the moduli space of Calabi-Yau threefolds which are not necessarily Kählerian. These lectures are intended to give an introduction to the geometry and analysis of these partial differential equations, divided in three different parts. In Part I we will introduce the equations and review some known methods for the construction of solutions (invariant solutions, perturbation arguments, Fu-Yau reduction to Monge-Ampere type equations), as well as Yau’s Conjecture for the Strominger System. Part II is concerned with the interrelation of the Strominger with the notion of string class, thatwill lead us naturally to a suitable modification of Hitchin’s theory of Generalized Geometry. In particular, we will discuss the relevance of this new geometry for the moduli problem of the Strominger System. In Part III we will use this geometric framework to prove a Strominger-Yau-Zaslow principle for the Strominger system .





Basics in complex differential geometry and algebraic geometry.





M. Garcia-Fernandez, Lectures on the Strominger system, Travaux Mathématiques, Special Issue: School GEOQUANT at the ICMAT, Vol. XXIV (2016) 7--61, arXiv:1609.02615.


M. Garcia-Fernandez, R. Rubio and C. Tipler, Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry, Mathematische Annalen, doi:10.1007/s00208-016-1463-5, arXiv:1503.07562.


M. Garcia-Fernandez, Ricci flow, Killing spinors, and T-duality in generalized geometry, arXiv:1611.08926.