Title of the course: Klein’s quartic curve
Instructor: Assoc. Prof. Ali Özgür Kişisel
Institution: ODTÜ
Dates: 21-27 August 2023
Prerequisites: Roughly, third year level undergraduate mathematics must courses in most universities (Complex Analysis, Abstract Algebra, Real Analysis).
Level: Advanced Undergraduate and graduate
Abstract: Klein’s quartic curve is an extremely symmetric object, which can be studied from many different perspectives. It is a canonically embedded genus 3 curve in complex projective plane with the maximal possible number of symmetries, 168, for this genus. The group of symmetries is the unique simple group of that order, which admits an interpretation as a complex reflection group. Furthermore, Klein’s quartic can be viewed as one of the first interesting examples of regular tesselations of the hyperbolic plane. From the viewpoint of number theory, it is a modular curve. The goal of this minicourse is to use these special features of Klein’s quartic as an excuse to talk about these seemingly diverse areas of mathematics and to hint on their very interesting connections. The course is intended for advanced undergraduate and graduate students.
Language: TR, EN