On The Perfect Reconstruction Of The Structure Of Dynamic Networks, 2016 University of Dayton

#### On The Perfect Reconstruction Of The Structure Of Dynamic Networks, Alan Veliz-Cuba

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Non-Commutative Automorphisms Of Bounded Non-Commutative Domains, 2016 Washington University in St Louis

#### Non-Commutative Automorphisms Of Bounded Non-Commutative Domains, John E. Mccarthy, Richard M. Timoney

*Mathematics Faculty Publications*

We establish rigidity (or uniqueness) theorems for non-commutative (NC) automorphisms that are natural extensions of classical results of H. Cartan and are improvements of recent results. We apply our results to NC domains consisting of unit balls of rectangular matrices.

On The Free And G-Saturated Weight Monoids Of Smooth Affine Spherical Varieties For G=Sl(N), 2016 The Graduate Center, City University of New York

#### On The Free And G-Saturated Weight Monoids Of Smooth Affine Spherical Varieties For G=Sl(N), Won Geun Kim

*All Graduate Works by Year: Dissertations, Theses, and Capstone Projects*

Let $X$ be an affine algebraic variety over $\mathbb{C}$ equipped with an action of a connected reductive group $G$. The weight monoid $\Gamma(X)$ of $X$ is the set of isomorphism classes of irreducible representations of $G$ that occur in the coordinate ring $\mathbb{C}[X]$ of $X$. Losev has shown that if $X$ is a smooth affine spherical variety, that is, if $X$ is smooth and $\mathbb{C}[X]$ is multiplicity-free as a representation of $G$, then $\Gamma(X)$ determines $X$ up to equivariant automorphism.

Pezzini and Van Steirteghem have recently obtained a combinatorial characterization of the weight ...

K-Theory Of Root Stacks And Its Application To Equivariant K-Theory, 2016 The University of Western Ontario

#### K-Theory Of Root Stacks And Its Application To Equivariant K-Theory, Ivan Kobyzev

*Electronic Thesis and Dissertation Repository*

We give a definition of a root stack and describe its most basic properties. Then we recall the necessary background (Abhyankar’s lemma, Chevalley-Shephard-Todd theorem, Luna’s etale slice theorem) and prove that under some conditions a quotient stack is a root stack. Then we compute G-theory and K-theory of a root stack. These results are used to formulate the theorem on equivariant algebraic K-theory of schemes.

Topological And Hq Equivalence Of Prime Cyclic P-Gonal Actions On Riemann Surfaces, 2016 Rose-Hulman Institute of Technology

#### Topological And Hq Equivalence Of Prime Cyclic P-Gonal Actions On Riemann Surfaces, Sean A. Broughton

*Mathematical Sciences Technical Reports (MSTR)*

Two Riemann surfaces *S*_{1} and *S*_{2} with conformal *G*-actions have topologically equivalent actions if there is a homeomorphism *h :* *S _{1} -> S_{2} *which intertwines the actions. A weaker equivalence may be defined by comparing the representations of

*G*on the spaces of holomorphic

*q-*differentials

*H*and

^{q}(S_{1})*H*In this note we study the differences between topological equivalence and

^{q}(S_{2}).*H*equivalence of prime cyclic actions, where

^{q}*S*and

_{1}/G*S*have genus zero.

_{2}/GThe Implicit Function Theorem And Free Algebraic Sets, 2016 Washington University in St Louis

#### The Implicit Function Theorem And Free Algebraic Sets, Jim Agler, John E. Mccarthy

*Mathematics Faculty Publications*

We prove an implicit function theorem for non-commutative functions. We use this to show that if *p* ( X;Y ) is a generic non-commuting polynomial in two variables, and X is a generic matrix, then all solutions Y of *p* ( X;Y ) = 0 will commute with X

Aspects Of Non-Commutative Function Theory, 2016 Washington University in St Louis

#### Aspects Of Non-Commutative Function Theory, Jim Agler, John E. Mccarthy

*Mathematics Faculty Publications*

We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.

The Log-Exponential Smoothing Technique And Nesterov’S Accelerated Gradient Method For Generalized Sylvester Problems, 2016 Thua Thien Hue College of Education

#### The Log-Exponential Smoothing Technique And Nesterov’S Accelerated Gradient Method For Generalized Sylvester Problems, N. T. An, Daniel J. Giles, Nguyen Mau Nam, R. Blake Rector

*Mathematics and Statistics Faculty Publications and Presentations*

The Sylvester or smallest enclosing circle problem involves finding the smallest circle enclosing a finite number of points in the plane. We consider generalized versions of the Sylvester problem in which the points are replaced by sets. Based on the log-exponential smoothing technique and Nesterov’s accelerated gradient method, we present an effective numerical algorithm for solving these problems.

Topology Of The Affine Springer Fiber In Type A, 2016 University of Massachusetts - Amherst

#### Topology Of The Affine Springer Fiber In Type A, Tobias Wilson

*Doctoral Dissertations May 2014 - current*

We develop algorithms for describing elements of the affine Springer fiber in type

A for certain 2 g(C[[t]]). For these , which are equivalued, integral, and regular,

it is known that the affine Springer fiber, X, has a paving by affines resulting from

the intersection of Schubert cells with X. Our description of the elements of Xallow

us to understand these affine spaces and write down explicit dimension formulae. We

also explore some closure relations between the affine spaces and begin to describe the

moment map for the both the regular and extended torus action.

