Open Access. Powered by Scholars. Published by Universities.®

Geometry and Topology Commons™

Open Access. Powered by Scholars. Published by Universities.®

2022

Discipline
Institution
Keyword
Publication
Publication Type
File Type

Articles 61 - 64 of 64

Full-Text Articles in Geometry and Topology

Bft2: A General Class Of 2d N = (0, 2) Theories, 3-Manifolds And Toric Geometry, Sebastían Franco, Xingyang Yu Jan 2022

Bft2: A General Class Of 2d N = (0, 2) Theories, 3-Manifolds And Toric Geometry, Sebastían Franco, Xingyang Yu

Publications and Research

We introduce and initiate the study of a general class of 2d N = (0, 2) quiver gauge theories, defined in terms of certain 2-dimensional CW complexes on oriented 3- manifolds. We refer to this class of theories as BFT2’s. They are natural generalizations of Brane Brick Models, which capture the gauge theories on D1-branes probing toric Calabi-Yau 4-folds. The dynamics and triality of the gauge theories translate into simple transformations of the underlying CW complexes. We introduce various combinatorial tools for analyzing these theories and investigate their connections to toric Calabi-Yau manifolds, which arise as their …

Go to article

2d N = (0, 1) Gauge Theories And Spin(7) Orientifolds, Sebastían Franco, Alessandro Mininno, Ángel M. Uranga, Xingyang Yu Jan 2022

2d N = (0, 1) Gauge Theories And Spin(7) Orientifolds, Sebastían Franco, Alessandro Mininno, Ángel M. Uranga, Xingyang Yu

Publications and Research

We initiate the geometric engineering of 2d N = (0, 1) gauge theories on D1-branes probing singularities. To do so, we introduce a new class of backgrounds obtained as quotients of Calabi-Yau 4-folds by a combination of an anti-holomorphic involution leading to a Spin(7) cone and worldsheet parity. We refer to such constructions as Spin(7) orientifolds. Spin(7) orientifolds explicitly realize the perspective on 2d N = (0, 1) theories as real slices of N = (0, 2) ones. Remarkably, this projection is geometrically realized as Joyce’s construction of Spin(7) manifolds via quotients of Calabi-Yau 4-folds by antiholomorphic …

Go to article

Stroke Clustering And Fitting In Vector Art, Khandokar Shakib Jan 2022

Stroke Clustering And Fitting In Vector Art, Khandokar Shakib

Senior Independent Study Theses

Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.

Go to article

The Kepler Problem On Complex And Pseudo-Riemannian Manifolds, Michael R. Astwood Jan 2022

The Kepler Problem On Complex And Pseudo-Riemannian Manifolds, Michael R. Astwood

Theses and Dissertations (Comprehensive)

The motion of objects in the sky has captured the attention of scientists and mathematicians since classical times. The problem of determining their motion has been dubbed the Kepler problem, and has since been generalized into an abstract problem of dynamical systems. In particular, the question of whether a classical system produces closed and bounded orbits is of importance even to modern mathematical physics, since these systems can often be analysed by hand. The aforementioned question was originally studied by Bertrand in the context of celestial mechanics, and is therefore referred to as the Bertrand problem. We investigate the qualitative …

Go to article

First Prev