
Giles Auchmuty
Professor
of Mathematics
 University
of Houston
Office
Location:
PGH 696
Telephone:
(713) 7433475
Fax:
(713) 7433505
Email:
auchmuty@uh.edu
Physical,
and mail,
address is
University of
Houston
Department of
Mathematics
4800 Calhoun Ave,
Houston, TX
772043008 
Teaching:
In
Spring
2018,
I will teach
Math
6327
Partial
Differential
equations.
Office
hours are 2.30
3.30pm
on Tuesdays
and Thursdays
in PGH 696.
Research Interests:
Currently
my research centers on
the properties of
Steklov eigenproblems
for linear elliptic
operators and
their applications in
a range of areas
including the
equations of fluid
mechanics,
approximation theory,
numerical analysis and
gravitational field
theories. A
particular interest is
how solutions of
various problems
depend on boundary
data and their
application to
solving inverse
problems.
Steklov eigenproblems
are eigenproblems for
partial differential
equations where the
eigenparameter is in
the boundary
conditions. They
are important for
studying boundary
conditions and trace
theorems for elliptic
problems; the
eigenvalues provide
best constants in
important
inequalities. They
provide analytic
approximations to
solutions of various
boundary value
problems. An important
recent result is the
construction of the
singular value
decomposition for
the Poisson
kernel and of
Reproducing Kernels
for associated spaces
of harmonic functions.
Another current
interest is the
question of what are
wellposed boundary
value problems for
various equations
arising in the
analysis of vector
fields in classical
field theories?
These includes
divcurl systems,
Stokes equations and
Maxwell's equations.
The issues center on
what boundary
conditions are
required for the
equations to be
wellposed and how can
the solutions be
represented?
Motivations for much
of this work comes
from problems in
classical fluid
mechanics,
electromagnetic field
theories and
geophysical problems
where the solutions
are determined as much
by the boundary
conditions as by the
equations.
Most of this is
theoretical
mathematics, involving
convex and
functional
analysis, partial
differential equations
and variational
principles. I have
many interesting, open
questions that would
benefit from more
computational study 
including issues such
as efficient ways to
solve boundary value
problems for the
Laplacian on polygons.
Students
interested in working
on these problems are
welcome to come and
discuss possible
projects. You
should have a good
grounding in real
analysis or
computational work.
Research Students and
Projects:
Here is a
listing of
Ph.D.
graduates
whose theses
I have
supervised. Currently
Juan F. Lopez is
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. There are
many interesting
open questions and
problems
involving
computational
simulation of these
equations.
Background:
Received
an
undergraduate
degree in pure
and applied
mathematics from
the Australian
National
University and
S.M. and Ph.D.
degrees from the
University of
Chicago in
applied
mathematics. Held
positions at
SUNY, Stony
Brook and
Indiana
University,
Bloomington
before coming to
UH as a
Professor of
Mathematics in
1982. Was
President of UH
Faculty Senate in
2004
and have
served on many
departmental, college
and UH search and
other advisory committees.
A short
CV is available here.
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.
