Research
General Information
Each project will consist of a small research team consisting of typically 2-4 undergraduates, a graduate mentor, and a faculty mentor. The graduate mentor and undergraduates will meet on a weekly basis, with full team meetings every few weeks as determined by the faculty mentor.
Undergraduates who have been accepted into a project must sign up for the 3-credit "Purdue Experimental Math Lab" course (currently listed under MA 490) and must pledge that they are able to dedicate 10 hours of effort per week to the project. For information on how to apply, click on the tab 'Join PXML' at the top of the screen.
Fall 2026 Projects
Understanding Transfer Maps for Finite Groups
Faculty Mentor: Prof. Daniel Johnstone
Level: Advanced
Skills required: Completion of proof-based courses in real analysis, linear algebra, and abstract algebra. Completion or taking concurrently with at least one of MA 42800 or MA 45401 recommended.
Description: The Fourier Transform is an operation central to many areas of mathematics, both pure and applied, and understanding the Fourier Transform on a space of interest requires an understanding of its “dual group” (the homomorphisms from it to the complex numbers of unit norm). Given two (abelian) groups H and G, a natural identification (group homomorphism) of the dual group of H to a subset of the dual group of G gives rise to a corresponding transfer map of functions on G to functions on H. Many well-known operations on functions can be interpreted as transfer maps, notably but not limited to the convolution product of functions.
This project aims to better understand transfer maps in the comparatively accessible case of finite groups. After spending some time discussing pertinent preliminaries, the project will aim to explicitly compute and qualitatively interpret a number of transfer maps of particular interest. Eventually, after considering a number of simpler warm-up examples, the goal will be to understand fully a non-abelian analogue of convolution on the group of 2 by 2 invertible matrices over a finite field.
This is an ambitious project for undergraduates which is likely to continue into the spring semester and beyond.
Some Counting Sequences
Faculty Mentor: Prof. Irena Swanson
Level: Intermediate
Skills required: Completion of at least one proof-based mathematics course. Programming experience is preferable.
Description: We would modify an interesting and well-studied sequence to a different and not previously studied context. Preliminary work shows some strong patterns in the new sequence. The goals including proving any true patterns, possibly in multiple ways, and describing possible but false patterns. Any true patterns may be postable in the Online Encyclopedia of Integer Sequences (https://oeis.org/).