2025/2026🔗
Tomasz Wieczorek🔗
Warsaw University of Technology
Date: 2026 June 2nd
Title: Affine Properties of Convex Equal-Area Polygons
Abstract: This presentation is a thorough review of properties of convex equal-area polygon, which is a simple polygon bounding a convex planar domain such that all triangles formed by three consecutive vertices have the same area. We will also look at its connections to convex curves and properties that are analogous for discrete counterpart. Presentation is based on work:
- M. Craizer, R. Teixeira and M. Horta, “Affine properties of convex equal-area polygons”; Discrete & Computational Geometry, October 2012, Volume 48, Issue 3, pp 580-595.
Maksymilian Filip Safarewicz🔗
Warsaw University of Technology
Date: 2026 May 26th
Title: Banach manifolds (cont.)
Maksymilian Filip Safarewicz🔗
Warsaw University of Technology
Date: 2026 May 19th
Title: Banach manifolds
Abstract: This presentation offers a coherent introduction to the theory of manifolds in Banach spaces - a natural infinite-dimensional generalization of finite-dimensional Riemannian manifolds. We will also explore applications of this framework to the study of higher-dimensional singular sets, like the Wigner caustic.
Christophe Eyral🔗
Institute of Mathematics of the Polish Academy of Sciences in Warsaw
Date: 2026 March 24th
Title: Zariski pairs of surface singularities (cont.)
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.