Saul-Schleimer

This is a special topology seminar on Monday, 4th August 2014, in Lecture Room C, James Clerk Maxwell Building, featuring two speakers who
are topologists actively involved both in the theory and practice of the artistic representations of spaces.

The talks are introduced by Michael Atiyah

15.00 Henry Segerman (OSU)
https://www.math.okstate.edu/~segerman/
"Sculpture in four-dimensions"

Abstract - Humans evolved in a three-dimensional environment. As a result we are very good at visualising three-dimensional objects. But what about four-dimensional objects? The best we can do is look at their three-dimensional "shadows".

Just as the shadow of a three-dimensional object squishes it into a two-dimensional plane, we can squish a four-dimensional shape into three-dimensional space. If the four-dimensional object is not too complicated, and if we choose a good way to squish it, then we can get a very good sense of what it is like. We will explore the sphere in four-dimensional space, the four-dimensional polytopes (which are the four-dimensional versions of the three-dimensional polyhedra - the shapes of dice), and various sculptures and puzzles that have come from thinking about these things.

See also:
http://www.segerman.org/
https://www.math.okstate.edu/~segerman/#art_exhibitions
https://www.shapeways.com/shops/henryseg
https://www.youtube.com/user/henryseg
http://www.thingiverse.com/henryseg/designs

16.00 Saul Schleimer (Warwick)
http://homepages.warwick.ac.uk/~masgar/
"Minimal and Seifert surfaces"

Abstract - "Surfaces" are interfaces; boundaries between this and that. The peel of an orange, the crust of a bagel, the skin of a person, the bark of a tree: all are examples of surfaces. These are studied mathematically using the tools of geometry and topology. Important examples arise in geometry in the guise of "minimal surfaces": the soap films pondered by child and professor alike. In topology Seifert surfaces serve as an interface between knots, one-dimensional loops, and knot complements, three-manifolds of startling beauty.

I will describe these objects via many two-dimensional pictures and three-dimensional prints. Most are constructed in the three-sphere and then stereographically projected into our three-dimensional space.