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Now showing items 1-10 of 13

#### Maxwell-Bloch and nonlinear Schrodinger systems with nonzero background

(State University of New York at Buffalo, 2018)

This thesis is concerned with the study of two main types of nonlinear evolution equations of physical significance: (i) Maxwell-Bloch (MB) systems and (ii) nonlinear Schr\"{o}dinger (NLS) type.

#### Specht Modules of Trivial Source and the Endomorphism Ring of the Lie Module

(State University of New York at Buffalo, 2018)

The source of a Specht module is not generally known, unless it is a projective or irreducible module and in this case the source is trivial. Are these the only Specht modules with trivial source? To address this question, ...

#### Integrating Network Science and Computational Topology with Applications in Neuroscience Data Analytics

(State University of New York at Buffalo, 2018)

Real world systems are complex, dynamic and exist across multiple scales. Recent revolutions in data collection and storage have provided researchers with unprecedented access to information about these systems in greater ...

#### Beyond Hyperbolicity; GeneralizingClassical Results from Hyperbolic groupsto all Finitely Generated Groups

(State University of New York at Buffalo, 2019)

Let $X$ be a proper geodesic metric space. We give a new construction of the Morse Boundary that realizes its points as equivalence classes of functions on $X$ which behave similar to the ``distance to a point" function. ...

#### Detecting Mapping Spaces and Spaces with Complexity One

(State University of New York at Buffalo, 2019)

In this thesis we will prove two main results regarding a space A following from information about mapping spaces out of a space A. We show if A is a finite CW-complex such that algebraic theories detect mapping spaces out ...

#### Exponential Sums and Ramification Data of Artin-Schreier-Witt Extensions

(State University of New York at Buffalo, 2019)

This thesis contains two parts:In part 1, we introduce and develop T-adic Dwork theory for L-functions of exponential sums associated to one-variable rational functions, interpolating p-power order exponential sums over ...

#### On the Induced Module of the symmetric group from the Gelfand-Zetlin subalgebra

(State University of New York at Buffalo, 2018)

In my dissertation, the induced modules $\Ind[\alpha]$ are studied. For a weight $[\alpha]\in \F^n$, $\Ind[\alpha]$ is defined to be an $\F\S_n$-module, that is induced from a module $I[\alpha]$, over the Gelfand-Zetlin ...

#### The Second Moment of Hecke-Maass forms for SL(3,Z)

(State University of New York at Buffalo, 2018)

The motivation of this thesis comes from Quantum Unique Ergodicity (QUE) conjecture. Our goal is to investigate QUE conjecture for a rank 2 group.

#### Connected-sum decompositions of surfaces with minimally-intersecting filling pairs

(State University of New York at Buffalo, 2018)

Let Sg be a closed surface of genus g and let (α, β) be a filling pair on Sg; then i(α, β) ≥ 2g−1, where i is the (geometric) intersection number. Aougab and Huang demonstrated that (exponentially many) minimally-intersecting ...

#### Permutation Equivalence of Quartic 2-Rotation Symmetric Boolean Functions

(State University of New York at Buffalo, 2018)

A Boolean function is considered to be rotation symmetric if it is invariant under cyclic rotation, ρ, of the input variables, and is considered to be 2-rotation symmetric if it is invariant under ρ2. A 2−rotation symmetric ...