Helge Pedersen (ICMC-USP)

Tuesday, May 16th, 10:20, Room 4-111

**Title: **Lipschitz normal embeddings in the space of matrices

**Abstract: **** ** The germ of an algebraic variety is naturally equipped with two different metrics up to bilipschitz equivalence. The inner metric and the outer metric. One calls a germ of a variety Lipschitz normally embedded if the two metrics are bilipschitz equivalent. In this talk we prove Lipschitz normal embeddedness of some algebraic subsets of the space of matrices. These include the space of matrices, symmetric matrices and skew-symmetric matrices of rank equal to a given number and their closures, the upper triangular matrices with determinant 0 and linear space transverse to the rank stratification away from the origin.