
Giles Auchmuty
Professor
of Mathematics
 University
of Houston
Office
Location:
PGH 696
Telephone:
(713) 7433475
Fax:
(713) 7433505
Email:
auchmuty@uh.edu
My
physical, and
mail, addresses
are
University of
Houston
Department of
Mathematics
4800 Calhoun Ave,
Houston, TX
772043008 
Teaching:
In
Fall
2015
I will
teach M3340,
Introduction
to Fixed
Income
Mathematics.
The
syllabus for
this course is
available on
the Math
department
website. The
course will
cover much of
the material
required for
one of the
actuarial
examinations
as
well as providing
an introduction
to
the
calculation of
many standard
financial models.
Students
will
use
spreadsheets
to solve the
problems.
Research Interests:
My
recent
research has centered
on the mathematical
analysis of
various boundary
value problems
of importance in the
analysis of classical
vector fields. These
include problems from
fluid mechanics,
electromagnetic and
gravitational field
theories. A particular
effort has been to
treat problems in
exterior regions and
problems with
interfaces. The
representation and
approximation of these
solutions has
typically involved the
descriptions of
specific bases of
certain solution
spaces. This leads to
questions about
Steklov, and other,
eigenproblems for
elliptic
operators and
the dependence
of solutions on
boundary data.
Recent papers have
proved new results
about harmonic
functions and fields,
boundary values
(traces) of Sobolev
functions, the
representation of
solutions of boundary
value problems in
exterior regions, the
existence and
properties of scalar
and vector potentials
and the wellposedness
of divcurl
systems that
arise in either
electromagnetic field
theory or in fluid
mechanics.
Many of these results
followed from the use
of variational methods
and principles and
functional analysis
including topics such
as Reproducing Kernel
Hilbert Spaces. The
results have often
depended on proving
new inequalities and
developing special
representation
results.
This
research
is currently supported
by NSF award DMS
1108754 to study
"Steklov spectra and
Divcurl
analysis".
Maxwell's equations
are the most important
examples of divcurl
systems. See the link
to Research for more
information.
The work on these
issues is theoretical
mathematics, involving
functional analysis
and variational
principles. It
does not involve
computational
studies and I do
not have paid
positions available
for
programmers.
Research Students and
Projects:
Here is a
listing of
Ph.D.
graduates
whose theses I
have supervised. Currently
Juan F. Lopez and
Pablo Lopez are
pursuing research
projects with me. I
have supervised many
M.S. theses and some
undergraduate honors
students on a
variety of
mathematical
topics. If you are
interested in
studying
problems that
involve partial
differential
equations or the
calculus of
variations 
especially ones that
arise from
applications  feel
free to contact me
about possible
projects.
Editorial:
Currently I am on the
editorial board of the
SIAM Journal of
Mathematical Analysis
(SIMA). For
information on SIMA
please go to the SIAM
website www.siam.org
I am
also on the board of
Nonlinear Analysis and
Differential
Equations, published
by Hikari Press and of
the Electronic
Problems section,
SIAM Review.
This
section associated
with SIAM Review
welcomes unsolved
problems in applied
and applicable
mathematics.
Contributors should
send proposed problems
to Cecil C Rousseau.
If you can solve
posted problems please
let the proposer and
SIAM know about your
solutions.
