Clayton Shonkwiler (@shonk) header
Clayton Shonkwiler (@shonk) profile picture

Clayton Shonkwiler

@shonk

Math and art. @shonk@mathstodon.xyz

 Fort Collins, CO
shonkwiler.org
Joined August 2007
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Photo by Clayton Shonkwiler (@shonk)Photo by Clayton Shonkwiler (@shonk)Photo by Clayton Shonkwiler (@shonk)Photo by Clayton Shonkwiler (@shonk)Photo by Clayton Shonkwiler (@shonk)Photo by Clayton Shonkwiler (@shonk)Photo by Clayton Shonkwiler (@shonk)Photo by Clayton Shonkwiler (@shonk)Photo by Clayton Shonkwiler (@shonk)Photo by Clayton Shonkwiler (@shonk)
Check out this new video on the Riemann Hypothesis from @QuantaMagazine and @AlexKontorovich: youtu.be/zlm1aajH6gY (I contributed a number of animations)
The Riemann Hypothesis, Explained

The Riemann Hypothesis, Explained

The Riemann Hypothesis is the most notorious unsolved problem in al...

youtube.com
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Modular flow Inspired by @KangarooPhysics and @etiennejcb
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A small, white, square grid interleaved with a larger, black, diamond grid. Produced by plotting the phase of the square of the Weierstrass ℘-function (for the square lattice).

ALT A small, white, square grid interleaved with a larger, black, diamond grid. Produced by plotting the phase of the square of the Weierstrass ℘-function (for the square lattice).

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An image showing blue/red gradients with colors meeting at infinitely many points forming a complicated pattern in the plane.

ALT An image showing blue/red gradients with colors meeting at infinitely many points forming a complicated pattern in the plane.

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Life advice from my (two-year-old) son: “Try be happy. Try be nice. Try not hitting.”
This paper has now been published at JKTR: doi.org/10.1142/S02182165225…

Journal of Knot Theory and Its Ramifications

Knot Theory & Topology | JKTR Dive into knot theory and topology with JKTR. Access top-tier research, submit papers, and stay updated with groundbreaking findings!

worldscientific.com
arXiv math.GT Geometric Topology (@mathGTb) profile picturearXiv math.GT Geometric Topology@mathGTb15 Jun 2022
Clayton Shonkwiler: New Superbridge Index Calculations from Non-Minimal Realizations arxiv.org/abs/2206.06950 arxiv.org/pdf/2206.06950
One of my old GIFs
Wolfram (@WolframResearch) profile pictureWolfram
@WolframResearch19 Sep 2022
A personalized light show from lines on a surface! Check out how to make your own in #WolframLanguage: wolfr.am/17qtz0B0K
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Fusion Frame Homotopy and Tightening Fusion Frames by Gradient Descent, by Tom Needham and Clayton Shonkwiler In which we generalize the Frame Homotopy Theorem and the Benedetto–Fickus theorem to fusion frames. arxiv.org/abs/2208.11045
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New paper: Toric Symplectic Geometry and Full Spark Frames, written with Tom Needham. arxiv.org/abs/2110.11295 (1/7)
Toric Symplectic Geometry and Full Spark Frames

Toric Symplectic Geometry and Full Spark Frames

The collection of $d \times N$ complex matrices with prescribed column norms and prescribed (nonzero) singular values forms a compact algebraic variety, which we refer to as a frame space....

arxiv.org
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The main idea is to show that these spaces are closely related to certain highly structured and extremely symmetric manifolds called toric symplectic manifolds (or toric varieties, if you’re more of an algebraic geometer). (7/7)
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This paper has now been published in Applied & Computational Harmonic Analysis: authors.elsevier.com/a/1fTYT…
Clayton Shonkwiler: New Superbridge Index Calculations from Non-Minimal Realizations arxiv.org/abs/2206.06950 arxiv.org/pdf/2206.06950
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The main product of my sabbatical in Fall 2020 is finally on arXiv: arxiv.org/abs/2205.09049
Random graph embeddings with general edge potentials

Random graph embeddings with general edge potentials

In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes...

arxiv.org
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Hey #mathtwitter, what are some of your favorite books with strong authorial voices? Some examples: @AxlerLinear’s Linear Algebra Done Right, Tristan Needham’s Visual Complex Analysis, and Petkovsek, Wilf, and Zeilberger’s A=B.
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Dustin G. Mixon, Tom Needham, Clayton Shonkwiler, Soledad Villar: Three proofs of the Benedetto-Fickus theorem arxiv.org/abs/2112.02916 arxiv.org/pdf/2112.02916
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Clayton Shonkwiler: All Prime Knots Through 10 Crossings Have Superbridge Index $\leq 5$ arxiv.org/abs/2112.10902 arxiv.org/pdf/2112.10902
All Prime Knots Through 10 Crossings Have Superbridge Index $\leq 5$

All Prime Knots Through 10 Crossings Have Superbridge Index $\leq 5$

This paper gives new upper bounds on the stick numbers of the knots $9_{18}$, $10_{18}$, $10_{58}$, $10_{66}$, $10_{68}$, $10_{80}$, $10_{82}$, $10_{84}$, $10_{93}$, $10_{100}$, and $10_{152}$, as...

arxiv.org
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