**Speaker: **Mohammad Sadek

**Title:** Computing (Hyper)Elliptic Curves Over the Rationals

**Date/Time:** 11 November 2020/ 13:40 - 14:30

**Zoom: Meeting ID**: 916 4029 5656

**Passcode: **Algebra

**Abstract:** The discriminant of a (hyper)elliptic curve encodes the primes of bad reduction of the curve. The number of isomorphism classes of (hyper)elliptic curves over a number field with the same discriminant is known to be finite. A more involved task is to count, if not list, all such isomorphism classes. In this talk, we survey old and recent results for elliptic curves. We also explain how one may tackle the same question for genus 2 curves

**Bio:**Mohammad Sadek studied Mathematics at Cairo University (Egypt). He obtained the Certificate of Advanced Studies in Mathematics from Cambridge University in 2006. He earned his Ph.D. from Cambridge University in 2010 under the supervision of Tom Fisher. He then joined the American University in Cairo as an assistant professor in 2010 and was promoted to a tenured associate professor in 2016. He joined the Mathematics group of the Faculty of Engineering and Natural Sciences at Sabanci University in 2018. The research area of Mohammad Sadek lies within computational number theory and arithmetic algebraic geometry. In particular, he is interested in the arithmetic of elliptic curves, hyperelliptic curves, and arithmetic dynamics.