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The Hull-Strominger system in complex geometry

Picard, Sebastien F.

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.

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More About This Work

Academic Units
Mathematics
Thesis Advisors
Phong, Duong H.
Degree
Ph.D., Columbia University
Published Here
April 13, 2018