The Hull-Strominger system in complex geometry
By: Sebastien F. Picard
Publisher: [publisher not identified]
Published: 2018
Place of publication: [New York, N.Y.?]
Language: eng
Description: In this work, we study the Hull-Strominger system. New solutions are found on hyperkahler fibrations over a Riemann surface. This class of solutions is the first which admits infinitely many topological types. Next, we study the Fu-Yau solutions of the Hull-Strominger system and their generalizations to higher dimensions. We solve the Fu-Yau equation in higher dimensions, and in fact, solve a new class of fully nonlinear elliptic PDE which contains the Fu-Yau equation as a special case. Lastly, we introduce a geometric flow to study the Hull-Strominger system and non-Kahler Calabi-Yau threefolds. Basic properties are established, and we study this flow in the geometric settings of fibrations over a Riemann surface and fibrations over a K3 surface. In both cases, the flow descends to a nonlinear evolution equation for a scalar function on the base, and we study the dynamical behavior of these evolution equations.
Notes: Department: Mathematics.

Thesis advisor: Duong H. Phong.

Thesis (Ph.D.)--Columbia University, 2018.