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  2018, I will teach Math 3364 Introduction to Complex Analysis. Classes are in CB120 from
2.30-4pm on Tuesday - Thursday.
  Office hours are 1 -2pm on Tuesdays and Thursdays in PGH 696 or by appointment

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 well-posed boundary value problems for various equations.  These includes div-curl systems, Stokes equations and Maxwell's equations. The issues center on what boundary conditions are required for the equations to be well-posed 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 real  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 Papers.
        This research has been partially supported  by 11 individual NSF grants and a variety  of other awards. 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. 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. I have  some research problems that would be greatly assisted if we had better  computational simulation of the solutions and  do not need much theoretical mathematics.

Background:

        Received  my 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. Was a program director at the National Science Foundation in 2005-2008 and currently serve on a number of national and international award and review 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.




 

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