Department of

August 2015 September 2015 October 2015 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 1 2 3 4 5 1 2 3 2 3 4 5 6 7 8 6 7 8 9 10 11 12 4 5 6 7 8 9 10 9 10 11 12 13 14 15 13 14 15 16 17 18 19 11 12 13 14 15 16 17 16 17 18 19 20 21 22 20 21 22 23 24 25 26 18 19 20 21 22 23 24 23 24 25 26 27 28 29 27 28 29 30 25 26 27 28 29 30 31 30 31

Thursday, September 24, 2015

**Abstract:** Let $X$ be an elliptic curve over $\mathbb{Q}$. Let $f:Y \rightarrow X$ be an étale cover, ramified only above one point. The pair $(X,f)$ is called an origami. The name comes from a picture that I will draw during the talk. We study the relationship between the pre-images of rational point on $X$ under the map $f$ and Galois representations. This is joint work with Edray Herber Goins.