Overview

The study of automorphism groups of Riemann surfaces is classical with major results dating back to Klein and Wiman. It is also a wide reaching topic with strong links to topology, number theory and combinatorics in the area of mapping class groups, Teichmüller spaces, and the theory of dessins d'enfants. In the last couple of decades there has been a major revival in this area mainly due to great advances in computer algebra systems, such as GAP, and advances in finite group theory, such as the classification of finite simple groups. The goal of this session is to explore recent advances in this area and applications to other areas of mathematics such as arithmetic geometry, arithmetic dynamics, machine learning, etc. This session is the latest in a long series of related sessions over 18 years which have each brought together recent PhDs in the field with senior researchers. Based on the interests of past speakers and popularity of past topics, the topics of the session include, but are not limited to:

• Compact Riemann surfaces and their automorphisms

• Moduli and Teichmuller space, families of surfaces

• Dessins d’enfant (quasi-platonic Riemann surfaces) and graphs on surfaces 

• Klein surfaces, symmetries, and pseudo-real surfaces

• Genus spectra and signatures of group actions

• Jacobians and their automorphisms

• Automorphisms of rational maps P^d -> P^d

• Automorphisms of algebraic surfaces