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