Junior Colloquium Department of Mathematics 1

Knots are obtained by embedding a circle in R. Pictures and handicrafts of knots have appeared in ancient Chinese art several hundred years B.C. The first systematic study of knots though started in the 19th century by a Scottish physicist Peter Guthrie Tait who classified all knots to 10 crossings and made several important conjectures about knots (the most recent of these conjectures is proven in 1991). In my talk, I will recall some elementary notions of knots (such as prime knots, torus knots, fibered knots, pretzel knots, alternating knots, satellite knots, etc.). Nowadays, knots are interesting objects not just to mathematicians, but also to physicists, biologists, chemists, etc. In my talk, I will recall some elementary notions of knots (such as prime knots, torus knots, fibered knots, pretzel knots, alternating knots, satellite knots, etc.). Many, many examples and pictures will be provided. I’ll also briefly mention several well known knot invariants, but concentrate mostly on computing the Alexander polynomial of knots. Speaker: Liz Sattler Title: Hausdorff dimension of sub-fractals associated with sub-shifts Date: February 26 Abstract: Many fractals can be defined by an iteration function system (IFS) consisting of finitely many maps. We can associate a letter to each map and use a symbolic space to describe the fractal. One way to define a sub-fracta is to relate the IFS to a sub-shift of finite type (SFT) on the symbolic space. In this talk, we will formally describe the connection between such sub-fractals and SFTs. We will also discuss some techniques for calculating the Hausdorff dimension of these sets. Many fractals can be defined by an iteration function system (IFS) consisting of finitely many maps. We can associate a letter to each map and use a symbolic space to describe the fractal. One way to define a sub-fracta is to relate the IFS to a sub-shift of finite type (SFT) on the symbolic space. In this talk, we will formally describe the connection between such sub-fractals and SFTs. We will also discuss some techniques for calculating the Hausdorff dimension of these sets.