Geometry MMA Seminar: Extremal {p,q}-animals

Speaker:   Rosemberg Toalá-Enríquez, George Mason University

Title:   Extremal {p,q}-animals

Abstract:  An animal is a planar shape formed by attaching congruent regular polygons along their edges. Usually, these polygons are a finite connected subset of tiles of a regular planar tessellation. These tessellations can be parameterized using the Schläfli symbol {p, q}, where p denotes the number of sides of the regular polygon forming the tessellation and q is the number of tiles meeting at each vertex. If (p − 2)(q − 2) > 4, or = 4 then the tessellation corresponds to the geometry of the hyperbolic plane or the Euclidean plane, respectively. In this talk, I will focus on animals defined on hyperbolic tessellations. I will present a family of spiral animals and prove that they attain the minimum numbers of edges and vertices within the class of animals with n tiles. 

Time: Monday, November 6, 2023 – 10:30am-11:30am

Place: Exploratory Hall, Room 4106