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  \vfill
  \Large Knots in Three and Four Dimensions
  \vfill
  \par\normalsize Dror Bar-Natan, \url{http://drorbn.net/syr21} (see ``handout''!)
  \vfill
  \par\large Syracuse by Web, April 2021
  \end{center}

  \vfill\normalsize
  {\bf Abstract.} Much as we can understand 3-dimensional objects by staring
at their pictures and x-ray images and slices in 2\nobreak-dimensions, so can we
understand 4-dimensional objects by staring at their pictures and x-ray
images and slices in 3-dimensions, capitalizing on the fact that we
understand 3-dimensions pretty well. So we will spend some time staring at
and understanding various 2-dimensional views of a 3-dimensional elephant,
and then even more simply, various 2-dimensional views of some
3-dimensional knots. This achieved, we'll take the leap and visualize some
4-dimensional knots by their various traces in 3-dimensional space, and
if we'll still have time, we'll prove that these knots are really knotted.
\end{frame}

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\begin{frame}
Thanks for inviting me to Syracuse! As most of you have never seen it, here's a picture of the lecture
room:
\[ \includegraphics[width=0.85\linewidth]{../MoscowByWeb-2104/LectureRoom.jpg} \]
\vfill If you can, please turn your video on! (And mic, whenever needed).
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