Alan Roche

Department of Mathematics
University of Oklahoma
Norman, OK 73019-3103

Office: PHSC 1112
Email: aroche (at) ou (dot) edu

Welcome! The picture is not me: it's Aoibhe, pronounced A V as in the letters. Mine was merely the mortal hand and eye that dared to frame her fearful symmetry.

Aoibhe studies CATegory theory and purr‒obability. My research area is algebra, mainly representation theory. And in representation theory, I've mainly studied representations of p‒adic groups, a subject with close ties to number theory. Recently, however, I've found myself writing semi-expository pieces on more elementary topics. Some are listed below.

Some Recent Notes and Papers

In Preparation

The paper needs some work.


This semester I'm teaching Intro. to Abstract Algebra II (MATH 4333).

Grab Bag

Sam—A Triptych

Sam is Aoibhe's pal. Here are three sides of this sometimes risible, always delightful creature—studious Sam, singing Sam, sitting Sam. My son took the first picture. My daughter took the second. I'm just out of the frame about to hand Sam his dinner: the little guy routinely bursts into song at dinnertime. I took the picture of sitting Sam.


Can you tell we are fond of cats in our family? Too much so? Yes, some tell us. My wife and I once invited a good friend over for dinner. Her response: she would be delighted to come on one condition—no talk about cats!

A favorite poem

The Sunlight on the Garden
The sunlight on the garden Hardens and grows cold, We cannot cage the minute Within its nets of gold, When all is told We cannot beg for pardon. Our freedom as free lances Advances towards its end; The earth compels, upon it Sonnets and birds descend; And soon, my friend, We shall have no time for dances. The sky was good for flying Defying the church bells And every evil iron Siren and what it tells: The earth compels, We are dying, Egypt, dying And not expecting pardon, Hardened in heart anew, But glad to have sat under Thunder and rain with you, And grateful too For sunlight on the garden. Louis MacNiece (1936)