Grant Barkley Title: Coxeter Groups and the Lattice of Total Orders Abstract: A Coxeter group is a group generated by elements of order 2, called reflections, along with certain relations between the elements. The group of permutations on n elements (generated by swapping 1 and 2, 2 and 3, etc.) is an important…
Imagine tying up your shoelaces into a knot. How can we measure the difficulty of unknotting this mess? In this talk, we will study mathematical knots and various measurements of their complexity with a view towards efficient unknotting. This talk should be accessible to all undergraduates.
The 21st century has seen a boom in the production of data as well as methods to analyze data. One such methodology is Topological data analysis (TDA), where concepts from topology are used to infer the patterns underlying data sets. I will provide a basic and accessible introduction to persistent homology, a common type of TDA that is…