Project Exploration of Groups using Topology Program Purdue Experimental Mathematics Lab Term Spring 2026 Status Accepted Research Area Mathematics Description Groups encode the symmetry of spaces. The goal of this project is to explore the notion of generalized torsion in certain explicit groups using topological ideas (surfaces built out of polygons). As part of the exploration, we may develop and implement algorithms to do computations and computer experiments. Depending on the progress and interest, we may explore other related group theoretic notions or invariants. Supervisor Thomas J Sinclair Mentor Type of work required 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. Websites https://www.math.purdue.edu/pxml/join-pxml.html Qualifications Knowledge of Group Theory or Topology (MA571). Knowing some programming language like Python would be helpful. Credit Hours 3 Weekly Hours 10 (estimated)