Emir Eray Karabiyik (Cornell University) will speak aboutA Classification of Low Genus Modular CurvesAbstract: Let \(G\) be an open subgroup of \(\operatorname{GL}_2(\widehat{\mathbb{Z}})\). There is a modular curve \(X_G\) which loosely parametrizes elliptic curves whose image of the Galois representation lies in \(G\). In this talk, we give a classification of modular curves of low genus; this is achieved by studying twists of modular curves. We also describe an algorithm for computing all families of modular curves of a fixed genus and for computing explicit models for them.

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