Sorry to be  so long in responding;  things have been  rather hectic.
However this note may give you a bit more information about the areas
which  interest me  and  which have  some  mathematically interesting
properties. ( I am also involved in machine architecture, interactive
programming and computing  systems -- design and  implementation, but
these areas are more technological than mathematically substantial)

Basically,  the  application  of  mathematical  logic   to  computing
problems is a good cover  name for my interest. For  example, precise
specification  of  programming  languages,  explication  of computing
ideas in terms of abstract mathematical ideas, development of methods
for proving correctness and/or equivalence or algorithms, development
of  formalisms to  support program  synthesis; these  are interesting
areas.

The  basis  for   research are  founded  on  mathematical  logic; for
example Mendelson's book  (logic); Hartley Rogers  Recursive Function
Theory;  Kleene,  introduction  to  metamathematics  (old,  but still
valuable); Manna,  Mathematical theory of  computation, is  a  recent
work relating logic to computer science; a deeper book is Stoy's book
from MIT  press on Mathematical  semantics of  programming languages.
When  I was  a  UCLA they  had  a very  resptable  mathematical logic
program; they should be able to refer you to other sources.

Several  people  have  examines  semantic  issues  for  the algebraic
viewpoint.   In particular  there is  a person  at the  UCLA computer
science  department,  J.A.  Goguen who  is active  in the  field. You
might examine some of  his papers to see  if they are of  interest to
you. There is a recent  article co-authored by him in the  Journal of
the ACM; (recent = last two years), titles "Initial Algebra Semantics
and continuous  algebras" (sorry  I don't  know the  exact publishing
date)

The  more  general  background  about  the  structure  of programming
languages can  be found  in my book  (blush); alas  not much  else is
available outside of  research reports. Read  some of the  material I
suggest  above;  if the  general  area  appeals to  you  I  (or Peter
Schorer) can xerox some of these reports.

If you  would like to talk with someone at UCLA, I would suggest Dave
Martin in the computer science  department. I always found him  to be
an open, receptive person. His interests and inclinations are similar
to those outlined by me.

I  will  continue to  think  about  other areas  which  might  be  of
interest, but the references above will give you a place to start.

                                        Sincerely,



                                        John Allen