Abstract: Much of the research process in pure mathematics is invisible and mysterious, involving experimentation and partial results which do not appear in published papers.  The goal of this talk is to demystify the research process in the context of the following algebraic problem:  Given a pair of normal matrices with prescribed eigenvalues, what can the determinant of their sum be?  Marcus (1972) and de Oliveira (1982) independently conjectured bounds on this determinantal set within the complex plane.  We outline the steps we took to obtain a stronger statement which gives a complete geometric description of this set as a flattened twisted permutahedron.  

 

This is joint work with Luke Oeding.