Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- 11/8th conjecture (1)
- Bass Numbers (1)
- Braid Groups (1)
- Clique Graphs (1)
- Critical Infrastructure (1)
-
- Damage Assessment (1)
- Data Lineage (1)
- Data Provenance (1)
- Edge Ideals (1)
- Gauge theory (1)
- Geometric analysis (1)
- Graph Reachability (1)
- Group Cohomology (1)
- Local Cohomology (1)
- Low dimensional topology (1)
- Lyubeznik Numbers (1)
- Mathematical physics (1)
- Rarita-Schwinger operator (1)
- Seiberg-Witten theory (1)
- Temporal Graphs (1)
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Lyubeznik Numbers Of Unmixed Edge Ideals, Sara Rae Jones
Lyubeznik Numbers Of Unmixed Edge Ideals, Sara Rae Jones
Graduate Theses and Dissertations
Lyubeznik numbers, defined in terms of local cohomology, are invariants of local rings that are able to detect many algebraic and geometric properties. Notably they recognize topological behaviors of various structures associated to their rings. We will discuss computations of these numbers for unmixed edge ideals by giving a completely combinatorial construction which realizes the connectedness information captured by these numbers.
Cohomology Of The Symmetric Group With Twisted Coefficients And Quotients Of The Braid Group, Trevor Nakamura
Cohomology Of The Symmetric Group With Twisted Coefficients And Quotients Of The Braid Group, Trevor Nakamura
Graduate Theses and Dissertations
In 2014 Brendle and Margalit proved the level $4$ congruence subgroup of the braid group, $B_{n}[4]$, is the subgroup of the pure braid group generated by squares of all elements, $PB_{n}^{2}$. We define the mod $4$ braid group, $\Z_{n}$, to be the quotient of the braid group by the level 4 congruence subgroup, $B_{n}/B_{n}[4]$. In this dissertation we construct a group presentation for $\Z_{n}$ and determine a normal generating set for $B_{n}[4]$ as a subgroup of the braid group. Further work by Kordek and Margalit in 2019 proved $\Z_{n}$ is an extension of the symmetric group, $S_{n}$, by $\mathbb{Z}_{2}^{\binom{n}{2}}$. A …
Finite Dimensional Approximation And Pin(2)-Equivariant Property For Rarita-Schwinger-Seiberg-Witten Equations, Minh Lam Nguyen
Finite Dimensional Approximation And Pin(2)-Equivariant Property For Rarita-Schwinger-Seiberg-Witten Equations, Minh Lam Nguyen
Graduate Theses and Dissertations
The Rarita-Schwinger operator Q was initially proposed in the 1941 paper by Rarita and Schwinger to study wave functions of particles of spin 3/2, and there is a vast amount of physics literature on its properties. Roughly speaking, 3/2−spinors are spinor-valued 1-forms that also happen to be in the kernel of the Clifford multiplication. Let X be a simply connected Riemannian spin 4−manifold. Associated to a fixed spin structure on X, we define a Seiberg-Witten-like system of non-linear PDEs using Q and the Hodge-Dirac operator d∗ + d+ after suitable gauge-fixing. The moduli space of solutions M contains (3/2-spinors, purely …
A Novel Data Lineage Model For Critical Infrastructure And A Solution To A Special Case Of The Temporal Graph Reachability Problem, Ian Moncur
Graduate Theses and Dissertations
Rapid and accurate damage assessment is crucial to minimize downtime in critical infrastructure. Dependency on modern technology requires fast and consistent techniques to prevent damage from spreading while also minimizing the impact of damage on system users. One technique to assist in assessment is data lineage, which involves tracing a history of dependencies for data items. The goal of this thesis is to present one novel model and an algorithm that uses data lineage with the goal of being fast and accurate. In function this model operates as a directed graph, with the vertices being data items and edges representing …