Explanipedia

Application of Strain Functionals for Physics Informed Machine Learning Open

Edward M. Kober, Avanish Mishra, Colin Adams, Nithin Mathew · 2024

Hyperbolicity of Alternating Links in Thickened Surfaces with Boundary Open

Colin Adams, Joye Chen · 2023

Let $F$ be a compact orientable surface with nonempty boundary other than a disk. Let $L$ be a link in $F \times I$ with a connected weakly prime cellular alternating projection to $F$. We provide simple conditions that determine exactly w…

VERITAS follow-up observation of the BL Lac blazar B2 1811+31 2020 Flare Open

Pablo Drake, Colin Adams · 2023

VERITAS is an imaging atmospheric Cherenkov telescope (IACT) array most sensitive to gamma rays in the very-high-energy (VHE) energy band (85 GeV - 50 TeV). As a part of its active galactic nuclei (AGN) program, VERITAS focuses on the iden…

Modifications preserving hyperbolicity of link complements Open

Colin Adams, William H. Meeks, Álvaro Ramos · 2023

Given a link in a 3-manifold such that the complement is hyperbolic, we provide two modifications to the link, called the chain move and the switch move, that preserve hyperbolicity of the complement, with only a relatively small number of…

Virtual multicrossings and petal diagrams for virtual knots and links Open

Colin Adams, Chaim Even‐Zohar, Jonah Greenberg, Reuben Kaufman, David Lee , et al. · 2023

Multicrossings, which have previously been defined for classical knots and links, are extended to virtual knots and links. In particular, petal diagrams are shown to exist for all virtual knots.

Search for Axion-Like Particles with Observations of the Blazar Markarian 421 with VERITAS and Fermi-LAT Open

Colin Adams · 2023

Axion-like particles (ALPs) are light, pseudoscalar particles that are a beyond-the-standard-model generalization of the axion. Consequently, they are expected to couple to photons in external magnetic fields to compensate for spin differe…

Composition Properties of Hyperbolic Links in Handlebodies Open

Colin Adams, Daniel Santiago · 2023

We consider knots and links in handlebodies that have hyperbolic complements and operations akin to composition. Cutting the complements of two such open along separating twice-punctured disks such that each of the four resulting handlebod…

VERITAS Discovery of Very High Energy Gamma-Ray Emission from S3 1227+25 and Multiwavelength Observations Open

A. Acharyya, Colin Adams, A. Archer, P. Bangale, W. Benbow , et al. · 2023

We report the detection of very high energy gamma-ray emission from the blazar S3 1227+25 (VER J1230+253) with the Very Energetic Radiation Imaging Telescope Array System (VERITAS). VERITAS observations of the source were triggered by the …

Hyperbolic Knotoids Open

Colin Adams, Alexandra Bonat, Maya Chande, Joye Chen, Maxwell Jiang , et al. · 2022

In 2010, Turaev introduced knotoids as a variation on knots that replaces the embedding of a circle with the embedding of a closed interval with two endpoints. A variety of knot invariants have been extended to knotoids. Here we provide de…

Generalizations of Knotoids and Spatial Graphs Open

Colin Adams, Alexandra Bonat, Maya Chande, Joye Chen, Maxwell Jiang , et al. · 2022

In 2010, Turaev introduced knotoids as a variation on knots that replaces the embedding of a circle with the embedding of a closed interval with two endpoints which here we call poles. We define generalized knotoids to allow arbitrarily ma…

Turaev hyperbolicity of classical and virtual knots Open

Colin Adams, Or Eisenberg, Jonah Greenberg, Kabir Kapoor, Zhen Liang , et al. · 2021

By work of W. Thurston, knots and links in the 3-sphere are known to either be torus links, or to contain an essential torus in their complement, or to be hyperbolic, in which case a unique hyperbolic volume can be calculated for their com…

Lower Bounds on Volumes of Hyperbolic 3-Manifolds via Decomposition Open

Colin Adams, Michele Capovilla-Searle, Darin Li, Qiao Li, Jacob McErlean , et al. · 2021

In a variety of settings we provide a method for decomposing a 3-manifold $M$ into pieces. When the pieces have the appropriate type of hyperbolicity, then the manifold $M$ is hyperbolic and its volume is bounded below by the sum of the ap…

TG-Hyperbolicity of Composition of Virtual Knots Open

Colin Adams, Alexander Simons · 2021

The composition of any two nontrivial classical knots is a satellite knot, and thus, by work of Thurston, is not hyperbolic. In this paper, we explore the composition of virtual knots, which are an extension of classical knots that general…

Generalized Augmented Cellular Alternating Links in Thickened Surfaces are Hyperbolic Open

Colin Adams, Michele Capovilla-Searle, Darin Li, Qiao Li, Jacob McErlean , et al. · 2021

Menasco proved that nontrivial links in the 3-sphere with connected prime alternating non-2-braid projections are hyperbolic. This was further extended to augmented alternating links wherein non-isotopic trivial components bounding disks p…

Superbridge and bridge indices for knots Open

Colin Adams, Nikhil Agarwal, Rachel M. Allen, Tirasan Khandhawit, Alex Simons , et al. · 2021

We improve the upper bound on superbridge index [Formula: see text] in terms of bridge index [Formula: see text] from [Formula: see text] to [Formula: see text].

