Vorträge in der Woche 21.10.2024 bis 27.10.2024

Dienstag, 22.10.2024: The geometry of deformation rings and applications to the Langlands programme

Daniel Funck

Mittwoch, 23.10.2024: Study of Real Trigonal Curves and Applications

Andres Jaramillo Puentes (Tübingen)

A trigonal curve is a reduced, irreducible curve lying on a uniruled Hirzebruch surface, whose projection induces a three-to-one map to the projective line. In this talk, we will introduce the concept of the dessin d'enfant associated with a real trigonal curve, a type of graph embedding used to study Riemann surfaces and provide combinatorial invariants. We will describe the real properties of the dessins and explain their applications to real algebraic geometry and singularity theory. The first application is the classification of the chambers of the moduli space of real rational plane quintics, an instance of the modern formulation of Hilbert’s 16th problem. The second is the classification of the morsifications of a real semi-quasi-homogeneous singularity of type (3,k).

Mittwoch, 23.10.2024: Study of Real Trigonal Curves and applications

Andres Jaramillo Puentes (Tübingen)

A trigonal curve is a reduced, irreducible curve lying on a uniruled Hirzebruch surface, whose projection induces a three-to-one map to the projective line. In this talk, we will introduce the concept of the dessin d'enfant associated with a real trigonal curve, a type of graph embedding used to study Riemann surfaces and provide combinatorial invariants. We will describe the real properties of the dessins and explain their applications to real algebraic geometry and singularity theory. The first application is the classification of the chambers of the moduli space of real rational plane quintics, an instance of the modern formulation of Hilbert’s 16th problem. The second is the classification of the morsifications of a real semi-quasi-homogeneous singularity of type (3,k).