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

Nov 6, 2023, 10:30 - 11:30 AM

**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