Jukka Tuomela, PhD, Professor

MSc in 1986 at the department of mathematics, Helsinki University of Technology.  Graduate studies in INRIA (Institut National de Recherche en Informatique et en Automatique), Rocquencourt and PhD in 1992 in Université Paris 7. From 1992 to 1998 various teaching and research positions at the department of mathematics, Helsinki University of Technology. From 1999 to present professor of mathematics at the department of (physics and) mathematics, University of Joensuu.

My research concentrates on the analysis of overdetermined differential equations. The general approach is based on formal theory of PDEs. Overdetermined problems are more challenging than the standard ones and require the use of algebraic and differential geometric methods which are not needed in the standard case. For ODEs I have implemented with my former students a code for solving general overdetermined problems (aka differential algebraic equations). We have also analysed problems with holonomic constraints and their singularities. In the PDE case I have worked on the constructive algebraic analysis of ellipticity and well-posedness of PDE systems. This work combined with the compatibility complex associated to the given PDE system has also interesting implications for the numerical solution of PDEs. The research on numerical aspects is done in collaboration with Bijan Mohammadi (Université Montpellier 2) and Frédéric Hecht (Université Paris 6).