Algebraicity Of Rational Hodge Isometries Of K3 Surfaces, 2016 University of Massachusetts Amherst

#### Algebraicity Of Rational Hodge Isometries Of K3 Surfaces, Nikolay Buskin

*Doctoral Dissertations May 2014 - current*

Consider any rational Hodge isometry

$\psi:H^2(S_1,\QQ)\rightarrow H^2(S_2,\QQ)$ between any two K\"ahler $K3$

surfaces $S_1$ and $S_2$. We prove that the cohomology class of $\psi$ in $H^{2,2}(S_1\times S_2)$

is a polynomial in Chern classes of coherent analytic sheaves

over $S_1 \times S_2$. Consequently, the cohomology class of $\psi$ is algebraic

whenever $S_1$ and $S_2$ are algebraic.

Skein Theory And Algebraic Geometry For The Two-Variable Kauffman Invariant Of Links, 2016 University of Massachusetts - Amherst

#### Skein Theory And Algebraic Geometry For The Two-Variable Kauffman Invariant Of Links, Thomas Shelly

*Doctoral Dissertations May 2014 - current*

We conjecture a relationship between the Hilbert schemes of points on a singular plane curve and the Kauffman invariant of the link associated to the singularity. Specifcally, we conjecture that the generating function of certain weighted Euler characteristics of the Hilbert schemes is given by a normalized specialization of the difference between the Kauffman and HOMFLY polynomials of the link. We prove the conjecture for torus knots. We also develop some skein theory for computing the Kauffman polynomial of links associated to singular points on plane curves.

Spherical Tropicalization, 2016 University of Massachusetts Amherst

#### Spherical Tropicalization, Anastasios Vogiannou

*Doctoral Dissertations May 2014 - current*

In this thesis, I extend tropicalization of subvarieties of algebraic tori over a trivially valued algebraically closed field to subvarieties of spherical homogeneous spaces. I show the existence of tropical compactifications in a general setting. Given a tropical compactification of a closed subvariety of a spherical homogeneous space, I show that the support of the colored fan of the ambient spherical variety agrees with the tropicalization of the closed subvariety. I provide examples of tropicalization of subvarieties of GL(n), SL(n), and PGL(n).

Quasi-Platonic Psl2(Q)-Actions On Closed Riemann Surfaces, 2015 Rose-Hulman Institute of Technology

#### Quasi-Platonic Psl2(Q)-Actions On Closed Riemann Surfaces, Sean A. Broughton

*Mathematical Sciences Technical Reports (MSTR)*

This paper is the first of two papers whose combined goal is to explore the dessins d'enfant and symmetries of quasi-platonic actions of *PSL _{2}(q)*. A quasi-platonic action of a group

*G*on a closed Riemann

*S*surface is a conformal action for which

*S/G*is a sphere and

*S->S/G*is branched over

*{0, 1,infinity}*. The unit interval in

*S/G*may be lifted to a dessin d'enfant

*D*, an embedded bipartite graph in

*S.*The dessin forms the edges and vertices of a tiling on

*S*by dihedrally symmetric polygons, generalizing the ...

Quasi-Platonic Psl2(Q)-Actions On Closed Riemann Surfaces, 2015 Rose-Hulman Institute of Technology

#### Quasi-Platonic Psl2(Q)-Actions On Closed Riemann Surfaces, Sean Broughton

*S. Allen Broughton*

This paper is the first of two papers whose combined goal is to explore the dessins d'enfant and symmetries of quasi-platonic actions of *PSL _{2}(q)*. A quasi-platonic action of a group

*G*on a closed Riemann

*S*surface is a conformal action for which

*S/G*is a sphere and

*S->S/G*is branched over

*{0, 1,infinity}*. The unit interval in

*S/G*may be lifted to a dessin d'enfant

*D*, an embedded bipartite graph in

*S.*The dessin forms the edges and vertices of a tiling on

*S*by dihedrally symmetric polygons, generalizing the ...

Integrability And Regularity Of Rational Functions, 2015 Washington University in St. Louis

#### Integrability And Regularity Of Rational Functions, Greg Knese

*Mathematics Faculty Publications*

Motivated by recent work in the mathematics and engineering literature, we study integrability and non-tangential regularity on the two-torus for rational functions that are holomorphic on the bidisk. One way to study such rational functions is to fix the denominator and look at the ideal of polynomials in the numerator such that the rational function is square integrable. A concrete list of generators is given for this ideal as well as a precise count of the dimension of the subspace of numerators with a specified bound on bidegree. The dimension count is accomplished by constructing a natural pair of commuting ...

Quasi-Platonic Psl(2,Q)-Actions On Closed Riemann Surfaces, 2015 Rose-Hulman Institute of Technology

#### Quasi-Platonic Psl(2,Q)-Actions On Closed Riemann Surfaces, Sean Broughton

*S. Allen Broughton*

*PSL(2,q)*. A quasi-platonic action of a group

*G*on a closed Riemann

*S*surface is a conformal action for which

*S/G*is a sphere and

*S -> S/G*is

*S/G*may be lifted to a dessin d'enfant

*D*, an embedded bipartite graph in

*S*.The dessin forms the edges and vertices of a tiling on

*S*by dihedrally symmetric polygons, generalizing the ...

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 ...

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 ...