2025/2026🔗

Christophe Eyral🔗

Institute of Mathematics of the Polish Academy of Sciences in Warsaw

Date: 2026 March 17th

Title: Zariski pairs of surface singularities

Abstract: A conjecture of S. Yau asserts that if two isolated surface singularities in C^3 have the same monodromy zeta-function and the same abstract topology, then they must also share the same embedded topology. This conjecture was disproved by E. Artal Bartolo, who explicitly constructed a pair made of two superisolated surface singularities with identical zeta-functions and abstract topologies but distinct embedded topologies. Today, any pair exhibiting this phenomenon is referred to as a "Zariski pair of surface singularities". Subsequent research has further explored Zariski pair-like phenomena, resulting in several recent developments in the field. In this talk, I will present a concise introduction to this subject and its main results.

Maksymilian Safarewicz🔗

Warsaw University of Technology

Date: 2026 January 13th

Title: Singular hedgehogs on a sphere

Abstract: This lecture offers a comprehensive exploration of hedgehogs in non-planar settings, with a particular focus on the sphere. We will examine the properties of their singularities and draw insightful comparisons with the behavior of hedgehogs in the more familiar planar case.

Izabella Konicer🔗

Warsaw University of Technology

Date: 2025 December 9th

Title: Asymmetrical symmetry (cont.)

Izabella Konicer🔗

Warsaw University of Technology

Date: 2025 November 25th

Title: Asymmetrical symmetry

Abstract: In this lecture, we mainly address the conditions for reconstructing a convex polygon with parallel opposite sides from its so-called defects of symmetry. This concept translates properties of ovals, defined by pairs of parallel tangents, into discrete polygon space. We discuss the discrete equivalents of cusps, Wigner caustic, Centre Symmetry Set, and affine lambda-equidistant sets. This is a joint work with B. Murawski, T. Wieczorek, and M. Zwierzyński.

Wojciech Domitrz🔗

Warsaw University of Technology

Date: Rescheduled to 2025 October 28th

Title: Singularities of 2-dimensional indefinite improper affine spheres determined by singular curves (continuation)

Wojciech Domitrz🔗

Warsaw University of Technology

Date: 2025 October 14th

Title: Singularities of 2-dimensional indefinite improper affine spheres determined by singular curves

Abstract: Improper affine spheres (IAS) are hypersurfaces whose affine Blaschke normal vectors are all parallel. They are given as the graphs of solutions of the classical Monge-Ampere equation. In 2013, F. Milan proved that 2-dimensional indefinite improper affine spheres are determined by their singular curves. We study singularities of IAS for generic singular curves.