ABHYANKAR 82nd BIRTHDAY CONFERENCE 

SPEAKER: Nick Inglis (Edinburgh)

TITLE: Small polynomials for big groups

ABSTRACT: The title is, of course, an homage to Abhyankar's paper
"Nice polynomials for nice groups", which was near the start of a sequence
of papers in which explicit polynomials were given in non-zero characteristic,
whose Galois groups were (almost) simple groups. These polynomials were small
in the sense that they had few non-zero terms.

We revisit polynomials affording the classical (linear, symplectic,
orthogonal and unitary) groups over finite fields and aim to show, using
tools such as E. H. Moore's generalisation of Fermat's little theorem, and
Abhyankar's mantra, how much of the structure of these big groups is
naturally encoded in these small polynomials.