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

My physical, and mail, addresses are
University of Houston
Department of Mathematics
4800 Calhoun Ave,
Houston, TX 77204-3008

Teaching:

         In Spring 2014,   I will teach Math 3338, Probability Theory and   Math 6361  Applicable Analysis   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 the dependence of solutions on boundary data and spectral theories. The topics I am interested in generally arise from from questions about  classical field theories - especially the analysis of electromagnetic and 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 well-posedness of  div-curl systems  that arise in either electromagnetic field theory or in fluid mechanics.

       Many of these results have involved either elliptic spectral theory, especially the theory of Steklov eigenproblems, or the theory of 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 3-d 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 3-dimensional 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 Div-curl analysis".   Maxwell's equations are the most important examples of div-curl 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.

        For a listing of recent papers see Recent Publications.
        For a full listing of research papers, arranged by topic, see Scientific Publications.
        See also Reviews from MathSciNet.

Research Students and Projects:    

      Here is a listing of  Ph.D. graduates whose theses I supervised.  Mauricio Rivas and  Puchen   Liu
have just defended their theses and are looking for postdoctoral positions. At present Manki Cho and Pablo Lopez
are working on their doctoral research with me.  
     I have also 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 following.

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