Friezes and resolutions of plane curve singularities
Eleonore Faber (University of Graz)
Abstract: Conway-Coxeter friezes are arrays of positive integers satisfying a determinantal condition, the so-called diamond rule. Recently, these combinatorial objects have been of considerable interest in representation theory, since they encode cluster combinatorics of type A.
In this talk I will discuss a new connection between Conway-Coxeter friezes and the combinatorics of a resolution of a complex curve singularity: via the beautiful relation between friezes and triangulations of polygons one can relate each frieze to the so-called lotus of a curve singularity, which was introduced by Popescu-Pampu. This allows to interprete the entries in the frieze in terms of invariants of the curve singularity, and on the other hand, we can see cluster mutations in terms of the desingularization of the curve. This is joint work with Bernd Schober.
algebraic geometrynumber theory
Audience: researchers in the discipline
Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).
We acknowledge the support of PIMS, NSERC, and SFU.
For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.
We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca
| Organizer: | Katrina Honigs* |
| *contact for this listing |