Friday, November 2nd, 4:00pm, Kerchof Hall 317
Speaker: Prof. Peter Abramenko (UVa Department of Mathematics)
Title: Platonic Solids and Their Symmetries

Abstract: In our real world (the 3-dimensional Euclidean space) there exist precisely five types of regular convex polyhedra, namely the tetrahedron, the cube, the octahedron, the dodecahedron and the icosahedron. These regular solids are known since thousands of years, and they have been studied extensively by Greek mathematicians (e.g. Theaetetus, Euclid). They also play a role in the philosophy of Plato who associated four of them with the four classical "elements" earth, air, water and fire - that's where the name "Platonic solids" comes from.

In my talk, I will try to explain what a "regular convex polyhedron" is, and why there are only five of them in Euclidean space. I will then speak about symmetries of these solids which are intuitively easy to understand. However, they also build a bridge to modern mathematics, namely group theory. The ensemble of all symmetries of a Platonic solid is an example of a Coxeter group, and these groups are the subject of ongoing very active and fruitful mathematical research. This provides a fascinating example of the way how our mathematical insight continuously develops and grows - from antiquity to modern days!

The talk will be accessible to all students interested in mathematics. No prior knowledge of group theory is required.