A Study Of Green’S Relations On Algebraic Semigroups, 2015 The University of Western Ontario

#### A Study Of Green’S Relations On Algebraic Semigroups, Allen O'Hara

*Electronic Thesis and Dissertation Repository*

The purpose of this work is to enhance the understanding regular algebraic semigroups by considering the structural influence of Green's relations. There will be three chief topics of discussion.

- Green's relations and the Adherence order on reductive monoids
- Renner’s conjecture on regular irreducible semigroups with zero
- a Green’s relation inspired construction of regular algebraic semigroups

Primarily, we will explore the combinatorial and geometric nature of reductive monoids with zero. Such monoids have a decomposition in terms of a Borel subgroup, called the Bruhat decomposition, which produces a finite monoid, **R**, the Renner monoid. We will explore ...

Algorithms To Compute Characteristic Classes, 2015 The University of Western Ontario

#### Algorithms To Compute Characteristic Classes, Martin Helmer

*Electronic Thesis and Dissertation Repository*

In this thesis we develop several new algorithms to compute characteristics classes in a variety of settings. In addition to algorithms for the computation of the Euler characteristic, a classical topological invariant, we also give algorithms to compute the Segre class and Chern-Schwartz-MacPherson (CSM) class. These invariants can in turn be used to compute other common invariants such as the Chern-Fulton class (or the Chern class in smooth cases).

We begin with subschemes of a projective space over an algebraically closed field of characteristic zero. In this setting we give effective algorithms to compute the CSM class, Segre class and ...

Dihedral-Like Constructions Of Automorphic Loops, 2015 University of Denver

#### Dihedral-Like Constructions Of Automorphic Loops, Mouna Ramadan Aboras

*Electronic Theses and Dissertations*

In this dissertation we study dihedral-like constructions of automorphic loops. Automorphic loops are loops in which all inner mappings are automorphisms. We start by describing a generalization of the dihedral construction for groups. Namely, if (*G* , +) is an abelian group, *m* > 1 and α ∈2 Aut(*G* ), let Dih(*m, G,* α) on Z_{m} × *G* be defined by

(*i, u* )(*j, v* ) = (*i + j* , ((-1)^{j}* u* + *v* )α^{ij} ).

We prove that the resulting loop is automorphic if and only if *m* = 2 or (α^{2} = 1 and *m* is even) or (*m* is odd, α = 1 and ...

Symbolic Powers Of Edge Ideals, 2015 Dordt College

#### Symbolic Powers Of Edge Ideals, Mike Janssen

*Faculty Work Comprehensive List*

No abstract provided.

Manipulating The Mass Distribution Of A Golf Putter, 2015 University of Rhode Island

#### Manipulating The Mass Distribution Of A Golf Putter, Paul J. Hessler Jr.

*Senior Honors Projects*

Putting may appear to be the easiest but is actually the most technically challenging part of the game of golf. The ideal putting stroke will remain parallel to its desired trajectory both in the reverse and forward direction when the putter head is within six inches of the ball. Deviation from this concept will cause a cut or sidespin on the ball that will affect the path the ball will travel.

Club design plays a large part in how well a player will be able to achieve a straight back and straight through club head path near impact; specifically the ...

Automorphisms Of Graph Curves On K3 Surfaces, 2015 Georgia Southern University

#### Automorphisms Of Graph Curves On K3 Surfaces, Joshua C. Ferrerra

*Electronic Theses and Dissertations*

We examine the automorphism group of configurations of rational curves on $K3$ surfaces. We use the properties of finite automorphisms of $\PP^1$ to examine what restrictions a given elliptic fibration imposes on the possible finite order non-symplectic automorphisms of the $K3$ surface. We also examine the fixed loci of these automorphisms, and construct an explicit fibration to demonstrate the process.

Computing Intersection Multiplicity Via Triangular Decomposition, 2014 The University of Western Ontario

#### Computing Intersection Multiplicity Via Triangular Decomposition, Paul Vrbik

*Electronic Thesis and Dissertation Repository*

Fulton’s algorithm is used to calculate the intersection multiplicity of two plane curves about a rational point. This work extends Fulton’s algorithm first to algebraic points (encoded by triangular sets) and then, with some generic assumptions, to l many hypersurfaces.

