Title: Matrix Tree Theorem

Abstract: The Laplacian matrix of a graph is a well studied object in mathematics. One of its more prominent roles comes in the famous Matrix Tree Theorem. In this talk, we first look at a classical proof of the Matrix Tree Theorem. Then we carefully explore a more recent proof through the work of Dall and Pfeifle using polytopes. Finally I will outline my research plan and present some preliminary results. This talk serves as my Qualifying Exam.