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    \href{\myurl}{Dror Bar-Natan}:
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\begin{document}

\noindent{\LARGE\bf Nobody Solves the Quintic Web Site}

\vskip 5mm

There is a truly lovely and relatively easy topological proof of one of the most fundamental results of Galois theory, that there isn't a ``formula'' for solving equations of degree 5 and up. I have given talks to explain that proof (e.g., \url{https://www.math.toronto.edu/~drorbn/Talks/Sydney-1708} and \url{https://www.math.toronto.edu/~drorbn/Talks/CMU-1504/}) and they are on video. But the animations I have used are clunky and need to be modernized. Would you be interested in doing that?

At minimum you will need to re-implement the animations in my talks so as to run stably within a web browser. Even better if you will be able to add and improve, perhaps making it into a full web site explaining and exploring the proof.

\vskip 2mm\noindent{\bf Requirements.} You must learn and feel fully comfortable with the proof and you must care for presentation. You must feel comfortable with graphics programming.

\vskip 2mm\noindent{\bf Warning.} There is a fair chance that I will be away for a good portion of the summer, or possibly even for all of it. So much of our communications will have to occur over zoom.

\vskip 2mm\noindent\noindent{\bf Posted} on November 4, 2024.

\vskip 2mm\noindent\noindent{\bf Status.} Not assigned. If you are interested, see \href{https://www.mathematics.utoronto.ca/undergraduate/current-students/summer-research-awards-undergraduates}{Summer Research Awards for Undergraduates} on the math department web site.

\eject

\noindent{\LARGE\bf Drawing Large Knots and Seifert Surfaces}

\vskip 5mm

The software I currently have for drawing large knots wastes a lot of real estate (e.g., \url{https://drorbn.net/AcademicPensieve/Talks/UBC-241004/DK300SnapPyDiagram.pdf}). It ought to be possible to do better! Would you try? As for \href{https://en.wikipedia.org/wiki/Seifert_surface}{Seifert surfaces}, I don't even have a general program (though see some \href{https://drorbn.net/AcademicPensieve/Classes/23-FastComputations/Day1Gallery/SeifertSurfaces.png}{pictures} and an \href{https://drorbn.net/AcademicPensieve/Talks/CMS-2112/index.html?im=SeifertByRedelmeier.jpg}{illustration}). Would you fix that?

\vskip 2mm\noindent{\bf Requirements.} You must care for aesthetics and have ideas how to make it better. You must feel comfortable with graphics programming in Mathematica.

\vskip 2mm\noindent{\bf Warning.} There is a fair chance that I will be away for a good portion of the summer, or possibly even for all of it. So much of our communications will have to occur over zoom.

\vskip 2mm\noindent\noindent{\bf Posted} on November 4, 2024.

\vskip 2mm\noindent\noindent{\bf Status.} Not assigned. If you are interested, see \href{https://www.mathematics.utoronto.ca/undergraduate/current-students/summer-research-awards-undergraduates}{Summer Research Awards for Undergraduates} on the math department web site.

\eject

\noindent{\LARGE\bf Knot Families and their $\theta$ Invariant}

\vskip 5mm

The primary purpose of this project will be to code as many ``families'' of knots as you can identify in a way that will be clean and useful for others. A secondary purpose will be to compute the $\theta$ invariant of many knots in these families, in the hope of finding patterns and making conjectures. you may want to listen to my talk at \url{http://drorbn.net/to24} to see what $\theta$ is about.

Examples of families: torus knots, pretzel knots, twisted torus knots \arXiv{2411.13003}, \ldots

\vskip 2mm\noindent{\bf Requirements.} You must be excellent at combinatorial programming in Mathematica.

\vskip 2mm\noindent{\bf Warning.} There is a fair chance that I will be away for a good portion of the summer, or possibly even for all of it. So much of our communications will have to occur over zoom.

\vskip 2mm\noindent\noindent{\bf Posted} on November 4, 2024.

\vskip 2mm\noindent\noindent{\bf Status.} Not assigned. If you are interested, see \href{https://www.mathematics.utoronto.ca/undergraduate/current-students/summer-research-awards-undergraduates}{Summer Research Awards for Undergraduates} on the math department web site.

\end{document}
