Classification of Lipschitz simple function germs

It is well known by a result of Mostowski that the bi-Lipschitz (right) equivalence of complex analytic set germs does not admit moduli. This result was extended by Parusinski for subanalytic sets and by Nguyen and Valette for the o-minimal setting.  However, such a property is nolonger true for function germs. Henry and Parusinski showed that the bi-Lipschitz classification of function germs do allow moduli. More precisely, they constructed a bi-Lipschitz invariant that varies continuously in the family f_t(x,y) = x^3 + txy^3 + y^6. This led us the to ask if there exists a classification for bi-Lipschitz equivalence of function germs analogous to the smooth case. In the talk, we are going to introduce a notion of Lipschitz simple function germs and set out to classify them under bi-Lipschitz equivalence.