On the classification of singularities and report on a novel database for mathematical software

Speaker: Prof. Gert-Martin Greuel
Date: 23/06/2014
Time: 13:30 - 14:30

Location: RISC Seminar room

First I report on new results on the classification of isolated hypersurface singularities in positive characteristic. The corresponding classification over the real and complex numbers was achieved by V.I. Arnold in his pioneering work in the mid sixties. A surprising result of our work is that for every fixed positive characteristic there are only finitely many classes of the so called simple singularities. In particular, only finitely many of the ADE singularities have finite deformation type. This stands in strict contrast to Arnold's result in characteristic 0 where the simple singularities are exactly the infinitely many ADE singularities. Computations with the computer algebra system SINGULAR have been useful. This is joint work with Nguyen Hong Duc. In the second part I report shortly on the new database swMATH for mathematical software (www.swmath.org), as an information service to the mathematical community. This service is based on a novel approach to mathematical software through peer reviewed publications which cite the software. The reviewing service Zentralblat MATH (www.zbmath.org) provides the information on mathematical publications and links the corresponding articles with the relevant software and vice versa. swMATH is by far the most comprehensive database on mathematical software with currently more than 6.700 software packages and about 69.000 linked articles.