Academic Commons

Theses Doctoral

Lattice Subdivisions and Tropical Oriented Matroids, Featuring Products of Simplices

Piechnik, Lindsay C.

Subdivisions of products of simplices, and their applications, appear across mathematics. In this thesis, they are the tie between two branches of my research: polytopal lattice subdivisions and tropical oriented matroid theory. The first chapter describes desirable combinatorial properties of subdivisions of lattice polytopes, and how they can be used to address algebraic questions. Chapter two discusses tropical hyperplane arrangements and the tropical oriented matroid theory they inspire, paying particular attention to the previously uninvestigated distinction between the generic and non-generic cases. The focus of chapter three is products of simplices, and their connections and applications to ideas covered in the first two chapters.

Subjects

Files

  • thumnail for Piechnik_columbia_0054D_10081.pdf Piechnik_columbia_0054D_10081.pdf application/pdf 7.61 MB Download File

More About This Work

Academic Units
Mathematics
Thesis Advisors
Bayer, David
Pinkham, Henry Charles
Morrison, Ian
Jong, Aise Johan de
Gallagher, Patrick
Degree
Ph.D., Columbia University
Published Here
April 29, 2011
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.