Research topics and some recent papers
1) Singularities of real and complex mappings (deformations of
such singularities, study of their invariants, classification of
singularities up to left-right equivalence), see e.g.:
J.H. Rieger and M.A.S. Ruas
- ``M-deformations of A-simple $\Sigma ^{n-p+1}$-germs from
$R^n$ to $R^p$, $n\ge p$'',
Mathematical Proceedings of the Cambridge Philosophical Society
139 (2005), 333-349.
2) Applications of singularity theory to
knot theory, see e.g.
J.S. Carter, J.H. Rieger and M. Saito
- ``A combinatorial description of knotted surfaces and their isotopies'',
Advances in Mathematics 127:1 (1997), 1-51.
unimodular and symplectic geometry (i.e. to the study of mappings
from a manifold into another manifold with a volume or a symplectic
form that has to be preserved), see e.g.
W. Domitrz and J.H. Rieger
- ``Volume-preserving diffeomorphisms on varieties and
$A_{\Omega}$-equivalence of maps'', Singularities and Symplectic
Geometry - Part VII, Warsaw Singularity Theory seminar publication series,
2005, 2-41.
the differential geometry of generic submanifolds, see e.g.
S. Ghosh and J.H. Rieger
- ``Singularities of secant maps of immersed surfaces'',
Geometriae Dedicata 121 (2006), 73-87.
the computational geometry of real algebraic sets, see e.g.
J.H. Rieger
- ``Proximity in arrangements of algebraic
sets'', SIAM Journal on Computing 29 (1999), 433-458.
computer vision, see e.g.
J.H. Rieger
- ``On the complexity and computation of view graphs of
piecewise smooth algebraic surfaces'',
Philosophical Transactions of the Royal Society London Ser. A
354 (1996), Number 1714, 1899-1940.