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Filtering by: Academic Affiliation Mathematics Remove constraint Academic Affiliation: Mathematics Committee Member Guo, Ren Remove constraint Committee Member: Guo, Ren License All rights reserved Remove constraint License: All rights reserved

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Arithmetic dynamical questions with local rationality conditions

Creator:

Noytaptim, Chatchai

Abstract:

We introduce a numerical criterion which allows us to bound the degree of any algebraic integer having all of Galois conjugates in an interval of length less than 4. Using this criterion, we study two arithmetic dynamical questions with local rationality conditions. First, we classify all unicritical polynomials defined over...

Resource Type:

Dissertation
One-Parameter Deformations of the Bowen-Series Map Associated to Cocompact Triangle Groups

Creator:

Yiltekin-Karatas, Ayse

Abstract:

In 1979, for each signature for Fuchsian groups of the first kind, Bowen and Series constructed an explicit fundamental domain for one group of the signature, and from this a function on the unit circle tightly associated with this group. In general, their fundamental domain enjoys what has since been...

Resource Type:

Dissertation
Zeros of Replicable Functions

Creator:

Toomey, Benjamin J.

Abstract:

Following the work of Asai, Kaneko, and Ninomiya for Faber polynomials associated to the modular group, and Bannai, Kojima, and Miezaki's partial proof for the case of the Fricke group of level 2, we show that the zeros of certain modular functions for some low-level genus zero groups associated to...

Resource Type:

Dissertation
Explicit Dynamical Systems on the Sierpiński Curve

Creator:

Homsomboon, Worapan

Resource Type:

Dissertation
On the Logical Independence of (DR) and (CLA)

Creator:

Birnbaum. Dionysus A.

Abstract:

In 1941, J.H.C. Whitehead posed the question of whether asphericity is a hereditary property for 2-dimensional CW complexes. This question remains unanswered, but has led to the development of several algebraic and topological properties that are sufficient (but not necessary) for the asphericity of presentation 2-complexes. While many of the...

Resource Type:

Dissertation
A Computational Method for Building Spherical Pictures and Theoretic Results from Explicit Constructions

Creator:

Merzenich, Matthias C.

Abstract:

Let H be a cyclically-presented group on n generators with a single defining relator. Attempts have been made to classify such groups by their order, their status as a 3-manifold group, and the asphericity status of their presentations. For groups with a defining relator of length 3 these classifications are...

Resource Type:

Dissertation
On the Structure of the Orbit Spaces of Almost Torus Manifolds with Non-negative Curvature

Creator:

Dong, Zheting

Abstract:

An almost torus manifold $M$ is a closed $(2n+1)$-dimensional orientable Riemannian manifold with an effective, isometric $n$-torus action such that the fixed point set $M^T$ is non-empty. Almost torus manifolds are analogues of torus manifolds in odd dimension and share many of the characteristics of torus manifolds. For example, both...

Resource Type:

Dissertation
Zeros of Certain Combinations of Products of Eisenstein Series

Creator:

Klangwang, Jetjaroen

Abstract:

In this dissertation, we begin by presenting the result of F. K. C. Rankin and Swinnerton-Dyer on the location of the zeros of the Eisenstein series for the full modular group in the standard fundamental domain. Their simple but beautiful argument shows that all zeros are located on the lower...

Resource Type:

Dissertation
Shift dynamics for cyclically presented groups with length four positive relators

Creator:

Parker, Forrest W.

Abstract:

In 2014, W. Bogley identified a relation between the algebraic and geometric prop- erties of cyclically presented groups Gn (w) in the case where w = x0xkxl is a positive word of length three. Specifically, it was shown that the dynamics of the shift θG on the group G =...

Resource Type:

Dissertation
Topological and Dynamical Properties of Cyclically Presented Groups

Creator:

McDermott, Kirk M.

Abstract:

This dissertation investigates the structure and topological properties of cyclicallypresented groups. First, a family of groups called groups of type Z is considered. Withfew exceptions, the finiteness, asphericity, fixed point, and 3-manifold spine problemsare solved. Most groups of type Z have a central element of infinite order fixed by theshift....

Resource Type:

Dissertation

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Academic Affiliation

Mathematics[remove]12

Advisor

Bogley, William A.4
Schmidt, Thomas A.3
Escher, Christine1
Petsche, Clayton1
Searle, Catherine1
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Commencement Year

Commencement Year range begin – Commencement Year range end

Current results range from 2015 to 2023

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Committee Member

Guo, Ren[remove]12
Petsche, Clayton6
Escher, Christine3
Schmidt, Tom2
Aaron, Wendy Rose1
more Committee Members »

Creator

Birnbaum. Dionysus A.1
Chunikhina, Evgenia V.1
Dong, Zheting1
Edwards, Brandon1
Homsomboon, Worapan1
more Creators »

Date

Date range begin – Date range end

Current results range from 2014 to 2023

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Decade

2020-20296
2010-20196

Degree Field

Mathematics12

Degree Level

Doctoral11
Master's1

Degree Name

Doctor of Philosophy (Ph.D.)11
Master of Science (M.S.)1

Language

English [eng]12

License

All rights reserved[remove]12

Non-Academic Affiliation

Oregon State University. Graduate School4

Peer Reviewed

No12

Resource Type

Dissertation11
Masters Thesis1

Rights Statement

In Copyright12

Subject

Automorphic forms1
Combinatorial group theory1
Derivative securities -- Econometric models1
Discrete-time systems1
Elliptic functions1
more Subjects »

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