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Dror Bar-Natan:
Talks:
# The 17 Worlds of Planar Ants

#### Online, by invitation only.

**Abstract.** My goal is to get you hooked, captured and unreleased until you find
all 17 in real life, around you.

We all know that the plane can be filled in different periodic manners: floor tiles are
often square but sometimes hexagonal, bricks are often laid in an interlaced pattern,
fabrics often carry interesting patterns. A little less known is that there are precisely
17 symmetry patterns for tiling the plane; not one more, not one less. It is even less
known how easy these 17 are to identify in the patterns around you, how fun it is, how
common some are, and how rare some others seem to be.

Gotta Catch 'Em All!

**Handout:** 17Worlds.pdf

**Annotated Slides:** 17Worlds@.pdf

**Pensieve**.

**URL:** http://drorbn.net/mc21.

**Upload link:** http://drorbn.net/mc21/upload.

# Knots in Three and Four Dimensions

#### Online, by invitation only.

**Abstract.** Much as we can understand 3-dimensional objects by staring at their
pictures and x-ray images and slices in 2-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.

**Slides:** K34-Slides.pdf

**Annotated Slides:** K34-Slides@.pdf

**Pensieve**.

**URL:** http://drorbn.net/mc21.