Palestrante: Thiago Filipe da Silva

The study of Bi-Lipschitz equisingularity was started by Mostowski, whom proved that a large class

of analytic varieties has a vector field Lipschitz. In this talk we will show how Gaffney got conditions so

that a family of irreducible curves has a canonical vector field which is Lipschitz. These conditions are

related to the independence of some important algebraic invariants, namely, the Segre numbers and the

multiplicity of a pair of ideals. Inspired on these ideas for curves, after we will present how to ensure that

a particular family of determinantal surfaces also has a similar canonical vector field Lipschitz, which is

a work in progress with N. Grulha and M. Pereira.

References

1 Soares Ruas, Maria Aparecida; Da Silva Pereira, Miriam. Codimension two determinantal varieties with

isolated singularities. Math. Scand. 115 (2014), no. 2, 161-172. :

2 Gaffney, Terence. Bi-Lipschitz equivalence, integral closure and invariants, Proceedings of the 10th Inter-
national Workshop on Real and Complex Singularities. Edited by: M. Manoel, Universidade de S ̃ao Paulo,

M. C. Romero Fuster, Universitat de Valencia, Spain, C. T. C. Wall, University of Liverpool, London

Mathematical Society Lecture Note Series (No.380) November 2010.