March 1,  2024

on-line on zoom

• 10:00 - 10:50 Zbigniew Jelonek (IMPAN) Bi-Lipschitz equivalent cones with different degrees

  Abstract:
  We show that for every \(k\ge 3\) there exist complex algebraic cones of dimension \(k\) with isolated singularities, which are bi-Lipschitz and semi-algebraically equivalent but have different degrees. We also prove that homeomorphic projective hypersurfaces with dimension greater than 2 have the same degree. In the last part of this paper, we classify links of real cones with base \(\Bbb P^1\times \Bbb P^2.\)  Moreover we give examples of manifolds, which are not diffeomorphic to projective manifolds of odd degree.
  Finally,  we give an example of three four-dimensional real algebraic cones in \(\mathbb{R}^8\) with isolated singularity which are semi-algebraically and bi-Lipschitz equivalent but have non-homeomorphic bases.

• 11:00-11:50 Adam Różycki (Uniwersytet Łódzki) Bi-Lipschitz invariance of the Lê numbers of quasi-ordinary singularities

  Abstract:
  In the talk we will show that Lê numbers are bi-Lipschitz invariants in the class of quasi-ordinary singularities with one-dimensional critical locus. Moreover, if in this class singularities have only one characteristic pair, the Lê numbers are also topological invariants. (Joint work with Grzegorz Oleksik).