Out of necessity, we give a standard-basis free method (i.e. practically efficient method) for calculating tangent cones at points on curves.

Continuous Dependence Of Solutions Of Equations On Parameters, 2014 Rose-Hulman Institute of Technology

#### Continuous Dependence Of Solutions Of Equations On Parameters, Sean A. Broughton

*Mathematical Sciences Technical Reports (MSTR)*

It is shown under very general conditions that the solutions of equations depend continuously on the coefficients or parameters of the equations. The standard examples are solutions of monic polynomial equations and the eigenvalues of a matrix. However, the proof methods apply to any finite map *T : C^{n} -> C^{n}*.

Tilting Sheaves On Brauer-Severi Schemes And Arithmetic Toric Varieties, 2014 The University of Western Ontario

#### Tilting Sheaves On Brauer-Severi Schemes And Arithmetic Toric Varieties, Youlong Yan

*Electronic Thesis and Dissertation Repository*

The derived category of coherent sheaves on a smooth projective variety is an important object of study in algebraic geometry. One important device relevant for this study is the notion of tilting sheaf.

This thesis is concerned with the existence of tilting sheaves on some smooth projective varieties. The main technique we use in this thesis is Galois descent theory. We first construct tilting bundles on general Brauer-Severi varieties. Our main result shows the existence of tilting bundles on some Brauer-Severi schemes. As an application, we prove that there are tilting bundles on an arithmetic toric variety whose toric variety ...

Light Pollution Research Through Citizen Science, 2014 CSU Sacramento

#### Light Pollution Research Through Citizen Science, John Kanemoto

*STAR (STEM Teacher and Researcher) Presentations*

Light pollution (LP) can disrupt and/or degrade the health of all living things, as well as, their environments. The goal of my research at the NOAO was to check the accuracy of the citizen science LP reporting systems entitled: Globe at Night (GaN), Dark Sky Meter (DSM), and Loss of the Night (LoN). On the GaN webpage, the darkness of the night sky (DotNS) is reported by selecting a magnitude chart. Each magnitude chart has a different density/number of stars around a specific constellation. The greater number of stars implies a darker night sky. Within the DSM iPhone ...

The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, 2014 University of Nebraska-Lincoln

#### The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, Nora Youngs

*Dissertations, Theses, and Student Research Papers in Mathematics*

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can - in principle - be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, algebraic objects that encode ...

A Kleinian Approach To Fundamental Regions, 2014 Joshua L Hidalgo

#### A Kleinian Approach To Fundamental Regions, Joshua L. Hidalgo

*Electronic Theses, Projects, and Dissertations*

This thesis takes a Kleinian approach to hyperbolic geometry in order to illustrate the importance of discrete subgroups and their fundamental domains (fundamental regions). A brief history of Euclids Parallel Postulate and its relation to the discovery of hyperbolic geometry be given first. We will explore two models of hyperbolic $n$-space: $U^n$ and $B^n$. Points, lines, distances, and spheres of these two models will be defined and examples in $U^2$, $U^3$, and $B^2$ will be given. We will then discuss the isometries of $U^n$ and $B^n$. These isometries, known as M\"obius ...

The Dual Gromov-Hausdorff Propinquity, 2014 University of Denver

#### The Dual Gromov-Hausdorff Propinquity, Frédéric Latrémolière

*Mathematics Preprint Series*

Motivated by the quest for an analogue of the Gromov-Hausdorff distance in noncommutative geometry which is well-behaved with respect to C*- algebraic structures, we propose a complete metric on the class of Leibniz quantum compact metric spaces, named the dual Gromov-Hausdorff propinquity, which resolves several important issues raised by recent research in noncommutative metric geometry: our new metric makes *-isomorphism a necessary condition for distance zero, is well-adapted to Leibniz seminorms, and — very importantly — is complete, unlike the quantum propinquity which we introduced earlier. Thus our new metric provides a new tool for noncommutative metric geometry which offers a solution ...

