**Date and time:**

RepTile Workshop

Feb. 22, 2019

3:30pm

Eduard Duryev

Eigengons

**Abstract:** How can one visualize algebraic curves given by equations? Consider a polygon in the complex plane with parallel equal sides identified by translations. Complex structure of the plane descends to give a Riemann surface, hence an algebraic curve. But how one identifies which algebraic curve it is? Usually this question is impossible to answer. In our talk we will give a series of examples of such polygons together with the equations of algebraic curves that they define.

4:30pm

Peter Smillie & Philip Engel

Penrose tilings of compact surfaces, Part 1

**Abstract:** I'll give a few approaches to constructing tilings of compact surfaces by rhombuses glued according to Penrose's matching rules. I'll then give some bounds--a logarithmic lower bound and a polynomial upper bound -- for the growth of the function F_g(n) which gives the number of Penrose tilings of a genus g surface with n tiles.