We all tackle hard problems everyday, like finding a parking spot in the Dan Allen Deck. However, there are special types of problems which are hard even for a computer to solve. Reductions, conversions of one problem into another, play a critical role in determining the hardness of these computational problems, and lead to philosophical questions…

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…

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.