Giles Auchmuty
Professor of Mathematics - University of Houston

Office Location: PGH 696
Telephone: (713) 743-3475
Fax: (713) 743-3505
E-mail: auchmuty@uh.edu

Physical, and mail, address is
University of Houston
Department of Mathematics
4800 Calhoun Ave,
Houston, TX 77204-3008

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.


        For a full listing of research papers, arranged by topic, see Scientific Publications.
        See  also the Google Scholar   listing.
   or Reviews from    MathSciNet
 

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 2005-2007. 
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.




 

Current Address: Department of Mathematics, PGH Building, University of Houston, Houston, Texas 77204-3008
Phone(UH): (713) 743-3500 - Fax(UH): (713) 743-3505