Mathematics, Department of

 

Date of this Version

8-2013

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor Mark E. Walker. Lincoln, Nebraska: August, 2013

Copyright (c) 2013 Xuan Yu

Abstract

We study the geometry of matrix factorizations in this dissertation.
It contains two parts. The first one is a Chern-Weil style
construction for the Chern character of matrix factorizations; this
allows us to reproduce the Chern character in an explicit,
understandable way. Some basic properties of the Chern character are
also proved (via this construction) such as functoriality and that
it determines a ring homomorphism from the Grothendieck group of
matrix factorizations to its Hochschild homology. The second part is
a reconstruction theorem of hypersurface singularities. This is
given by applying a slightly modified version of Balmer's tensor
triangular geometry to the homotopy category of matrix
factorizations.

Adviser: Mark E. Walker