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Full-Text Articles in Physical Sciences and Mathematics
Investigations Into Non-Degenerate Quasihomogeneous Polynomials As Related To Fjrw Theory, Scott C. Mancuso
Investigations Into Non-Degenerate Quasihomogeneous Polynomials As Related To Fjrw Theory, Scott C. Mancuso
Theses and Dissertations
The motivation for this paper is a better understanding of the basic building blocks of FJRW theory. The basics of FJRW theory will be briefly outlined, but the majority of the paper will deal with certain multivariate polynomials which are the most fundamental building blocks in FJRW theory. We will first describe what is already known about these polynomials and then discuss several properties we proved as well as conjectures we disproved. We also introduce a new conjecture suggested by computer calculations performed as part of our investigation.
The Frobenius Manifold Structure Of The Landau-Ginzburg A-Model For Sums Of An And Dn Singularities, Rachel Megan Webb
The Frobenius Manifold Structure Of The Landau-Ginzburg A-Model For Sums Of An And Dn Singularities, Rachel Megan Webb
Theses and Dissertations
In this thesis we compute the Frobenius manifold of the Landau-Ginzburg A-model (FJRW theory) for certain polynomials. Specifically, our computations apply to polynomials that are sums of An and Dn singularities, paired with the corresponding maximal symmetry group. In particular this computation applies to several K3 surfaces. We compute the necessary correlators using reconstruction, the concavity axiom, and new techniques. We also compute the Frobenius manifold of the D3 singularity.
Poincaré Polynomial Of Fjrw Rings And The Group-Weights Conjecture, Julian Boon Kai Tay
Poincaré Polynomial Of Fjrw Rings And The Group-Weights Conjecture, Julian Boon Kai Tay
Theses and Dissertations
FJRW-theory is a recent advancement in singularity theory arising from physics. The FJRW-theory is a graded vector space constructed from a quasihomogeneous weighted polynomial and symmetry group, but it has been conjectured that the theory only depends on the weights of the polynomial and the group. In this thesis, I prove this conjecture using Poincaré polynomials and Koszul complexes. By constructing the Koszul complex of the state space, we have found an expression for the Poincaré polynomial of the state space for a given polynomial and associated group. This Poincaré polynomial is defined over the representation ring of a group …
An Algebra Isomorphism For The Landau-Ginzburg Mirror Symmetry Conjecture, Jared Drew Johnson
An Algebra Isomorphism For The Landau-Ginzburg Mirror Symmetry Conjecture, Jared Drew Johnson
Theses and Dissertations
Landau-Ginzburg mirror symmetry takes place in the context of affine singularities in CN. Given such a singularity defined by a quasihomogeneous polynomial W and an appropriate group of symmetries G, one can construct the FJRW theory (see [3]). This construction fills the role of the A-model in a mirror symmetry proposal of Berglund and H ubsch [1]. The conjecture is that the A-model of W and G should match the B-model of a dual singularity and dual group (which we denote by WT and GT). The B-model construction is based on the Milnor ring, or local algebra, of the singularity. …