Open Access. Powered by Scholars. Published by Universities.®

Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Electronic Theses and Dissertations

Algebraic geometry

Articles 1 - 2 of 2

Full-Text Articles in Mathematics

Z2-Orbifolds Of Affine Vertex Algebras And W-Algebras, Masoumah Abdullah Al-Ali Jan 2017

Z2-Orbifolds Of Affine Vertex Algebras And W-Algebras, Masoumah Abdullah Al-Ali

Electronic Theses and Dissertations

Vertex algebras arose in conformal field theory and were first defined axiomatically by Borcherds in his famous proof of the Moonshine Conjecture in 1986. The orbifold construction is a standard way to construct new vertex algebras from old ones. Starting with a vertex algebra V and a group G of automorphisms, one considers the invariant subalgebra VG (called G-orbifold of V), and its extensions. For example, the Moonshine vertex algebra arises as an extension of the Z2-orbifold of the lattice vertex algebra associated to the Leech lattice.

In this thesis we consider two problems. First, …


A Journey To Fuzzy Rings, Brett T. Ernst Jan 2017

A Journey To Fuzzy Rings, Brett T. Ernst

Electronic Theses and Dissertations

Enumerative geometry is a very old branch of algebraic geometry. In this thesis, we will describe several classical problems in enumerative geometry and their solutions in order to motivate the introduction of tropical geometry. Finally, fuzzy rings, a powerful algebraic framework for tropical and algebraic geometry is introduced.