A Metric On Max-Min Algebra, 2014 University of Oregon

#### A Metric On Max-Min Algebra, Jonathan Eskeldson, Miriam Jaffe, Viorel Nitica

*Mathematics*

No abstract provided.

Tropical Convexity Over Max-Min Semiring, 2014 West Chester University of Pennsylvania

#### Tropical Convexity Over Max-Min Semiring, Viorel Nitica, Sergei Sergeev

*Mathematics*

No abstract provided.

Early Investigations In Conformal And Differential Geometry, 2014 University of Arkansas, Fayetteville

#### Early Investigations In Conformal And Differential Geometry, Raymond T. Walter

*Inquiry: The University of Arkansas Undergraduate Research Journal*

The present article introduces fundamental notions of conformal and differential geometry, especially where such notions are useful in mathematical physics applications. Its primary achievement is a nontraditional proof of the classic result of Liouville that the only conformal transformations in Euclidean space of dimension greater than two are Möbius transformations. The proof is nontraditional in the sense that it uses the standard Dirac operator on Euclidean space and is based on a representation of Möbius transformations using 2x2 matrices over a Clifford algebra. Clifford algebras and the Dirac operator are important in other applications of pure mathematics and mathematical physics ...

Arithmetical Graphs, Riemann-Roch Structure For Lattices, And The Frobenius Number Problem, 2014 Harvey Mudd College

#### Arithmetical Graphs, Riemann-Roch Structure For Lattices, And The Frobenius Number Problem, Jeremy Usatine

*HMC Senior Theses*

If R is a list of positive integers with greatest common denominator equal to 1, calculating the Frobenius number of R is in general NP-hard. Dino Lorenzini defines the arithmetical graph, which naturally arises in arithmetic geometry, and a notion of genus, the g-number, that in specific cases coincides with the Frobenius number of R. A result of Dino Lorenzini's gives a method for quickly calculating upper bounds for the g-number of arithmetical graphs. We discuss the arithmetic geometry related to arithmetical graphs and present an example of an arithmetical graph that arises in this context. We also discuss ...

Function Of Several Variable, 2014 Parkland College

#### Function Of Several Variable, Weiting Li

*A with Honors Projects*

This Parkland A with Honors project discusses the function of several variables, it's limits and partial derivatives.

Geometric Study Of The Category Of Matrix Factorizations, 2013 University of Nebraska-Lincoln

#### Geometric Study Of The Category Of Matrix Factorizations, Xuan Yu

*Dissertations, Theses, and Student Research Papers in Mathematics*

We study the geometry of matrix factorizations in this dissertation.

It contains two parts. The first one is a Chern-Weil style

construction for the Chern character of matrix factorizations; this

allows us to reproduce the Chern character in an explicit,

understandable way. Some basic properties of the Chern character are

also proved (via this construction) such as functoriality and that

it determines a ring homomorphism from the Grothendieck group of

matrix factorizations to its Hochschild homology. The second part is

a reconstruction theorem of hypersurface singularities. This is

given by applying a slightly modified version of Balmer's tensor

triangular ...

Results On Containments And Resurgences, With A Focus On Ideals Of Points In The Plane, 2013 University of Nebraska-Lincoln

#### Results On Containments And Resurgences, With A Focus On Ideals Of Points In The Plane, Annika Denkert

*Dissertations, Theses, and Student Research Papers in Mathematics*

Let *K* be an algebraically closed field and *I* ⊆ *R*=*K*[**P**^{N}] a nontrivial homogeneous ideal. We can describe ordinary powers *I*^{r} and symbolic powers *I*^{(m)} of *I*. One question that has been of interest over the past couple of years is that of when we have containment of *I*^{(m)} in *I*^{r}. Bocci and Harbourne defined the resurgence of *I* as rho(*I*)=sup_{m,r}{m/r | *I*^{(m)} is not contained in *I*^{r}}. Hence in particular *I*^{(m)} ⊆ *I*^{r} whenever m/r is at least rho(*I*). Results by Macaulay, Ein-Lazarsfeld-Smith ...