The Rest of the Tilings of the Sphere by Regular Polygons Open

Colin Adams, Cameron Edgar, Peter Hollander, Liza Jacoby · 2021

We determine all non-edge-to-edge tilings of the sphere by regular spherical polygons of three or more sides.

Totally umbilic surfaces in hyperbolic 3-manifolds of finite volume Open

Colin Adams, William H. Meeks, Álvaro Ramos · 2020

We construct for every connected surface $S$ of finite negative Euler characteristic and every $H \in [0,1)$, a hyperbolic 3-manifold $N(S,H)$ of finite volume and a proper, two-sided, totally umbilic embedding $f\colon S\to N(S,H)$ with m…

Modifications Preserving Hyperbolicity of Link Complements Open

Colin Adams, William H. Meeks, Álvaro Ramos · 2020

Given a link in a 3-manifold such that the complement is hyperbolic, we provide two modifications to the link, called the chain move and the switch move, that preserve hyperbolicity of the complement, with only a relatively small number of…

Knot theory for proteins: Gauss codes, quandles and bondles Open

Colin Adams, Judah Devadoss, Mohamed Elhamdadi, Alireza Mashaghi · 2020

Bipyramid decompositions of multicrossing link complements Open

Colin Adams, Gregory Kehne · 2020

Generalizing previous constructions, we present a dual pair of decompositions of the complement of a link L into bipyramids, given any multi-crossing projection of L. When L is hyperbolic, this gives new upper bounds on the volume of L giv…

Generalized bipyramids and hyperbolic volumes of alternating k-uniform tiling links Open

Colin Adams, Aaron J. Calderon, Nathaniel Mayer · 2019

Triple-crossing number and moves on triple-crossing link diagrams Open

Colin Adams, Jim Hoste, Martin Palmer · 2019

Every link in the 3-sphere has a projection to the plane where the only singularities are pairwise transverse triple points. The associated diagram, with height information at each triple point, is a triple-crossing diagram of the link. We…

TG-Hyperbolicity of Virtual Links Open

Colin Adams, Or Eisenberg, Jonah Greenberg, Kabir Kapoor, Zhen Liang , et al. · 2019

We extend the theory of hyperbolicity of links in the 3-sphere to tg-hyperbolicity of virtual links, using the fact that the theory of virtual links can be translated into the theory of links living in closed orientable thickened surfaces.…

Hyperbolicity of links in thickened surfaces Open

Colin Adams, Carlos Albors-Riera, Beatrix Haddock, Zhiqi Li, Daishiro Nishida , et al. · 2019

2018 T Division Lightning Talks Open

Marilyn Ramsey, Colin Adams, L. Adams, Lewis Baker, Siddharth Bhela , et al. · 2018

Densities of hyperbolic cusp invariants of knots and links Open

Colin Adams, Rose Kaplan-Kelly, Michael H. Moore, Brandon Shapiro, Shruthi Sridhar , et al. · 2018

We find that cusp densities of hyperbolic knots in include a dense subset of and those of links are a dense subset of . We define a new invariant associated with cusp volume, the cusp crossing density, as the ratio between the cusp volum…

2017 T Division Lightning Talks Open

Marilyn Ramsey, Jayalath Abeywardhana, Colin Adams, Luke Adams, Austin Carter , et al. · 2017

All members of the T Division Community, students, staff members, group leaders, division management, and other interested individuals are invited to come and support the following student(s) as they present their Lightning Talks.

Generalized bipyramids and hyperbolic volumes of alternating $k$-uniform\n tiling links Open

Colin Adams, Aaron J. Calderon, Nathaniel Mayer · 2017

We present explicit geometric decompositions of the hyperbolic complements of\nalternating $k$-uniform tiling links, which are alternating links whose\nprojection graphs are $k$-uniform tilings of $S^2$, $\\mathbb{E}^2$, or\n$\\mathbb{H}^2…

Bipyramids and bounds on volumes of hyperbolic links Open

Colin Adams · 2017

Waist size for cusps in hyperbolic 3-manifolds II Open

Colin Adams · 2017

The waist size of a cusp in an orientable hyperbolic 3-manifold is the length of the shortest nontrivial curve generated by a parabolic isometry in the maximal cusp boundary. Previously, it was shown that the smallest possible waist size, …

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