Anja Sneperger (University of Leeds) – Some determinants and relations in Heronian friezes

Motivated by computational geometry of point configurations on the Euclidean plane, and by the theory of cluster algebras of type A, Sergey Fomin and Linus Setiabrata have recently introduced Heronian friezes - the Euclidean analogues of Coxeter’s frieze patterns.  I will explain the way these friezes arise from a polygon in the complex plane, and that a sufficiently generic Heronian frieze is uniquely determined by a small proportion of its entries. Then, I shall proceed to some of my results, that hold in the cyclic case, i.e.  when the vertices of the polygon are placed on the circle. Namely, I will speak about vanishing of certain determinants in the cyclic case, as well as explain some interesting algebraic relations that hold between the entries of the cyclic Heronian frieze.