School of Mathematics and Statistics
Number Theory Seminar 

Ever wondered what a Shimura curve is? They lie at the crossroads of many areas of mathematics: complex analysis, number theory, Diophantine equations, group theory, noncommutative algebra, algebraic geometry, Lie theoryeven coding theory! The study of the first examples of these curves (the modular curves) can be traced back as far back as Gauss, and then later Klein and Fricke; recently, they have played an important role in the proof of Fermat's last theorem and in the solution of other number theoretic problems. In this survey, we introduce Shimura curves for the nonexpert with an algebraic outlook and provide a brief exposition of their relationship to other areas of mathematics. 