A
| Singularities |
|---|
Classification and derivation of analytic and topological invariants of singularities of complex analytic and differentiable maps. Lojasiewicz exponents and nondegeneracy conditions for analytic maps. Study of Vassiliev-type semilocal invariants.
B
| Generic geometry |
|---|
Differential geometry of smooth submanifolds with singularities in Euclidean spaces. A comprehensive classification of stable maps, flows, and foliations on surfaces and 3-manifolds. Complete invariants for second-order geometry. Application to string theory.
C
| Applied singularities and geometry |
|---|
Conformal geometry: Rational curves of the Pythagorean hodograph in computer-aided design. Geometric applications to microwave circuit design. Design of Bézier surfaces with predefined boundary properties.
