The Łojasiewicz exponent of non-degenerate singularities
Speaker: Grzegorz Oleksik (Faculty of Mathematics and Computer Science, University of Lodz, Poland)

Time: 14h00-15h00, Thursday, September 30,  2021 (Vietnam time)

Link Online: meet.google.com/zsh-jnxc-eit

Abstract: Let f be an isolated singularity at the origin of C^n.  One of many invariants that can be associated with f is its Łojasiewicz exponent Ł_0(f), which measures to some extent, the topology of f. We give, for generic surface singularities f, an effective formula for Ł_0(f) in terms of the Newton polyhedron of f.  This is a realization of one of  Arnold's postulates. We are trying to prove the appropriate formula in an n-dimensional case. As a corollary we prove Tessier's Conjecture in this case i.e. the constancy of the Milnor number in non-degenerate deformations of the surface singularities implies the constancy of the Łojasiewicz exponent.