
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
Fall
2017, I will
teach Math 3340 Introduction
to Fixed
Income
Mathematics
and Math
6326
Partial
Differential
equations.
Use
the links to
find more
information
about these
courses.
Office
hours are 1
2pm
on Tuesdays
and Thursdays
in PGH 696.
Research Interests:
Currently
my research is
centering on the study
of Steklov
eigenproblems for
linear elliptic
operators and
their applications in
a range of areas
including functional
analysis,
approximation theory,
numerical analysis and
classical field
theories.
Also the analysis of
harmonic and
biharmonic functions
and equations that
arise in fluid
mechanics and
electromagnetic field
theory.
A particular interest
is how solutions of
various problems
depend on boundary
data.
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. The major
recent result is the
construction of the
singular value
decomposition for
the Poisson
kernel and the
Reproducing kernel for
associated spaces of
harmonic functions.
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. It is
important for issues
of boundary control of
various situations.
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.
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.
Have
held visiting
positions
at
the University
of Bonn, Oxford
University,
University of
Sydney, the
Fields Institute
in Toronto and
the Institute
for Advanced
Studies,
Princeton
amongst others.
Elected Fellow
of the
Australian
Mathematical
Society in
2015. Was
a Program
Director in the
Division of
Mathematical
Sciences of NSF
in
20052007.
Have
served on many
national award and
review panels
including, currently,
Fulbright awards in
Mathematical
Sciences.
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.
