
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:
Currently
( Fall 2014)
I am
teaching Math 3340, Introduction to Fixed
Income
Mathematics.
This course
provides
an
introduction
to the theory
of interest
and the
analysis of
loans,
bonds and
leverage. It
covers much of
the theory
required for one
of the
introductory
actuarial exams.
The prerequisite
is calculus 2
and an ability
to use Excel
spreadsheets is
expected.
Next semester
(Spring 2015), I
will teach Math
3338
(probability
theory) and Math
6398
(Introduction to
Sobolev spaces
and Variational
Methods). A
description of
the graduate
course is
available here.
For more information
about these
courses and a
listing of courses
taught in recent
years please
select the
Teaching
link above.
Research Interests:
My
research centers on
the mathematical
analysis of elliptic
boundary value
problems; especially
eigenvalue problems
and the
dependence of
solutions on boundary
data. Recently I have
worked extensively on
questions about
Steklov eigenproblems
and the
representations of
solutions of boundary
value problems.
The topics I am
interested in
generally arise
from questions
about the analysis of
problems in fluid
mechanics or in
classical
(nonrelativistic)
electromagnetic or
gravitational fields.
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. Recently
I proved new
extensions of the
Sobolev imbedding
theorems for 3d
fields where
integrability
conditions are imposed
on the Laplacian of a
potential  but not on
the function itself.
This is the
physical
situation for
gravitational and
electrostatic
potentials.
Another
continuing research
interest is in the
theory of potentials
for various classes of
3dimensional vector
fields when various
types of boundary
conditions are
imposed.
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.
