## Mathematics, Department of

#### Date of this Version

8-2013

#### 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

## 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