[loginf] PhD Studies in Symbolic Functional Analysis

Markus Rosenkranz markus.rosenkranz at risc.uni-linz.ac.at
Tue Mar 9 10:40:26 CET 2004


        [Apologies for multiple copies]

PhD Studies in Symbolic Functional Analysis
===========================================

Qualifications
--------------

We offer PhD research assistantships for students with the following
qualifications:

* You want to work in an exciting new area of mathematics,
  emerging at the borderline of two modern core disciplines of
  mathematics, symbolic computation and functional analysis.

* You have some basic knowledge of symbolic computation (computer
  algebra), including in particular the theory of Groebner bases.

* You have also basic knowledge of advanced analysis,
  including in particular the theory of ordinary and partial
  differential equations as well as some abstract functional analysis.

* You have good practical skills in programming and using mathematical
  software.

* You have finished your diploma or master's degree (or equivalent)
  and you want to start on a PhD thesis.

* Your knowledge of English is sufficient for fluent
  conversation in mathematics.


Application
-----------

Strong students are encouraged to send their application to Dr.~Markus
Rosenkranz. Research assistantships are available starting from
April~2004 in the frame of a research project directed by Professors
Bruno Buchberger and Heinz W.~Engl.

Dr. Markus Rosenkranz
Research Institute for Symbolic Computation (RISC)
E-mail: Markus.Rosenkranz at risc.uni-linz.ac.at
Internet: www.risc.uni-linz.ac.at


Details about the Project
-------------------------

Symbolic functional analysis (SFA) is defined as the continuation of
symbolic computation towards operator problems of functional analysis,
including so-called inverse problems.

Recently, in the frame of this project, a typical SFA problem has been
solved algorithmically: finding the Green's operator for a given
linear two-point boundary value problem at the abstract operator
level.

The next goal is to analyze/generalize this approach to various other
SFB problems: linear partial differential equations, non-linear
problems, non-BVP type problems (e.g. exterior Dirichlet problems,
single-layer potential), and inverse problems of all types.



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