College of Science and Health > Academics > Mathematical Sciences > Research > 2022 NREUP

2022 Research Experience for Undergraduates

In Summer 2022, four DePaul University undergraduates will spend 8 weeks engaging in full-time mathematical research, thanks to funding from the Mathematical Association America's (MAA) National Research Experience for Undergraduates Program (NREUP).

The NREUP supports the participation of mathematics undergraduates from historically underrepresented groups, through focused and challenging research experiences, to increase their interest in advanced degrees and careers in mathematics. The 2022 NREUP at DePaul University is being run by Department of Mathematical Sciences faulty Karl Liechty and Emily Barnard.

The 2022 NREUP at DePaul University will focus on the relatively new field of  dynamical algebraic combinatorics. Broadly speaking, problems in dynamical algebraic combinatorics investigate enumerative questions about the orbit of a combinatorially defined map on some algebraic object. We will focus on two key maps on the symmetric group: the pop-stack sorting map and the kappa map. A typical question is: For an invertible map, is the average of "size" of each orbit the same? Our students will build on existing results about the behavior of these maps for the set of all permutations and for permutations which are 312-avoiding to study the maps on other pattern-avoiding permutations. Students will leave with a toolbox for exploring research questions in a variety of interconnected mathematical fields, including dynamical systems, extremal, algebraic and geometric combinatorics, and possibly topology and representation theory.